If you are aware of an interesting new academic paper (that has been published in a peer-reviewed journal or has appeared on the arXiv), a conference talk (at an official professional scientific meeting), an external blog post (by a professional scientist) or a news item (in the mainstream news media), which you think might make an interesting topic for an FQXi blog post, then please contact us at forums@fqxi.org with a link to the original source and a sentence about why you think that the work is worthy of discussion. Please note that we receive many such suggestions and while we endeavour to respond to them, we may not be able to reply to all suggestions.
Please also note that we do not accept unsolicited posts and we cannot review, or open new threads for, unsolicited articles or papers. Requests to review or post such materials will not be answered. If you have your own novel physics theory or model, which you would like to post for further discussion among then FQXi community, then please add them directly to the "Alternative Models of Reality" thread, or to the "Alternative Models of Cosmology" thread. Thank you.
Can We Feel What It’s Like to Be Quantum?
Underground experiments in the heart of the Italian mountains are testing the links between consciousness and collapse theories of quantum physics.
Blogger Joy Christian wrote on Jul. 24, 2011 @ 18:06 GMT
“ ... what is proved by impossibility proofs is lack of imagination.”--John S. Bell
This post is in response to Florin Moldoveanu’s, “To Be Or Not To Be (a Local Realist),” which discusses my research. You can read his post for some background to the topic, and also view my own talk on my work at the 2009 FQXi conference in the Azores, below:
“ ... what is proved by impossibility proofs is lack of imagination.”--John S. Bell
This post is in response to Florin Moldoveanu’s, “To Be Or Not To Be (a Local Realist),” which discusses my research. You can read his post for some background to the topic, and also view my own talk on my work at the 2009 FQXi conference in the Azores, below:
I am grateful to Florin Moldoveanu for trying to understand my work on Bell’s theorem. My arguments use a rather unfamiliar language of Geometric Algebra, and for this reason many have found them less than comprehensible. I am relieved to note that geometric algebra has not been an obstacle for Florin. I am, however, quite surprised by his conclusions. I do not agree with most of the assertions he has made, both here and elsewhere. In particular, contrary to what Florin asserts, I do not start with mathematical assumptions different from those of Bell, and my local-realistic framework is fully capable of providing a strictly local and manifestly realistic understanding of all possible quantum mechanical correlations.
Let me begin by pointing out a number of alarming confusions in Florin’s reasoning---not only concerning my own work, but also concerning the significance of Bell’s theorem itself. The worse of these confusions occurs in his understanding of the notion of contextuality. Florin has painted this notion as something to be avoided at all cost. But that sharply differs from how Bell himself viewed the notion. Bell vigorously defended contextuality in his very first paper. He famously stressed that “the result of an observation may reasonably depend not only on the state of the system (including hidden variables) but also on the disposition of the apparatus.” I could not agree more! He goes on in the paper to strongly criticise the theorems by von Neumann, Jauch and Piron, and Gleason for neglecting contextuality, and argues that the demand of strict non-contextuality implicit in these theorems is “quite unreasonable” from the physical point of view. The idea of contextuality, he argues, should not be confused with the idea of realism. These are two completely separate notions.
Indeed, some of our best classical theories are deeply contextual. For example, Einstein’s theory of gravity---in which the results of observations are unavoidably dictated by the disposition of the apparatus---is a profoundly contextual theory. But this certainly does not make general relativity any less realistic, or non-local. Thus Florin is simply wrong to assert that “contextual realism is almost a contradiction in terms.” Bell would have strongly disagreed, and so do I, because that would imply that Einstein’s theory of gravity is almost a contradiction in terms! Worse still, Florin claims that contextual ontology is “at least just as strange as quantum mechanics itself.” This is quite wrong too. Contextual hidden variable theories do not admit any of the quantum mechanical oddities like superposition, entanglement, objective chance, or objective indefiniteness at the fundamental level. There is no unsharpness of any kind in these theories. Thus quantum mechanics is ontologically quite distinct from the contextual hidden variable theories. The crucial point of the latter theories is not that they are any less realistic (or less local), but that the reality they accommodate is far less rigid than what we would normally expect from our theories. This is analogous to how Einstein’s dynamic theory of space-time is far less rigid compared to Newton’s static theory of space-time. Thus, what we need to exorcise from physics is not contextuality in general, but *remote* contextuality (or “non-locality”). And that is exactly what I have set out to do.
In fact, the issue of contextuality brought up by Florin is largely irrelevant for my program, because the framework I am using happens to be non-contextual at heart. Florin has been misled to think otherwise, because he has largely relied on my older, preliminary papers, and neglected my latest preprints. Had he studied my latest preprint (arXiv:1106.0748v3) he would have realized that even the local non-commutativity of the local beables in my models---which he claims makes contextuality inevitable in general---is only an intermediate calculational tool. The actual eventualities, A, B, etc., in the models (i.e., the actual measurement results) always commute with each other, because they are simply scalar numbers, +1 or -1. In statistical terms, these actual measurement results are raw scores, and the corresponding non-commuting local beables---i.e., the bivectors---are standard scores. The standard scores---or the standardized variables---in my models indeed do not commute in general, but they are simply intermediate mathematical constructs, not something that is actually observed in the experiments. Therefore Florin is quite wrong to build his case around the non-commutativity of these intermediate constructs (although I must admit that my earlier papers do not make this distinction between the raw scores and standard scores very clear). Moreover, the mystique of the classical non-commutativity within my models completely evaporates when one realizes that it can always be understood as a vector addition in a higher-dimensional space. Thus non-commutativity within my models does not have the ontological significance Florin seems to think it has.
Furthermore, the actual eventualities in the models (i.e., the actual measurement results A, B, etc.) are not contextual at all. Although they may refer to the disposition of the measuring apparatus, they do not actually depend on it. One can see this most clearly in the explicit example constructed in this preprint: arXiv:1103.1879v1. This fact may seem to be at odds with the well known theorems like those of Gleason and Kochen and Specker, but these theorems are not directly applicable to my framework. This is because none of them even remotely address the topological concerns I have raised within the context of Bell’s theorem. Thus it is not appropriate to apply these theorems to my framework without due consideration of the fact that I am working at the level of probability amplitudes within a fundamentally different geometrical and topological framework, whereas these theorems are formulated at the level of the probabilities themselves within the traditional models of the physical space. Florin’s analysis of my work does not respect this crucial distinction, and therefore it cannot be taken seriously.
Moreover, I feel that it is not appropriate to try to fit my framework in any pre-existing conceptual box, not the least because it uses the unusual tools of Geometric Algebra. Therefore, instead of worrying about Florin’s analysis (or what implications the formalistic “impossibility theorems” may or may not have for my framework) let me spell out exactly how and why it is capable of reproducing quantum mechanical correlations in a purely local-realistic and non-contextual manner. This can be summarized by the following theorem.
Theorema Egregium: Every quantum mechanical correlation among a set of measurement results can be understood as a purely classical, local-realistic correlation among a set of non-contextual scalar points within a parallelized 7-sphere.
Here “local” means that the measurement results among which the correlations are exhibited are determined by a “common cause” (i.e., a common event), which has originated in their common past; “realistic” means that all such results have a definite value, predetermined by this common cause; “a non-contextual scalar point” means a measurement result that refers to but does not depend on the disposition of the apparatus; and “parallelized” means that the 7-sphere we are considering has a zero curvature but a non-vanishing torsion that may have different values for different points of the manifold.
The claim I am making here is much stronger than what has appeared in some of my papers. The main ingredients of the proof of the above theorem are already there in several of my papers, but I will try to put it together in one place in a future publication.
Now 7-sphere has a very rich topological structure. To begin with, it happens to be homeomorphic to the space of unit octonions. And as is well known, octonions form the most general possible division algebras. In the language of fiber bundles one can view 7-sphere simply as a 4-sphere worth of 3-spheres. In other words, in the language of fiber bundles each fiber of the 7-sphere is a 3-sphere, and each one of these 3-spheres is a 2-sphere worth of circles. Thus the four parallelizable spheres---S7, S3, S1, and S0---can all be viewed as nested into a 7-sphere, much like the Russian dolls. The EPR-Bohm correlations, for example, can then be understood as correlations among the equatorial points of one of the fibers of this 7-sphere; namely, a parallelized 3-sphere. Thus, in my picture, the EPR-Bohm correlations are what they are because of a nontrivial twist in the Hopf fibration of the 3-sphere. They have nothing to do with entanglement or non-locality per se.
Alternatively, the 7-sphere can be thought of as a 6-sphere worth of circles. Thus the above theorem can be framed entirely in terms of circles, each of which can be described by a classical, octonionic spinor, with a well-defined sense of rotation (i.e., whether it describes a clockwise rotation within the 7-sphere or a counter-clockwise rotation). This sense of rotation in turn defines a definite handedness about every point of the 7-sphere. Let us designate this handedness by a random number, +1 or -1. The local measurement results for a give physical scenario, A, B, etc., can then be shown to depend only on this random handedness (or orientation) of the 7-sphere, as explained in the latest two of my papers: arXiv:1103.1879v1 and this one arXiv:1106.0748. The correlations among all such local results (which are simply numbers that may refer to but do not depend on the disposition of the apparatus) are then determined purely by the topological subtleties of where they are situated within the 7-sphere. That is to say, the devil is in the details of the 7-sphere. I have shown how this works only in the simple cases of EPR, GHZ, and Hardy states, but the same logic works (at least formally) for any arbitrary quantum mechanical state. In practice, however, the calculations for more involved states are horrendously complicated, because the topology of the 7-sphere is far from straightforward.
What is important to note here is that, since the eventualities A, B, etc., are pure numbers, there is no non-commutativity involved. Thus contrary to Florin’s assertions, I do not start with assumptions any different from those of Bell as far as the eventualities themselves are concerned. Moreover, as already mentioned, there is no contextuality involved either, because all local eventualities are predetermined entirely by the orientation of the 7-sphere. Only the correlations among these eventualities depend on the dispositions of various apparatus, as they must. Thus the reason for the existence of the quantum correlations is not the local variables themselves, but the global twists and turns within the 7-sphere. The local variables are, as always, purely random, and hence they by themselves cannot possibly reproduce the quantum mechanical correlations, as correctly recognized by Bell. But what Bell failed to recognize is that this conclusion depends on the topology of the co-domain of the variables A, B, etc. In my view this topology, in general, is that of a parallelized 7-sphere.
In conclusion, Florin is simply wrong to think that local-realistic models of quantum correlations may not always be possible within my framework. He is also wrong to paint contextuality so negatively; and wrong again to think that I start with assumptions different from those of Bell. Both Bell and I start only with commuting numbers, A = +1 or -1, B = +1 or -1, etc. Both Bell and I defend local contextuality as a natural physical concept fully compatible with realism. The only difference between our assumptions is that I take measurement results to be the points of a parallelized 7-sphere, whereas Bell incorrectly assumed that they are points of the real line. More importantly, my framework is entirely consistent with the EPR criteria of locality, reality, and completeness, and it also fully respects Bell’s own criterion of factorizability. Therefore, in my opinion---although Bell’s theorem may well retain some of its relevance for the information and communication engineering as Florin has argued---it has no relevance for the future “theory of everything.” Indeed, in the light of my results I believe that the successful “theory of everything” will be a *locally causal* theory in which contextuality will play a role no different from the role it plays in general relativity. In other words, in my opinion all attempts to build a non-local theory of quantum gravity will fail miserably, just as anticipated by Einstein.
Finally, let me thank Florin again for his serious efforts to understand my work. His is the most civilized, honest, and thoughtful reaction to my work I have encountered so far.
Wow! Thank you to Joy Christian and Florin Moldoveanu for this excellent, interesting discussion as bloggers. Am looking forward to more exchanges, hopefully contributed to by qualified others.
Florin Moldoveanu wrote on Jul. 24, 2011 @ 23:50 GMT
Dear Joy,
Thank you for your post. I appreciate very much that you took the time to write such a detailed answer. I have many things I want to say, and it will take a little while to compile them all. Please give me about a weak to prepare my reply.
You said "What is important to note here is that, since the eventualities A, B, etc., are pure numbers, there is no non-commutativity involved."
Your 7-sphere is closely related to an Octonion. Jonathan Dickau and I recently wrote a paper about an octonion-like 7-torus. Octonions allow non-associativity. Quaternions allow non-commutativity. Which is then most fundamental - Real, Complex, Quaternion, or Octonion 'numbers'?
There are different ways to look at these Normed Division Algebras (NDA's). We could use Cayley-Dickson construction to build up complex numbers out of pairs of real numbers, to build up quaternions out of pairs of complex numbers, and to build up octonions out of pairs of quaternions. Or we can go the other direction and take the real component of a complex number (and likewise decompose the other NDA's).
Jonathan and I would argue that entropic considerations drive physical systems to sample ALL possibilities, and that the most complex of those 'numbers' (Octonions) must be fundamental because they contain the greatest possible number of options - thus maximizing entropy and complexity. It is thus a mistake to overlook non-associativity and non-commutativity. Obviously, simple examples of non-commutativity exist in quantum theory.
Back to your statement: "What is important to note here is that, since the eventualities A, B, etc., are pure numbers, there is no non-commutativity involved." The act of measurement might compress the 'true' nature of reality into the real eventualities A, B, etc, and overlook effects from quaternions and octonions, but I do not think we should remove these mathematical properties from consideration.
Joy Christian replied on Jul. 25, 2011 @ 08:03 GMT
Hi Ray,
You have misunderstood what I am trying to say. The whole point of using the 7-sphere is of course to exploit its non-trivialities---namely, the non-commutativity and non-associativity of the octonions. But in the geometro-algebraic formulism I am using, the octonions can be represented as spinors in such a way that the real numbers, +1 and -1 (i.e., the measurement results) appear as certain limiting cases. Moreover, these limiting cases in statistical terms are the raw scores. The corresponding standard scores are indeed the non-commuting and non-associating octonions. An example of how this works in the simpler case of the 3-sphere is already given in the two preprints I mention. The devil is in the details. Thus I am by no means overlooking or neglecting the non-commutativity and non-associativity of the octonions. But at the same time it is possible in the formalism to have the commuting real numbers appear as measurement results.
I would agree that the genius is in the generalities and the devil is in the details. If you are allowing the geometry to do the work of representing non-commutativity and non-associativity, then that is good enough for me. It sounds like I need to read those two preprints to better understand your statistics. IMO, simple Bose and Fermi statistics will not work unless they are operating in different spaces, thus requiring dual 7-spheres. I also anticipate my 7-torus to contain the M2 black-brane and Anyonic statistics.
and then you write "where denominators in (5) are standard deviations".
As I understand, and please correct me if I'm wrong, this is supposed to be a standard formula for correlation:
where
is the expectation value and
is the standard deviation. As far as I understand, in Bell's case individual outcomes +1 and -1 are equally probable, therefore expectation E=0 and standard deviation sigma=1.
Can you please explain how you calculated standard deviation you used in denominator of eq (5).
Joy Christian replied on Jul. 25, 2011 @ 20:13 GMT
If you look at how the variables A and B are defined in equations (1) and (2), you will see that their standard deviations cannot possibly be the same (or unity), because they are generated with different scales of dispersion for each directions a and b. It is also important to remember that A and B are occurring within a parallelized 3-sphere, and that they are products of two “extensive magnitudes” (or bivectors) in the language of Grassmann. Therefore one has to be very careful in calculating the standard deviations. If you are able to think of “extensive magnitudes” as simply different kind of numbers, then it is trivial to read-off the correct standard deviations from the equations (1) and (2). But if you are not familiar with the language of Geometric Algebra, then I suggest you go through the calculations given in this preprint: http://arxiv.org/abs/1106.0748 (see especially equation (22) onwards).
1. At the end of the day functions A(alpha,mu) and B(alpha,mu) are bi-valued functions with the range of {-1, +1}. Therefore their standard deviations can be computed directly using standard textbook formula for standard deviation which I gave you previously. Can you explain why your computation gives different result?
2. Can you explain how is it at all possible for a standard deviation of a real-valued variable to be grassman bivector?
3. Eq (23),(24) are correct in ordinary algebra using ordinary meaning of addition, multiplication and square root. You would have to demonstrate they are still correct in whatever algebra you are using. In particular, where did the norm operation come from? It was not there in the original formula for standard deviation.
4. Here is a counter-example: consider a scalar product
where x and y are orthogonal unit vectors (good old Euclidian vectors) and k is a random variable with values {-1, +1} (fair coin toss). It is clear that
and therefore
However if we follow your strange kind of logic, we can write
This is clearly wrong on so many counts, but this is exactly the kind of thing you are doing in eq (23), (24)
Florin Moldoveanu replied on Jul. 27, 2011 @ 03:57 GMT
DK,
I wish I am more profficient with Latex for this editor but I am not, so please bear with me. I did not see any mathematical mistakes in Joy's papers and I think can quicky point out your error in point 4 above. In your example ky is kept orthogonal on x while in Joy's example it can vary all over S3. Therefore your last line is incorrect and in your case sigma(s) is indeed zero.
Steve Dufourny replied on Aug. 5, 2011 @ 10:20 GMT
Who is in my computer??? and why I can put the mathjematical program ibn my pc????yOU FEAR AT THIS POINT BAND OF FRUSTRATED. You fear of my maths aahahah You want a course of maths, ok you know at school I had so facilities in this topic and you know what I was in the better college of my region, and you know what in OPTION LATIN MATHS SCIENCES STRONGS AND WHAT ? yOU WANT A COURSE ABOUT HOW YOU MUST STUDY A FUNCTION WITHA MAXIMUM AND A MINIMUM YOU WANT MY DERIVATIONS AHAHAHAH YOU WANT WAHT ,
Joy Christian replied on Jul. 26, 2011 @ 12:44 GMT
Much of your difficulties stem from the fact that you are not familiar with the language of geometric algebra. But before we get to the correct language, there are errors in your understanding of basic statistics that need to be addressed.
Contrary to what you have written, the range of a function by itself *cannot* be used to determine the dispersion generated by the function. The...
Much of your difficulties stem from the fact that you are not familiar with the language of geometric algebra. But before we get to the correct language, there are errors in your understanding of basic statistics that need to be addressed.
Contrary to what you have written, the range of a function by itself *cannot* be used to determine the dispersion generated by the function. The dispersion is generated by how the function depends on its arguments---in particular, how it depends on the random variable lambda. Even if you know nothing about geometric algebra, it is quite obvious from just looking at the definitions of A and B that the dispersions generated by them are different for different directions. No calculations are necessary to see this. What you have calculated is therefore a statistical nonsense. You cannot determine the standard deviations by simply looking at the outputs of the functions A and B, when they clearly depend differently on the argument lambda. The very fact that you are getting the same answer for both A and B should have told you that what you are doing is wrong. If you do not see this then we have a problem more basic than your unfamiliarity with the language of geometric algebra.
So, to reiterate, the functions A and B are generated with different scales of dispersion for different directions. Now for me, personally, calculation is not necessary to see the exact forms of the two standard deviations. The exact forms are obvious to me just by looking at the definitions of A and B. But to understand fully why they have the form they do, it is important to realize that the range of the functions A and B is actually not {+1, -1}, but a 3-sphere. Thus A and B are points of a 3-sphere. This is not obvious unless you know what a bivector is, and what it represents physically. In geometric algebra the intensive magnitudes, like numbers +1, -1, etc., and the extensive magnitudes, like vectors, bivectors, etc., are all treated equally. They are all real numbers, and they all have real geometrical properties. If you are not familiar with this perspective, then you are likely to find this strange. If I tell you that I can add a scalar to a vector, you might think that I am making things up. Sadly, we are all indoctrinated from childhood that one cannot add a scalar to a vector. But in geometric algebra it is not only natural to add numbers of different grades, but it is often necessary to do so. This is obviously not the place to give you a full course on geometric algebra, but until you appreciate the basic fact that numbers of different grades are all treated equally in this framework (much like the ordinary real numbers), you are unlikely to understand my calculations. In particular, you need to understand how these extensive magnitudes behave as random numbers. They behave much like how the complex random numbers behave. The usual formulas for standard deviation are then similarly generalized to accommodate this wider understanding of the real numbers. Thus, from the perspective of geometric algebra, what I am doing in my papers is completely elementary and not at all strange, not to mention entirely correct.
In your paper you write: "These deviations can be calculated easily. Since errors in linear relations such as (16) and (17) propagate linearly, the standard deviation of A-script(alpha,mu) is equal to (-I * a-tilde) times the standard deviation of (+mu * a-tilde) (which we write as sigma(A))" And then you write your eq (23) which after substitution amounts to
I pointed out that standard deviation is not a linear function and gave you two examples to show it, the first one (with vectors) directly applicable to the case at hand.
I also noted that you introduced a norm operation in eq(24) with no justification for doing that. I could give you another example to show that sum of squares of norms is not the same as sum of squares when we deal with complex numbers, not to mention grassman numbers.
I also expressed incredulity that a standard deviation of a function that returns the outcome of measurement (either -1 or 1) turns out to be a grassman bivector and asked how to reconsile all that with textbook definition of standard deviation.
You did not address any of these points.
I reiterate: functions A and B were introduced by Bell as returning the outcome of measurement. Their range is a set of integers {-1,1} by definition. Since the functions are themselves deterministic and the probability distribution of random parameter lambda is known (as it happens in your case), their means and standard deviations can be computed directly using textbook definitions of mean and std. deviation. These computations unsurprisingly produce results agreeing with Bell.
Now I'll summarize the bag of tricks:
* You have a function which is a scalar product of two vectors, one constant and another random. You want to compute its standard deviation (sigma)
* You pretend that sigma is linear with respect to scalar product. You pull the constant vector outsude of the sigma, leaving only the random vector inside
* Since you cannot compute standard deviation of a vector, you just quietly replace the vector with its norm. As a result the 'sigma' comes out as a scalar
* What used to be scalar product now quietly becomes a product of a vector and a scalar.
* As a result the value for standard deviation comes out as a vector
Joy Christian replied on Jul. 26, 2011 @ 17:26 GMT
Neither Bell’s, nor your calculations agree with what is observed in the experiments. This is because neither Bell, nor you are calculating the correlations correctly. Your calculation, as I pointed out to you more than once, produces statistical nonsense, because it is based on elementary errors. My calculation, on the other hand, agrees with the experiment, event-by-event, number-by-number, because it is based on a conceptually superior framework, and is entirely free of error. It is based on the correct model of the physical space introduced by Grassmann some 160 years ago, and further developed by many people, including Clifford and Hestenes. It is a pity that you do not have the proper background to see this.
Charles Francis replied on Aug. 13, 2011 @ 18:51 GMT
Extraordinary. You do not evcn address Delta Kilo's points, and simply make wild and patently false claims with regard to the very well known calculations by Bell, and the very well known results of experiments. Should it not occur to you that if you think you are the only person in the world who can do statistics (since no one else does it the way you do) then perhaps the mistake is yours?
"...and simply make wild and patently false claims with regard to the very well known calculations by Bell, and the very well known results of experiments. ..."
As an interested reader, do you have some examples of wild and patently false claims?
"...Should it not occur to you that if you think you are the only person in the world who can do statistics (since no one else does it the way you do) then perhaps the mistake is yours?"
Your apparent purpose for writing this sentence seems critically incomplete without pointing to 'the mistake' or mistakes.
Joy Christian replied on Aug. 13, 2011 @ 20:05 GMT
The "points" made by Delta Kilo are based on his total lack of understanding of geometric algebra. His errors are pointed out to him, not only by me, but also by at least one other person knowledgeable in the subject. Fortunately geometric algebra is not practiced *only* by me. It is a well established branch of mathematics, with wide-ranging application in physics. The statistical concepts used in my papers are extremely elementary, at least to those well-versed in geometric algebra. It is unfortunate that many people remain unfamiliar with this powerful branch of mathematics.
What is extraordinary is that the elementary error made by Bell in the very first of his equations remains unrecognized even after being exposed in this paper.
I know that I do not know enough to do anything more that learn from the exchanges. However, this statment has the 'ring' of truth:
"What is extraordinary is that the elementary error made by Bell in the very first of his equations remains unrecognized even after being exposed in this paper."
Anytime that I have followed competent mathematical derivations and concluded that an error was made, it was always something the theorist injected into their very first equation.
Joy Christian replied on Aug. 14, 2011 @ 04:14 GMT
James,
It is abundantly clear from their comments that neither Delta Kilo nor Charles Francis knows anything about geometric algebra. Unfortunately that is not unusual. Even Grassmann's own pioneering contributions to the subject remained completely unrecognized during his own lifetime. And most "experts" on Bell's theorem remain ignorant of geometric algebra even today.
Several places in this thread, I have explained in general terms -- mostly in responses to Cristi -- why conventional statistical methods don't apply in a simply connected space, i.e. the topological space as defined by Joy and which he demonstrates is identical to physical space. One can't choose one or another of pair measurements made "at a time," as we assume in conventional quantum mechanics, and project the rest of the results over physical spacetime as a probability distribution. In Joy's deterministic model, we have to sacrifice fundamental supporting assumptions of probability theory, such as the equally likely hypothesis and axiom of choice.
As Bell implies and we normally assume, quantum configuration space is identical to physical space, in terms of pair correlations, because Bell's theorem explicitly shows that quantum configuration space cannot be mapped to physical space without a nonlocal model.
That is why Joy calls his model "locally real" in contrast to nonlocal models, because even though not consistent with conventional notions of space and time, it IS consistent with EPR and with general relativity.
I'm working on proving the theorem: "Pair correlations of events in physical spacetime are independent of pair correlations in quantum configuration space." If it pans out, I'll post it.
Joy Christian replied on Aug. 14, 2011 @ 11:28 GMT
Tom,
This is one of the clearest of your statements which I can agree with and support. I would only add a minor point: My models are not only consistent with the EPR criterion of local reality, but also with a much more precise criterion of local causality formulated by Bell. One can quibble about my use of the word "disproof" in this context (which, by the way, is not objected by everyone), but Bell and his followers did claim---and continue to claim---that no model of quantum mechanics satisfying the EPR criterion of reality and Bell's criterion of locality can exist. Nothing can be farther from the truth, as is abundantly clear from my papers.
I can understand why a physicist might not be bothered by use of the term "disproof." Physical theories are ejected from the canon when they are no longer useful (e.g., phlogiston; luminiferous aether). The mathematical canon, however, is a structure to which a proof once added, is not subtracted. So I would be quite surprised if a mathematician agreed with the concept of...
I can understand why a physicist might not be bothered by use of the term "disproof." Physical theories are ejected from the canon when they are no longer useful (e.g., phlogiston; luminiferous aether). The mathematical canon, however, is a structure to which a proof once added, is not subtracted. So I would be quite surprised if a mathematician agreed with the concept of "disproving" a theorem.
Thing is, Bell's theorem (represented mathematically as Bell's inequality) is still a useful theorem. Even though its physical applications are probably greater than its mathematical uses (I'm guessing, since I haven't researched the question) it neverthless exists as a true closed judgment on a connected space of separated points or quantum elements.
EPR asked a direct question in the title of their Phys. Rev. paper: "Can quantum-mechanical descriptions of physical reality be considered complete?" And you're right -- history decided (mostly) in favor of Bell and nonlocality. Problem is, Einstein et al had a different idea of "completeness" than the QM supporters. Relativity -- special and general theory -- is mathematically complete because it starts with proven mathematical principles (Minkowski space-time, Riemannian geometry, Lorentz transformation) and smoothly makes its conclusions independent of any experiment. The QM folk, on the other hand, had long had experimental confirmation of their conclusions (2-slit experiment) and the mathematics was built around that result.
QM in the EPR meaning is not and never was mathematically complete. The theory was only complete in the pragmatic sense of mapping experimental results to a configuration space -- a space that already existed a priori by the unexplained results of previous experiments -- and adding nonlocality.
Here you, Joy, come along with something that should have been as clear to me as the freckles (okay, some call them age spots) on the back of my hand, though it wasn't. On any separated space of quantum elements or points -- where the statistical tools of Gaussian distribution, et al, play a role -- nonlocality is a primary assumption and the space (like the spaces of R^n) is necessarily multiply connected. So any real measurement (under the assumption that "reality" is described only by measurement, an assumption shared both by EPR and quantum theory proponents) "at a time," a discrete moment, is discontinuous with the physical spacetime of general relativity. Therefore -- and I like the way Peres describes it as "the experiment not performed" -- all the multiple connections left over are probable and not physically real.
Special relativity has always been a limiting case for simply connected spaces. I think you've hopped over that barrier by introducing topological distance, and I've got to believe it won't be much longer before your theory goes to press in a peer reviewed journal. You'll only know that you've really arrived, though, when the blogosphere is filled with claims that "Joy Christian isn't so smart -- I had this theory all along!" :-)
"It is abundantly clear from their comments that neither Delta Kilo nor Charles Francis knows anything about geometric algebra. ..."
Neither do I. However, I do think that when challengers come on as strongly as did these two, that they must finish the job or back off. That decision usually depends upon whether or not the challenger or challengers actually know what they are talking about. I ought to know I have been in that position frequently. So, I extend my invitation to both Charles Francis and Delta Kilo to answer whether or not they are knowledgeable about geometric algebra?
f they said no, I still wouldn't know yet whether or not your work is correct due to my own limitations. However, I think that they should argue their case on the same stage on which you have presented your work. They either argue that geometric algebra is faulty or they argue that it has not been correctly applied or they back off.
Joy Christian replied on Aug. 15, 2011 @ 03:34 GMT
Dear James,
I agree with you fully and second your invitation to both of them.
Just for the record, Delta Kilo has used all sorts of illegal operations in geometric algebra to arrive at his conclusions, and Charles Francis has made similar hostile and unsubstantiated claims about my work elsewhere. As you can see, both Florin and I tried to explain to Delta Kilo that what he is doing is illegal in geometric algebra, but he did not listen. Many people are hostile to my work mainly because they do not like my conclusions, and partly because they do not understand the unusual language of geometric algebra.
Charles Francis replied on Sep. 3, 2011 @ 05:28 GMT
As it happens, I have an MA in mathematics from Cambridge and a Ph.D. in Mathematics from London, and I have read Geometric Algebra. Geometric algebra is a branch of mathematics, not license to abandon mathematics and say that correct mathematical statements are "illegal in geometric algebra". In fact what Christian calls the "unusual language of geometric algebra" is simply Christian's abuse of a language which he does not understand, and which he uses as a smokescreen for the use of incorrect formulae in his papers.
It is true that I have made specific criticisms regarding the mathematics in Christian's papers elsewhere, and I have seen other knowledgeable posters also make specific criticisms. Christian's response is always the same. He ignores the criticisms and makes ad hominem claims about the other's knowledge of geometric algebra, just as he did here.
It is also true that I am hostile to cranks posting on arxiv, since this creates undue noise and wastes the time of those who take the trouble to assess those papers. Christian has been given some lassitude, because the difficulty in reading his papers may be in part due to the fact that English is not his first language. However this does not detract from the fact that none of Christian's papers adheres to a form or standard acceptable for publishable papers either in mathematics or physics.
I have just come back from the FQXi conference where I had the privilege to meet David Hestenes (the originator of geometric algebra) and discuss my work on Bell's theorem with him. He did not treat me as a "crank", nor did he think I was abusing the language of geometric algebra. In fact he warmly remembered our past correspondence and seeked me out for breakfasts and lunches where we had many discussions about his work and mine. I also had discussions with many of my fellow FQXi members, such as Garrett Lisi and Tevian Dray, both of whom are experts on geometric algebra. They too did not treat me as a "crank." In fact, in the past four years I have had many discussions with numerous experts on both Bell's theorem and geometric algebra---for example, people like the distinguish Berkeley mathematician Jenney Harrison, the probability expert Derek Abbott and his several post-doctoral associates (all very knowledgeable in geometric algebra), and numerous lesser known physicists, philosophers, and mathematicians, both at Oxford and elsewhere.
At the FQXi conference we also discussed (officially)---quite independently of my work or anyone else's---how difficult it is to pass through the censorship of peer review if you have an innovative idea going against the dogma of the day (take a look for example at this insightful discussion of the peer review problem). For this reason FQXi has already given me a mini-grant to publish my work as a book. So, whether you like it or not, my work is here to stay.
And since you are flaunting your credentials, let me also point out that I have been trained in the foundations of quantum physics by one of the world experts on Bell's theorem---namely, Professor Abner Shimony (the S in the CHSH)---and I have also been privileged to have had discussions with Bell himself on several occasions. Moreover, many other distinguished experts on Bell's theorem---such as Lucian Hardy, for example---are my close friends. Thus having a controversial view, or using an unusual mathematical framework, does not automatically make one a "crank." Historically, "crank" has been a convenient label used by those who have been unable to stomach a new idea. Someone like you who is committed to believing only that which is accepted by the community for the day will have to work harder to understand my work, provided, of course, that you are willing to learn something new and innovative.
Charles Frances, you are not going to intimidate me with your thinly veiled ad hominem attacks, whatever your true motivations are. In the past four years I have endured far worse.
Charles Francis replied on Sep. 3, 2011 @ 09:48 GMT
Remarkable, again. Since you say that David Hestenes is the originator of Geometric algebra, he must be nearly 200 yrs old. Usually it is attributed to Grassman. See e.g. http://en.wikipedia.org/wiki/Geometric_algebra#History for an account of the origins of geometric algebra. In fact vector analysis has completely overshadowed GA, for good reason. According to that article Hestenes contribution is that he " reinterpreted the Pauli and Dirac matrices as vectors in ordinary space and spacetime, respectively". In fact, they are not vectors, but something rather more subtle, so it is perhaps a good idea to ignore his contribution.
Let me first apologize for misspelling your name in my previous message. That was unacceptable.
Now you often cite Wikipedia articles to support your arguments. That by itself is quite telling. It tells me about the level of your understanding of various things. It also confirms my suspicion that you have actually no clue about what geometric algebra is all about. You have cited Wikipedia article without any understanding of the distinction between Grassmann's original introduction of the extensive magnitudes without inhomogeneous mixing (of which vectors are but a special example), Clifford's insightful introduction of the all important geometric product, and Hestenes's comprehensive reformulation of the subject as a whole, which today goes by the name of geometric algebra, or GA. Wikipedia articles are often good sources of information, but they are unlikely to give deeper understanding of such subtle distinctions. In any case, you are welcome to ignore Hestenes's contribution, as well as my own work based on it. We will not be offended.
Charles Francis replied on Sep. 3, 2011 @ 10:24 GMT
Joy Christian says
>Thus having a controversial view, or using an unusual mathematical framework, >does not automatically make one a "crank."
However simply replacing perfectly correct formulae in probability theory with other formulae, which (if they are not miscalculated) do not satisfy the axioms of probability theory, as you do in your papers, does make one a crank.
Similarly, using an unusual mathematical framework, which gives different results from the well established results of classical probability theory and classical results and then calling your framework "classical" makes one a crank.
Likewise, describing correct mathematics which has been established independently and objectively by numerous mathematians as "dogma" makes one a crank. If you think mathematics, such as the mathematics used in proofs of Bell's theorem, is "dogma", then you have no understanding of mathematics at all.
>Someone like you who is committed to believing only that which is accepted by >the community for the day will have to work harder to understand my work, >provided, of course, that you are willing to learn something new and >innovative.
On the contrary, my work, including my published work, does dispel ideas accepted by the community of today. This does not mean that I have abandoned mathematical proof.
The mathematical formulas used in my latest papers do indeed satisfy the axioms of random variables, just as standardly used within the framework of geometric algebra. You are welcome to your opinions, but you are not going to intimidate me by using abusive language. Things that are beyond your understanding does not automatically become "crank."
Of course one thing Wikipedia articles do is tell us what goes under what name, whereas you are using the name of a respectable branch of mathematics to describe something else.
which purports to be an introduction to Hestenes' work. But then we find in the sections Geometric Algebra of the Plane and The Algebra of 3-Space definitions of so called "linear spaces" of "multivectors" which are patently inconsistent, and from this point on the whole subject is nonsense. It is no wonder the language is unusual. It is gibberish.
I don't think that just being on a public forum gives one license to abandon collegiality. Carelessly throwing around the "C" word isn't helpful, and reflects poorly on one's intellectual pedigree.
At a conference a few years ago, I listened to a presenter argue through several claims, among them a claim to having resolved Zeno's paradoxes of motion. At the Q & A following, I asked...
I don't think that just being on a public forum gives one license to abandon collegiality. Carelessly throwing around the "C" word isn't helpful, and reflects poorly on one's intellectual pedigree.
At a conference a few years ago, I listened to a presenter argue through several claims, among them a claim to having resolved Zeno's paradoxes of motion. At the Q & A following, I asked (completely innocently, since I was sure I had missed something), "Okay then, is motion possible?" By the reaction, one would have thought I had grown an extra head or two. Fact is, though, the presenter had gone through a 15 minute argument without ever actually asking the question that Zeno had asked, quoted above.
The same applies, I observe, to many critics of Joy Christian's framework. Even though Joy has been quite clear that the question he asks is identical to the question that EPR asked ("Can a quantum mechanical description of reality be complete?") followed by an argument in the EPR tradition of mathematical completeness (elements of a mathematical theory correspond 1 for 1 to elements of the physical result), that the answer is negative. (Heinz Pagels -- The Cosmic Code, Simon & Schuster 1982 -- gives a nice plain language description of EPR's assumptions and the outcome of testing Bell's inequality.)
Problem is, while EPR's idea of completeness is independent of experiment, quantum theory is not independent of experiment. Compromise between the two viewpoints, then, boils down to whether action at a distance is causal; classical physics is only locally causal -- and what all physics firmly demands of "reality" is that it be measurable. The EPR assumption is that properties of particles (position and momentum, e.g.) that remain unmeasured have objective existence; i.e., so-called hidden variables help determine the outcome of every measurement.
In the EPR context, reality is observer-dependent, in opposition to Bohr and the Copenhagen Interpretation that reality is observer-created. Because of this disconnect, Bell-Aspect type demonstrations of Bell's inequality, which are arguably observer-created, cannot capture the continuous measurement functions in a physical model. (I have re-attached here, my sketchy proposal for demonstrating Joy Christian's conclusion--thanks again, Albert Jan.) Observer dependence and orientation entanglement explain the objective reality of unmeasured correlations existing off the axis of measured correlations, because the time dependent relation, which is equivalent to observer dependence, demands 100% knowledge of the initial condition 100% of the time (vice the upper limit of 50% correlation aggregated over time, as Bell-Aspect predicts).
Getting down in the weeds over geometric algebra is a red herring. We are dealing with first principles, and one should not confuse the tool with the architecture. Also, the probability discussion is not relevant. The only statistical analysis involved in Joy's framework is an elementary judgment on confidence intervals for repeated observations of physical pair correlations. It should be obvious that Joy Christian's proposal does not in any way require fundamental assumptions of probability analysis -- the equally likely hypothesis, central limit theorem, axiom of choice -- although it does seem that he applies a Bayesian type assumption on information contained in the integral of the real analysis (this is a technical detail that I personally feel will eventually be found unnecessary).
I truly hope we can discuss Joy's framework on its own merits and skip all this posturing.
You have just described the lifetime-work of one of the most distinguished and honoured FQXi members---an Emeritus Professor and a winner of the Oersted Medal among other honours---by words like "nonsense" and "gibberish." Worse still, by your own comments you have confirmed that you have been making unjustified and false criticisms of my work without knowing the first thing about geometric algebra. Only now you are looking up some introductory websites to learn about it, and yet you have the audacity to criticize Hestenes's lifetime-work. You are simply wasting everyone's time and acting unprofessionally.
The previous comments by me were meant of course for "Anonymous", which I presume is Charles Francis. I haven't had the chance to think about your argument yet, but I will get there soon.
Just for the record, not everyone who disagrees with your mathemtaics or interpretations is a 'hostile' (nor was I 'Anonymous'). As I recall, you and I 'agreed to disagree', but you have had challenges from Florin, Cristi, Delta Kilo, Charles, and myself, and - to Charles' point - "He (Joy) ignores the criticisms and makes ad hominem claims about the other's knowledge of geometric algebra". Tom tried harder to answer my question than you did, and yet Tom seems to be off on yet a different tangent. I asked two simple questions about your latest preprint (1106.0748 - because you criticized Florin for focussing on older preprints): 1) Do your answers to equation 8 include all possible complex solutions? (if not then equation 11 and so on is incomplete), and 2) Are your interpretations physically consistent? (recall my comments that complex statistics could lead to Anyons - a form of statistics that Jon Leinaas and Jan Myrheim helped develop, and we cannot discuss 'local reality' if faster-than-light tachyonic Anyons are involved).
The first book I read on Clifford Algebras was about twenty years ago, and was written by David Hestenes, but he did not invent that field of study. It seems to me that Sir William Rowan Hamilton and Arthur Cayley had a lot to do with that.
And I don't throw the 'crank' word around because I wouldn't want someone to use that word against me. I have a PhD in Particle Physics from Florida State University, and would rather be called a 'maverick'.
If you haven't been called a crank yet (I have), you need wider exposure. :-)
Apparently, from your comment about my going off on a tangent, my point about applying probability theory to simply connected spaces has been either lost or ignored ("all real functions are continuous"). It obviates your concerns.
Perhaps if we get away from the credentials-sniffing and other sociological concerns, we would have a productive technical discussion. Speaking for myself, and I think for you, too among others -- that would be most enjoyable.
Most people on this site have been quite civilized. The discussions between us, in particular, have been quite collegial. I am not the aggressive type, but I will not put up with abusive language. My goal here is to make my point of view understood. But there is limit to which I could contribute to that understanding. There are some people who would never understand my point of view for reasons that have nothing to do with my work, and I have no ambition to make them understand. You, on the other hand, have shown genuine interest in my work and asked semi-informed questions. The trouble is that I think you do not understand the difference between the kind of non-locality Bell and I are concerned about and the kind of non-locality you are concerned about. This is quite clear to me from your two questions. Let me, therefore, try to first explain the difference between the "quantum non-locality", by which one cannot send a signal, and the relativistic non-locality of the kind you are concerned about, by which one can indeed send a signal. I am not at all concerned about the relativistic non-locality in my work. I am afraid you too are off on a tangent when you bring up things like tachyonic anyons etc., which have absolutely nothing to do with my argument. I also do not see what my argument has to do with the solutions of equation (8). That equation is simply a demonstration of the fact that a unit bivector represents an equatorial point of a 3-sphere. There are no complex numbers in geometric algebra. So I have no idea what complex solutions you are talking about. And I have no idea what they have to do with Bell's theorem or my argument concerning the no-signalling non-locality. Moreover, my equation (11) is simply a version of the bivector subalgebra, which relates various real points of the 3-sphere. Let me stress once again, there are only real, geometric objects in geometric algebra, no complex numbers. Thus my interpretations are perfectly consistent with the EPR-Bell criteria of locality and reality. And that is all that matters as far as my argument is concerned. Why do I feel like I have answered your questions before?
I probably have been called a 'crank' behind my back - I was saying that I prefer not to call others cranks. If you haven't made a mistake, you aren't trying hard enough. Regarding the 'credentials sniffing' - I meant no disrespect to you or Cristi. I think you have as much sense and ability as do these PhD's, and Cristi is working on his PhD. But I would prefer it if Joy took these criticisms - most by PhD's - a little bit more seriously.
You said "all real functions are CONTINUOUS". That is fine - I'm not here to argue that with you. My point is that quantum statistics normally have symmetric (Bosons with +1) or anti-symmetric (Fermions with -1 & the origin of the Pauli Exclusion Principle) wavefunctions. If we admit complex quantum statistics, then we allow a CONTINUOUS complex symmetry phase of exp(i*theta) for our wavefunction - i.e. ANYONS. Anyons may exist on a 2-D plane (certainly the 7-sphere has enough of those) and may have tachyonic (faster-than-light) properties. If we are dealing with tachyons of any sort, then this negates 'locality' and 'simultaneity'. We might as well throw both Einstein and Bell out of the conversation.
And this is just considering complex symmetry phases. What happens if we admit properties of hypercomplex (quaternion or octonion) numbers into our quantum statistics?
I realize that you never mentioned Anyons - I'm saying that a different interpretation might yield Anyons.
You said "There are no complex numbers in geometric algebra". Once again, I think that depends on your specific model. A pure octonion will have one real (scalar) component and seven imaginary (vector) components, and I thus model a physically-significant hyperbolic octonion 7-sphere with 7 real space-like hyper-surface dimensions, and one imagimary time-like radius. When you make assumptions about unit-radius hyperspheres, you are discarding the time-like radial component - perhaps without sufficient physical motivation. If all 8 of your 7-sphere dimensions are real, then it does not represent octonion algebra, and you might as well call it a real 8-ball because it is radically different from a hyperbolic octonion 7-sphere.
Charles Francis replied on Sep. 3, 2011 @ 17:47 GMT
Hi, Christian,
I understand this part of your work very well indeed. I refer to arXiv:quant-ph/0703179v3 22 Apr 2010 "Disproof of Bell’s Theorem by Clifford Algebra Valued Local Variables".
This rests on replacing the classical (local realistic) expectations
eqs (9) (10) with "analogous" (your word) expressions, eqs (18)
(19). Let us suppose you have evaluated the expressions correctly, if so the conclusion is obvious. This is a fundamental change to probability theory. I.e. it is not probability theory. You are not disproving Bell's theorem but simply calculating something different.
What you have done, dressed up in gobbledy gook to make it look difficult, and to give yourself the opportunity to accuse others of a failure of understanding,
is very simple, very obvious, and plain wrong. While you are making mistakes on this level, do not pretend to have anything useful to say about Bell's theorem.
Not true, Ray, not true. There can be no different interpretation, because there are only real geometric objects in geometric algebra. It would have to be a different model, not using geometric algebra, to admit the kind of interpretation you are suggesting. A parallelized 7-sphere can indeed be formulated within geometric algebra, with all of its components real. To be sure, one of them will be a scalar component and the other seven will be bivector components, but these bivectors will be real geometric objects, not complex numbers. What is more, time---either real or imaginary---does not enter into Bell's argument, and hence it does not enter into mine. I feel that you are expecting the model to do something it is not meant to be doing. It seems to me that we are talking not only different model and different language, but also different physics.
CF has said "goodbye." I will miss him terribly. Who would I now tell that probabilistic reformulation of Bell's original argument is precisely the Achilles' heel of Bell's theorem? Why? Because it predicts a wrong result---2 instead of 2\/2.
We certainly are on different wavelengths. I will simplify my point regarding the so-called 'realness' of geometric algebra. Some of this is partial repitition, but my point is to make this crystal clear for everyone who might read this blog post.
Consider modeling quaternion Spacetime with a 3-sphere. According to the original definition by Hamilton, quaternions have one real (scalar) component, and three imaginary (vector) components. This phase difference between scalar and vector components is crucial. Standard relativistic notation (such as the Minkowski metric) assigns an overall imaginary 'i' phase to time (such that -1=i^2 yields the time-like component of the Minkowski metric), and a real phase to space. As long as you stay on the hypersurface of the 3-sphere (this constraint specifies fixed time), everything is 'real' and we need not worry about imaginary phases. But as soon as you manipulate the time-like radius (and you arbitrarily set the radius to '1' without consideration of a time measure OR an overall phase difference between time an space) then you are introducing complex numbers. Typically, we measure time as another 'real' quantity, and reintroduce this imaginary 'i' phase with the covariant and contravariant operators of Relativity. We have hidden the complex numbers nature of Spacetime, but it is still there, and it could be a critical mistake to ignore this complex phase.
The octonion 7-sphere is similar, but we now have 7 real hypersurface space-like dimensions, and one imaginary time-like radius. Seriously, if you assign a real phase to all 8 dimensions, then you might as well call it a 'timeless 8-ball'.
You seem to want to separate Relativity, Particle Physics, and Bell's Theorem as if they all generate different physics. The point is that physics is our way of representing nature with mathematics - it isn't different physics - IT IS ALL PHYSICS!
If you don't understand it the way Joy explained, I don't know what to add that would make it clearer.
The only more general point I can contribute, is that fundamentally, real continuous functions are native to topology. Joy's framework doesn't lack a time component -- indeed, it DEPENDS on it. It is the assumed 2 pi rotation of Bell-Aspect that violates continuity and time=reverse symmetry.
Well, I guess I could be a little clearer. Time-dependence does not imply a metric, yet it does imply transitivity. This is the necessary condition (along with reflexivity) that produces equations of the algebraic variety. Because the solutions are all real, they fit a physical model.
As before, we will have to agree to disagree. We are concerned about very different things, and we are using very different languages. The geometric algebra version of spacetime physics is an entirely different ball game. It is very different from what you have described, and my work also has nothing much to do with it. I think we both have made our points and it is best to leave it at that.
Tom - My interpretation is that the wavefunction statistics of this particular model should involve complex phases of exp(i*theta) where theta ranges from 0 to 2*pi. This function is CONTINUOUS - it is a circle of unit radius in the Argand plane. Anyons actually provide those CONTINUOUS wavefunction symmetry phases between the seemingly discrete Bosons and Fermions. Yet - it simultaneously provides the sort of modulo arthmatic that we might anticipate based on the cycling properties of the normed divisor algebras (R,C,H,O and start over) and properties of fundamental particles (where intrinsic spin of greater than two is not expected such that spin = 0 (Higgs), 1/2 (Fermions), 1 (Photons), 3/2 (Gravitinos), and 2 (Gravitons)).
Have Fun - I'm off to enjoy a new College Football season...
Charles Francis replied on Sep. 3, 2011 @ 22:52 GMT
Hi, Christian,
You wrote:
"You have just described the lifetime-work of one of the most distinguished and honoured FQXi members---an Emeritus Professor and a winner of the Oersted Medal among other honours---by words like "nonsense" and "gibberish." Worse still, by your own comments you have confirmed that you have been making unjustified and false criticisms of my work without knowing the first thing about geometric algebra. Only now you are looking up some introductory websites to learn about it, and yet you have the audacity to criticize Hestenes's lifetime-work. You are simply wasting everyone's time and acting unprofessionally."
And so we come full circle. You again fail to respond to specific criticisms about statements of mathematics and instead make ad hominem remarks about the others understanding.
I use easily found internet references so that it is quite clear what is being said, while you hide behind vague references and appeals to authority, which have no place in mathematics or in science.
The statements I criticised were clear mathematical nonsense. It is you who says that this undermines Hestenes' lifetime work. So be it. It matters not a jot who he was. He is an emeritus professor. That just means "retired teacher". He was a physicist but not one of the top universities. The Oersted medal is for contributions to teaching, not for contributions to mathematics. You say his lifetime work was to try to supercede the work of great mathematicians of history. That is true audacity. If his work stood up as mathematics, then fine. But you say it doesn't. It does at least explain why your own work is so full of the abuse of mathematics.
If you had something to say you would work at making it understandable to as wide an audience as possible. As it is you only seek to impress those with no mathematical background, and to make ad hominem attacks on those with a mathematical background, while hiding behind spurious mathematical claims. It is time you stopped taking money for this stuff. It is fraud. The money is given in good faith to assist in the advance of science, but your papers are just noise, and are more likely to give science a bad name. You use "unusual language" for the simple reason that you don't know what the words mean.
Historically "cranks" are not those who might advance science. They are the circle-squarers, after it is proven that pi is transcendental, they are the creators of perpetual mobile machines, after the proof of the second law of thermodynamics. And in this case they are those who do not understand that Bell's theorem is actually a theorem, and who think that a "disproof" can be provided through the use of illegal mathematical operations, like substituting a wrong formula for the calculation of a probability and calling it "classical".
And welcome back. You are entitled to your opinions, but I have no interest in quibbling with you about petty things. I prefer to spend my time in more constructive aspects of my work. And I prefer to explain my work only to those who have genuine interest in understanding it. If you are at all interested in understanding it, then it has been introduced and developed in detail in the first nine papers listed here. Each of these papers contains extensive citations to scholarly literature, and I have gone out of my way to explain every concept I use as clearly as possible. You will find all the answers to your questions if you actually read my papers. Fortunately, my work has not been incomprehensible to everyone. It has indeed been incomprehensible to some, but mostly to those who look at it in bits and pieces and with extreme prejudice.
Lawrence B. Crowell replied on Sep. 4, 2011 @ 00:37 GMT
Charles,
This observation of mathematical substitution and calling it classical boils down to equating 1 = -1. This sign problem is simply an inconsistencey, and is at the heart of JC's claim for "disproving" Bell's theorem. This was something which struck me several years ago when I encountered this.
How do you find this false equivalence? In terms of integrable quantities, - oo to + oo, sign change is not only allowed, but mandatory. Vector analysis carries the sign change operation to corresponding points of bivector rotation, completely consistent with Euler's geometric interpretation of the complex plane. I keep emphasizing the Lebesgue integrability of Joy's framework, which results from the continuous function clearly defined on the equator of S^3, whose only results are + 1, - 1, and i. Put in terms of a rotational matrix, the real analysis yields only continuous real valued results. Applied to physics, that is, most certainly, classical.
You're way off base. It's hardly the case that Joy can abuse probability theory when the concept doesn't even appear in his framework. His is not an alternative formulation of QM.
Although I too disapprove of the idea of "disproof," and have said so in strong terms, that is not sufficient reason to savage a very rich body of research
Charles Francis replied on Sep. 4, 2011 @ 07:29 GMT
Hi Tom,
Expectations are a part of probability theory. They do appear in Christian's work. In fact Bell's theorem is about expectations. Nothing alters the fact that Christian simply substitutes incorrect formulae, and calls it "disproof", then dresses it up in language designed to be obscure.
Here is my disproof of Bell's theorem. You do not have to be Einstein to understand it. You also do not have to be Einstein to see where Bell went wrong. You do have to know a thing or two beyond the level of Wikipedia, however. Bell's error is in his very first equation of his famous paper, as explained here. There are no errors in my papers.
Charles Francis replied on Sep. 4, 2011 @ 12:35 GMT
Well, Joy, you certainly don't need to be Einstein, or even at the level of Wikipedia, to spot the schoolboy errors in this paper. For example The CHSH inequality is
Thanks, I see your source of misunderstanding now. You're confusing the analysis of experimental data with the expectation of experimental outcome. What Bell expected of the outcome is that local hidden variables exist; if they don't, action at distance rules and God rolls the dice every time we perform an experiment.
Thanks, I see your source of misunderstanding now. You're confusing the analysis of experimental data with the expectation of experimental outcome. What Bell expected of the outcome is that local hidden variables exist; if they don't, action at distance rules and God rolls the dice every time we perform an experiment.
It's all about causality. Bell accepted EPR's challenge to show that causality is local in spite of anything else happening in the universe, and so quantum mechanics cannot possibly be complete (the proposition cannot be more clearly stated than in the very title of EPR's Phys. Rev. paper, "Can quantum-mechanical descriptions of physical reality be considered complete?")
It is important to understand that Bell made his judgments by the CLASSICAL criteria of EPR and not by the probabilistic interpretation we assign to Bell's Inequality today. Both EPR and Bell assumed their experimental domain to be the entire observable universe -- and this is where Joy Christian spots the chink in Bell's armor. Bell's program rests on a coin toss probability: the world is either nonobjective and does not exist in a definite state, or events are nonlocal and action at a distance is causal. Joy Christian correctly identifies the difference between the quantum nonlocality that Bell speaks of (which assigns a value of nonlocality to "the experiment not performed" as Asher Peres phrased it) and the signal nonlocality of special relativity. Big difference -- EPR had not even imagined that one could confuse the signal nonlocality of special relativity with the cosmic initial condition that makes general relativity a mathematically complete theory. But they did.
Pagels (The Cosmic Code) writes of EPR's proposal from Bell's point of view, "Such a subquantum theory would actually restore determinism and objectivity. If we imagine that reality is a deck of cards, all the quantum theory does is predict the probability of various hands dealt. If there were hidden variables it would be like looking into the deck and predicting the individual cards in each hand."
In other words, if the cards could communicate with one another, they would assign positions to each other that correlate over infinite distance. If aces and eights are always paired, they could tell each other where they are regardless of how far apart they've traveled. (This is actually the seeming case in tests of quantum mechanics, where particles are released independently and seem to "know" where the others have gone, regardless of the time at which they were released.)
Joy Christian says that's not an apples to apples comparison. And it isn't. In EPR's world, all physics is local. That's not just an assumption; it follows directly from the mathematical completeness of relativity. Christian didn't redefine "local," he just put it back into the context where EPR's assumptions apply -- a universe of complete and continuous functions.
And if you read my experiment sketch, I hope I made clear that Christian's criteria fit REGARDLESS of what definition one assigns to "local."
So if the function space is complete and the function continuous, we expect pair correlation of data contained in the initial condition on one changing axis all the time -- as contrasted to quantum mechanical data measured on one nonchanging axis that correlates with a coin toss probability over an arbitrarily long time. Joy's is not in any way a probabilistic framework -- random variables (unmeasured and thus nonphysical), off the axis of correlation, are simply not oriented in the interval of time that defines the orientation of the continuously correlated pair. That correlated pair is Lebesgue integrable, analytically real and oriented to all points of S^3.
As far as the "disproof" issue goes, I have no more to say about it than you can read elsewhere in the forum.
There is absolutely nothing wrong with my sentence "The corresponding CHSH string of expectation values gives..." and the inequality that completes it. Schoolboys would certainly not make the mistake you have made in reading it.
Lawrence B. Crowell replied on Sep. 4, 2011 @ 14:52 GMT
Tom,
What follows with Charles' writings on this thread is essentially the main problem. The "sign problem" comes about in the application of numbers which can't form probabilties. This assignment is a sort of 1 = -1 issue. I read a paper by JC three years ago and dug into it and this was my assessment then. I have not really followed the rest of these developments. Unless somebody can show otherwise I don't see much point in pursuing these lines. What would impress me about nonlocal hidden variables is an experimental result. Unless that comes to fruition all the theory in the world will fail to impress me.
Charles Francis replied on Sep. 4, 2011 @ 17:31 GMT
I don't know what happened to the rest of my post, but for some reason it got truncated mid formula, leaving what was left meaningless. I'll rewrite and hope it all comes through this time.
Well, Joy, you certainly don't need to be Einstein, or even at the level of Wikipedia, to spot the schoolboy errors in this paper. For example The CHSH inequality is
There is absolutely nothing wrong with my sentence "The corresponding CHSH string of expectation values gives..." and the inequality that completes it. Schoolboys would certainly not make the mistake you have made in reading it.
Charles Francis replied on Sep. 4, 2011 @ 17:56 GMT
I can assure you Joy, there is no way I, or any schoolboy, could misunderstand the sentence "This contradicts Bell's theorem".
The CHSH inequality is
CHSH string is less than or equal to 2
You claim to prove
CHSH string is less than or equal to 2*sqrt(2),
but then you say "This contradicts Bell’s theorem". But 15 year olds preparing for GCSE would recognise that these inequalities are perfectly consistent, and in fact that your result follows trivially from the CHSH inequality.
Also you have (at best) a serious inconsistency of notation between eqs (3) & (4), not to mention the serious abuse of mathematical language preceding those equations..
And then you say that "the variables A and B above respect both the remote parameter independence and the remote outcome independence", but actually the definitions in (1) and (2) show that they are perfectly correlated, which would also be obvious to a schoolboy.
And what btw, does it mean for an observer to be equipped with a variable? Can he buy one at the variable equipment store in the high street?
The comments you have made are all very stupid comments. They show how ignorant you are, not only about geometric algebra, but also about Bell's theorem itself. At first I thought that your confusions are because of your unfamiliarity with the language of geometric algebra. That is understandable (although in the beginning you lied to us that you have actual read geometric algebra---that was a lie, which became increasingly evident from your later posts). But your current comments make it abundantly clear that, let alone geometric algebra, you don't even understand Bell's theorem itself.
Bell-CHSH theorem says that the Bell-CHSH inequality cannot exceed the bound of 2 for any local and realistic model. It is evident from my equation (8) that this claim is false. I have produced an explicit local and realistic model---in the precise senses defined by EPR and Bell---which does exceed the bound of 2, and does so in a manner that agrees with the quantum mechanical prediction angel-by-angel, event-by-event. Therefore, my sentence "This contradicts Bell's theorem" is perfectly justified and correct. In fact it is quite an understatement. You have to be blind not to see that.
Now do you even know the difference between correlations and the two independence conditions I mention? Have you ever read the Clauser-Shimony report? I very much doubt that you have. One cannot infer anything about the correlations between the variables A and B by simply looking at equations (1) and (2). One has to calculate correlations using the concepts given to us by Galton and Pearson some 100 years ago, with due respect to the fact that A and B represent the points of a parallelized 3-sphere, and the fact that my model is formulated in the language of geometric algebra.
Does it not occur to you that what appears to you as "serious inconsistency of notation" and "serious abuse of mathematical language" could be due to your own intellectual limitations? (You really don't want to know my answer to that question.)
Charles Francis replied on Sep. 4, 2011 @ 20:06 GMT
I do not have to make very intelligent comments, Joy, because the mistakes you make it this paper are all very stupid mistakes. Your equation (8) says no such thing, and the fact that, even after your error is pointed out, you think it does tells me that you are incapable of mathematical reason at even the schoolboy level of GCSE. It is no wonder your papers say none of the things you claim, but consist largely of the abuse of mathematical terms used in randomly inappropriate ways.
Thanks, I see your source of misunderstanding now. You're confusing the analysis of experimental data with the expectation of experimental outcome. What Bell expected of the outcome is that local hidden variables exist; if they don't, action at distance rules and God rolls the dice every time we perform an experiment.
It's all about causality. Bell accepted EPR's... "
Lawrence B. Crowell replied on Sep. 5, 2011 @ 01:22 GMT
Tom,
Around the time the economy was falling apart in 2008 I read a couple of papers by JC. What Charles is writing is reminiscent of my critique. Florin’s critiques are more with later papers for the most part. I think this whole enterprise is a nonstarter, and honestly if the Bell Theorem were really disproved I think that after several years it would have risen to front page physics news. Also if you look at the exchanges here it is clear that anyone with objections “clearly does not understand … .“ Unfortunately the dialogue has become a sort of “t’is too, t’is not.”
Life is short and time is valuable. It is best not to spend too much time on things that don’t look like they are going anywhere.
There is no problem. Joy's framework is not probabilistic.
Tom"
I was looking forward to your reply. This seemed to require a yes or no type response with, hopefully, some qualifications. Agree or disagree, but expecting that others would have brought in the reporters was not what I thought would come in response.
I think this is a very important scientific discussion and it is presently occurring here. Did you see T H Ray's message below? It begins:
"Charles
Thanks, I see your source of misunderstanding now. You're confusing the analysis of experimental data with the expectation of experimental outcome. What Bell expected of the outcome is that local hidden variables exist; if they don't, action at distance rules and God rolls the dice every time we perform an experiment.
It's all about causality. Bell accepted EPR's... "
There are questions about whether the mathematics is correct (Tom thinks so, but the rest of us are not satisfied with the answers on this blog post), and about whether the interpretation is correct. As a phenomenologist, I was trained to use mathematics to model reality.
If Joy went astray at Equation 8 in his latest preprint (Joy's expectations of +1,-1 conflict with Tom's expectations of +1,-1,i and with my expectations of exp(i*theta)), then many of his results and conclusions are incomplete (but probably could be corrected, so I don't think it is fair to completely trash the man's work). Furthermore, Joy interprets +1,-1 as photon spin-up or spin-down, whereas I interpret this as the wavefunction symmetry statistics: +1 for Bosons, -1 for Fermions, and exp(i*theta) for general Anyons. Charles and Laurence are also interpreting this as a probabilistic result, although they have not specifically mentioned quantum statistics (probably because Joy and Tom argue that we don't need quantum anything - but we know that Bosons and Fermions have these properties and it is foolish to dismiss quantum statistics as unreal or unnecessary).
I don't understand why Joy insists on a photon spin-up or spin-down - photons are not necessarily part of every experiment that is performed. Furthermore, the Z boson sometimes behaves like a massive photon in ElectroWeak interactions, and the Z boson has a third option with spin projections of +1, 0, and -1. Joy's 'null' result is *NOTHING* whereas the longitudinal mode of the Z boson is *SOMETHING*. Once again, an improper modeling approach has been implemented.
Above, I said "it is foolish to dismiss quantum statistics as unreal or unnecessary". To give further REAL EXPERIMENTAL detail, the antisymmetric wavefunction symmetry of Fermions is directly responsible for the Pauli Exclusion Principle - without which White Dwarfs and Neutron Stars would not exist (they would collapse into Black Holes). Furthermore, Planck's Law of Blackbody Radiation is experimental confirmation of Bose-Einstein statistics, and many crystalline effects (such as the photoelectric effect) are experimental confirmation of Fermi-Dirac statistics.
I don't have an axe to grind with Joy or with Tom, and really don't want to get into silly playground name-calling. I just want you to understand why I have problems with Joy's works.
Lawrence B. Crowell replied on Sep. 5, 2011 @ 02:48 GMT
James.
I was nearly 3 years ago when I read papers by JC. My memory is not that fresh. However,. there are clear sign errors induced by writing things as probabilities which are not. I read a lot of papers, and frankly if I find fatal problems with them I drop following that line of research. I just read a paper by Mavromatos that is nonsense. As I say, life is short and you can't spend endless time on something which has problems.
Quantum mechanics is almost more than a theory and is some sort of logical structure. It is probably the most outstanding physical theory ever derived. It happens to be difficult to understand from a classical perspective. However, QM is a linear theory of states and waves, it has linear eigenvalues and ... . What could be simpler? The problem is that it conflicts with our classical or macroscopic world. What is mysterious is the existence of the macroscopic or classical world.
As I have pointed out to you before, I do appreciate your input. However, your concerns are entirely misguided. You clearly do not have the background in the logic and history of the EPR argument or Bell's theorem. Quantum mechanics does not enter Bell's theorem at all, at any level. Please at least read Bell's original paper to see what his argument is and what a local-realist is required to do to counter it. I have explained this to you several times, in several different ways, but to no avail.
As for Charles Francis: His vicious, personal, and unjustified attacks on me are due to his personal grudge against me. He was kicked out of sci.physics.foundations group as a moderator for making ad hominem attacks on me and libellous attacks on other physicists. It is important to keep this in mind while reading his posts.
Life is never short for discovering the truth. As Tom pointed out earlier, there is no sign problem in my framework, because it does not depend on the probabilistic reformulation of Bell's theorem.
Charles Francis replied on Sep. 5, 2011 @ 05:46 GMT
Christian,
You still have not explained how it is that if a number is less than two, it cannot be less than 2*sqrt(2) (the contradiction you claim in equation 8). Nor have you answered any other mathematical criticism of you papers.
If you put mathematical words into meaningless sentences, of the form "green ideas sleep furiously". It is not an ad hominem attack on you to say that you have put mathematical words into meaningless sentences. It is an objective comment on the quality of the papers you have posted on arxiv, made by someone who has the mathematical background to know what the words actually mean.
You write: "You still have not explained how it is that if a number is less than two, it cannot be less than 2*sqrt(2) (the contradiction you claim in equation 8)."
Your question, as I have already explained, is an utterly stupid one (for the detailed answer see my earlier post). It shows that you do not even have the most basic understanding of Bell's theorem. Read the basic literature on Bell's theorem first to recognize the mind-numbing stupidity of your question.
Then you write: "Nor have you answered any other mathematical criticism of you papers."
They have been repeatedly answered, not only on these pages, but also on the pages of sci.physics.foundations from which you have been kicked out as a moderator. Then there are nine papers of mine, which you have never bothered to read. By the way, your so-called "mathematical criticisms" are non-criticisms. They simply arise due to your total lack of understanding of both Bell's theorem and geometric algebra, not to mention basic statistics. Charles, I know you like to think that you are very clever. I am sorry to break it to you that you are not.
I agree with you about not being led down the primrose path by ideas that one finds clearly wrong. That was, in fact, my initial reaction to Joy's research, which is on record here. Since this is my first exposure to his work, perhaps I have an advantage in not having read the previous attempts and the criticism thereof. Being just a vagabond pencil and paper mathematician with no credentials worth sniffing, however, I don't feel it fair to pass judgment until I have independently exposed the error. I was surprised not to find it.
Yes, I have read the criticisms here, and they amount -- as you have pointed out -- to little more than accusations, not productive criticism at all and certainly lacking any resemblance to rigor.
So I will try and address objections to the application of sign change, and my opinion of the meaning of Joy's upper experimental bound, 2sqrt2, which I find are related:
I realize that this discourse on sign change will be elementary to the mathematically knowledgeable, and I don't mean to insult anyone's intelligence. I post it both for the benefit of the general reader, and to set the baseline for I want to further say.
Sqrt2 is a root in the integral that defines its own bounds by sign change, because it is continuous. We know it is continuous because it is the solution to an integral that has roots, and we know that sign change characterizes such an integral. The Bell-Aspect upper bound of experimental expectations, sqrt2, thus corresponds to the sign (+ or -) observed in a bipartite entanglement that over statistically sufficient observations will produce a coin-toss probability of 0.5. This means that the sign is unpredictable in any single observation.
Joy Christian's upper bound, 2sqrt2, therefore predicts a null result (parity, i.e., (+,+) and (-,-) ) on two axes of a full time interval, rather than analyzing the statistical probability of a single measure on a single axis at an arbitrary time interval. Christian's framework is therefore not probabilistic, as has been repeatedly noted.
It is only at this point that the sophisticated mathematics requiring geometric algebra, and the role of topological orientability, enter the argument.
Charles Francis replied on Sep. 5, 2011 @ 10:42 GMT
Christian,
The question is not a stupid one. It clearly demonstrates to almost everyone that you are not even numerate. ( You needed to prove a result greater than 2 to achieve a contradiction, not a result less that 2*sqrt(2) )
No wonder you fill your papers with mathematical gibberish. You simply do not understand a word you write. Your errors have been pointed out by numerous posters, and all you can ever say is "you don't understand". Of course no one understands gibberish, but we do understand that it is gibberish.
I had thought even you might realise that a number can be less than 2 and less than 2*sqrt(2) at the same time, but I suppose that was overly optimistic. If you did understand it, you would probably have to die of shame.
Your write: "You needed to prove a result greater than 2 to achieve a contradiction, not a result less that 2*sqrt(2)."
This is nonsense. It shows that, let alone Bell's theorem, you do not even understand the meaning of the word "bound" in a statistical inequality. Instead of keep responding to your foolish questions, I will let the readers be the judge of who is right and who is wrong.
I almost wish Joy hadn't brought up Galton and Pearson.
Almost. :-)
What I mean is, that while I was earlier identifying statistical notions (equally likely hypothesis, axiom of choice) that support probability theory and cannot be applied to Joy's framework, I wondered about regression to the mean, the result for which Galton is well known.
I decided not to include regression to the mean, because "mean" in this context does not imply the calculus of real number averages; it refers to the geometric mean of the 2-dimension projection, which is - 1, because it resides in hyperbolic space. I attach the relevant portion of my draft paper I linked somewhere earlier.
This is just a sidebar to the main discussion, but I hope someone will find it useful.
Lawrence B. Crowell replied on Sep. 5, 2011 @ 16:50 GMT
T H Ray,
I will not say my assessment is a final judgment on JC’s theory. I found it funny on first reading, and figured that if there was something to this there would be a percolating series of reports running to a boil. So far I fail to see this has happened. There are people more intellectually marinated in these matters than I am. Florin is one of those people for example. I read these developments, for my work centers around how quantum physics and general relativity are aspects of a single system with a functor equivalency. If JC’s results were correct I do have to admit that my efforts will by corollary collapse. I think QM is correct “all the way down,” which is to say that I dislike adulterations such as quantum interpretations and ideas which try to impose “billiard ball logic” underneath it.
Just to clarify one point: I do not think (nor did Einstein, or EPR, or Bell, or Bohm) that quantum mechanics is incorrect in any way. All I am trying to do is to provide a less mysterious interpretation of it so that we may (or may not) have a better luck uniting it with gravity. Local and realistic logic is not necessarily "billiard ball logic", but a more palatable logic.
How does one go about computing scalars and vectors, as it seems that out here in the real/physical world, they necessarily interact, such as the space shuttle requiring a heat shield?
Perhaps the Octonion-like '7-sphere' disentegrates into an M2-brane and its dual NS5-brane. Anyons of phase exp(i*theta), where theta varies from 0 to pi, live on the M2-brane. Theta equals zero corresponds to bosons with statistical phase of positive 1 (symmetric). Theta equals pi corresponds to fermions with statistical phase of negative 1 (anti-symmetric), and all theta between 0 and pi represents these weird 'mixed' statistical phases that may only exist on a 2-brane. The dual NS5-brane is then reponsible for your 5-fold symmetries.
Steve Dufourny replied on Jul. 26, 2011 @ 20:33 GMT
Yes of course and harry potter transforms the boson in virtual particules becoming light and travelling in time of course. What are your symmetries in fact and domains??? What are your foundamentals after all. And Lubos also perhaps , no but we dream in live. Make sciences please AND BE RATIONAL thanks for your understanding. We aren 't on a pub for Ex or for me for example. We discuss about the universe, this universal sphere, ooops sorry ,it's just that a sharing of knowledges. Quantum spheres oops sorry. You see Ray, sciences are simple and complex, but are relativelly the same , it's that the secret.
Statistical phases you say and a time travel also due to imaginary numbers and the - inserted like a central symmetry, no but frankly. In fact you have monney from string universities or what?
DEAR ALL THIS IS THE END, BEAUTIFUL STRING THE END ,Sorry to all stringy fans but this is the end of strings.....
Ps the 0 the - and the infinities must be interpreted relativelly.
In fact you don't understand the work of joy ,it's simple the rationalism you know, the laws are the laws. And the finite groups are the finite groups!!!
Bell confounds the "imagination ,subjective" with the" pure deterministic rationalism" of "pure proportions".Of course people can play with maths with a kind of creativity. What I don't understand is why they insist to be in the international language of unities and equations or constants. Bell's theorem is a king anti axiom simply. It's not even necessary to disproof it even....some evidences, indeed, appear easily ....the axioms of the pure generality of our laws are so evident.
Jonathan J. Dickau wrote on Jul. 27, 2011 @ 14:57 GMT
Greetings all,
I wish to thank Joy for taking the time to further explicate and defend his ideas on this forum. I think the great utility of geometric algebra is overlooked in Physics far too often, and I wish Jaime Keller was still around to explain some of the fine points of Joy's approach to me - because I am sure he could make a wonderful and engaging story out of things I'm struggling to understand. As it is; I've had to put in a lot of research to make sense of this thread, but it is a fascinating topic of with strong links to subjects of my interest.
As octonions were mentioned, I want to strongly agree with and emphasize his point that the Octonion algebra is simply the most general case, with quaternions, complex numbers, and the reals being special cases where some terms are set to zero for convenience (g=0 in QM and h=0 in Relativity) and therefore drop out. But the purview of Bell's experiments requires that we retain constants pertaining to both Quantum and Classical variables, and that makes a strong case for using the most general numbering system and algebra.
Anyhow; I think it bears mentioning that this ties in with the interesting fact that the Ball of dimension 5 (corresponding to the 4-sphere) has maximal content (hypervolume), as defined on MathWorld. What this means is that additional dimensions (beyond 4) are compact, rather than extended, which contributes to the interesting and complex topology of the 7-sphere. The simple fact of maximal content would seem to demand that 3 of its dimensions are rolled up or compact. Is this correct?
If so; it makes your result easy to explain as a confusion about the concept of interiority and exteriority which makes events appear to exhibit non-locality and in some sense still be local to each particle or photon's local reference frame. Very interesting thread. Thanks again.
Jonathan
this post has been edited by the author since its original submission
Steve Dufourny replied on Jul. 27, 2011 @ 17:59 GMT
yes E8 now Jonathan the packager you have a surfite(small disease about surf, me I smoke joint , I AM COOL ALSO you know ahahah) or what?
7 AND 8 NOW AND AFTER WHAT A CONNECTION WITH STRINGS ALSO AND THE BIG UNIFICATION AHAHAHA
QUANTUM SPHERES ...COSOMOLOGICAL SPHERES....UNIQUE UNIVERSAL SPHERE....mvv'V AND E=(c²o²s²)m there you have the maximum entropy it lacked something.And of course the number is the same for the quant number and the cosmological number, then the uniqueness appears , a little help of van nieuman and IBM,dear Jonathan or a courses about fourier series and the harmonical and spherical oscillations. 3D against what eight it's that ....let me laugh.
Steve Dufourny replied on Aug. 9, 2011 @ 16:48 GMT
I forget of course Jonathan the corrzlator of 7 to 8 dimensions with smolin.And after what Jonathan?, a beer in 8 dimensions also no? It is too late even with your biggest strategy.And after you ask why your country is in this state like our global economy.Well the loobyings are a pure joke. The China arrives my friend with India , Africa and Europa ................and of course the capitals are the capitals, yes of course and also we are going to pay soon the air .Smolin it is that .well Let's continue.
Jonathan J. Dickau wrote on Jul. 27, 2011 @ 15:32 GMT
One more thing...
Regarding your paper on Restoring Local Causality.." Joy. I think the idea of adopting Grassman's notion that point, lines, planes, and volumes be placed on an equal footing is particularly apt in questions like Bell's experiments. It is easy to take our privileged everyday view of 3-d plus 1 as fundamental, but perhaps this is a mistake. We must leave open the question of whether a particle or photon 'sees' the same dimensionality we do, and Grassman's prescription accomplishes this aim.
People forget that these issues are not only about the microworld, as they arise for all massive objects, according to Relativity. What dimensionality of space is 'seen' by a particle inside the Earth's gravitational radius? It appears that an octonionic framework (simply assuming that their generality or universality indicates they are fundamental) makes some of this confusion go away, by incorporating both the inward facing and the outward facing aspects equally in a unified geometric description.
To restate again; the failure to understand Joy's work is because there is confusion about concepts like proximal and distal space or interior and exterior of objects and spaces. Up to a point; adding more dimensions makes things more spacious, but past that point additional dimensions become increasingly compact - apparently topping out at 24-d in the Leech lattice, as the most compact regular arrangement. But the 7-sphere is both extended and compact, so it represents both local and non-local aspects simultaneously.
Jonathan J. Dickau wrote on Jul. 27, 2011 @ 15:46 GMT
A side comment to Steve Dufourny;
I think that Joy Christian has brought life and meaning to some of the concepts you have nurtured over the years. Yes too; I agree that they were and are your ideas, and that you deserve some credit for putting them out there. But I would not go so far as to say that Joy C. or Ray M. has stolen your ideas as you have chosen to remain vague and they are trying to create something more mathematically precise.
It takes more courage, or perhaps a willingness to look foolish on occasion, to put concrete ideas forward that are precise enough to be falsified. This requires some diligence. I think perhaps you have needed to write a paper or two showing exactly how your spheres within spheres are nested. In the meanwhile, the rest of us must make do with examining those ideas that have had their share of due diligence - in order to create a more precise description which can be tested or compared with other theories.
And for now; Joy has done us a great service by spelling things out about the geometry of spheres.
Steve Dufourny replied on Jul. 27, 2011 @ 17:44 GMT
a packaging of a part of the sceinces community. I am happy for them It's well , very good. In fact you have the answer in live why the world doesn't turn correctly Jonathan, It's that New York and The america, It's that Jonathan, Lisi, Ray, Joy..... I am simply sad and not angry after all, I understand your frustration and the fact that you have seen the potential of my theory. It's easy to steal...
a packaging of a part of the sceinces community. I am happy for them It's well , very good. In fact you have the answer in live why the world doesn't turn correctly Jonathan, It's that New York and The america, It's that Jonathan, Lisi, Ray, Joy..... I am simply sad and not angry after all, I understand your frustration and the fact that you have seen the potential of my theory. It's easy to steal a young belgium without monney and team. It's easy no Jonathan, I have understood you you know 2 or 3 years ago, with your "I"have understood Steve", it's that your real personality in fact, a kind of nice vanity and vengence. Just for vanity, power and this monney Jonathan. It's well , I congratulate you and your friends,or perhaps it's a strategy for some teamss to imply some confusions also. What a world Jonathan, I have said to Ray my opinion also by mails, I KNOW THE POTENTIAL OF MY THEORY AT SHORT MIDDLE AND LONG TERM? THEN OF COURSE THE PACKAGINGS I KNOW ....sad reality of our sphere. You seem loving the packagings dear Jonathan it's that in fact .Ok nobel prize to Joy Florin Ray and You and Lawrence because it's your axiom of choice, but perhaps you want discuss in live and transparence about the operators unbounded of wightman and the bounded of H.Kast. ...or perhaps van nieuman and the uniqueness ,there is no problem for me, we can discuss about all. The business sciences and its strategies are a simple under sciences for me. Perhaps for several people it's an axiom, but they exist the rationalists.
And you say what Jonathan, that Joy what? You are all angry and have hate ,it's that, a real band of frustrated and jealous and business strategists, that's all.
Jonathan, you can travel in plane, you can make conferences, but never, be sure, never don't forget my name,
Write pappers dear all, write about my thruth like a band of obliged frustrated. You can have my prizes after all, make what you want. A real band of business man, that's all. Congratulations Jonathan the packager, and of course the hater against steve just because you and your friends, you aren't able in fact to ponder this theory. A papper he says, write pappers dear Joy and Jonathan and companies, write pappers, it's not my problem, all rational scientist knows it's my theory. But we understand you, you have seen the potential of my discovery.
PACKAGINGS JUST PACKAGERS OF PACKAGINGS .....
To you Jonathan, here and in live now with joy and florin and Ray and Lawrence if you want dear Packagers....we can discuss with politeness, and I HAVE ALREADY EXPLAINED WHY I DONT PUBLISH i HAVE LOST ALL HERE IN BELGIUM DUE TO BAD PEOPLE? EVEN AN ENTERPRISE I CAN4T RECREATE IT.and like you see dear Jonathan the traveller and conferencer,that continues in the world now. Me I want well a paper but frankly it's a long work and that needs a resume, correct and well made. I can't resume , if i had a team I will make well the things. A good resume of my works and equations. I have nothing me and it's my theory, I find all that so incredible. I congratulate you dear all for the packagings. You know I speak about my theory since several years on the net. And now I must accept the packagings and that the others are recognized, let's me laugh dear Jonathan and kill me , really, or find a strategy to kill me as i have epileptic problems, i don't know but be sure, that never I will stop my works ABOUT SPHERIZATION .AND MY SPHERES. THEY ROTATE AND YOU HAVE SEEN THE PROPORTIONALITIES OF THESE ROTATIONS THEN THE MASS IT4S THAT MY DISCOVERY JONATHAN mvv'V=constant and E=(c²o²s²)m and also the universe is a sphere in optimization ......eureka no but I dream or what. Thanks steve.
Jonathan J. Dickau replied on Jul. 27, 2011 @ 18:09 GMT
Well said Steve.
I had thought that perhaps issuing a challenge would get you to take the plunge and write all the important details down. I apologize if I offended, as there is no hatred, but perhaps a bit of conceit. For many years, I let the barriers to publication be more real than the possibility of actually doing Science.
However now there are editors who will be glad to publish my next paper, once it is finished, but that is still a lot of work - unfunded by any institution. Likewise with the conferences. I have a chance to give two 15 minute talks at FFP12 - and to show a poster.
However, even neglecting budget and logistical issues which might prevent my attendance; the amount of effort required to prepare for my presentations is considerable. On the other hand, if I can do the work needed; one of the talks I'll be giving is on a topic I've been nurturing for 25 years - connections between the Mandelbrot Set and cosmology.
So; you might say I'm being rewarded for my patience, but I might say "consider yourself lucky, Steve, if it doesn't take 25 years to have the chance to present your ideas to a roomful of professional scientists." Otherwise; you should consider yourself lucky you don't have to do that yet.
Steve Dufourny replied on Jul. 27, 2011 @ 18:28 GMT
It's the reason why you are frustrated , just because you aren't recognized seriously, it's not my fault if you and yoyur friends you haven(t found an interesting thing. My works humbly are different and I understand that people are jealous.You know when a wotrk is rational and when the transparence is respected, it's not necessary to publish a papper. For what, for a pseudo recognizing and for the system Jonathan let me laugh. If you want really evolve , I suggest that you study my equations with a deeper analyze, more foundamental respecting a pure 3D and a time constant like duration in its pure proportionalities. But I doubt, when a person has no innovantions in sciences, why they insist then? you know if you and your freinds aren't simply generalists or if you aren't global in theory.Why you need to be like the real innovators, it's just that it's not your road simply. Then we return about the frustration. It's just frank, for example, I play piano and guitar, but I don't say I can play saxo for example. It's just that only a minority in the scientists see really the whole and the genrality. And of course we see a kind of false road simply chosen. There are persons who are skillings for theoretical physics and others no simply. I am not better than you Jonathan. I just say that some people see the globality , others no simply.
I am frank, you make a pub for e8 just because you are frustrated lisi, jonathan Ray....then you try in a kind of business pseudo sciences strategies. Some people , and i say that humbly, have the capacity to ponder an equation or a theory, and others utilise these equations. It's not a superior comportment, it's a simple reality. I think that the secret is that a real searcher, never stop, he searches in all centers of interests, and after a kind of globality or generality appears. I am obliged to speak like that Jonathan. Lisi, Ray and You are good scientists , even skillings, but you aren't generalists in theoretical physics and maths which are the most complicated matters.
Steve Dufourny replied on Jul. 27, 2011 @ 23:49 GMT
Theoretical physics is a difficult matter, where the universal laws are in a dance. A song of harmonious evolution. All is composed by the same essence you know dear Jonathan, the universe is complicated in its whole due to its immensity but so simple in its pure harmony, the sphere. It was only simple as that Jonathan....."one day we shall see all the truth and .......you know these words I suppose as many scientists. It was only simple as that, You know me since several years now, I just continue my works about this theory of Spherization. My equations are corrects dear Jonathan, you can verify if you want, and also you can calculate this number of uniqueness(quat and cosm) it's a finite system, and relativelly the same...The rotating spinning spheres quantics and cosmologics answer to all inside a closed evolutive sphere and a center ,...all turns around! It's a constant but what is this constant mvv'V ,mass vel of rot spinal, vel of rot orbital,volume of the spheres....more the number it's revolutionary. I just continue the road of foundamentals, i just found an interesting thing. The Universe is indeed a sphere, and our particules also, they have volumes and a number for uniqueness which is finite.And the rotations are proportionals with mass, the gravity is explained with a simple different sense of rotation for th spheres sorted or synchronized, you shall understand better the eletromagnetirm and the evolution where mass polarises laight. THE CODES ARE INTRINSIC IN GRAVITATIONAL STABILITIES.
Steve Dufourny replied on Aug. 9, 2011 @ 23:48 GMT
These equations are revolutionary, E=(c²o²s²)m and mcosV=constant...if the volumes are inserted and the finite number of uniqueness, you have the real unification. More the universal link, the universal sphere and its central sphere, the biggest volume......you shall understand that in fact our quantum world is just the smae relativistically speaking than our universal sphere and its cosmological spheres. The velocities of rotations are correlated of course.
SPACE MASS AND LIGHT ARE THE SAME IN FACT IN A PURE BEC ....they turn then they are....now insert the pure thermo.the universe is bounded and in evolution, the density increases......the universe is in spherization , it was evident.
Mass,Linear velocity, orbital velocity, spinal velocity, volume...of the sphere is a pure constant for all physical spheres, quantic and cosmological.
It was evident and so simple.The rotations and the spheres explain all in a pure constant of time and 3D.
And of course Joy possesses the diamond number 7, lisi the 8 and me the 3 for a rational logic in 3 dimensions, but of course the next world and universal festival won't speak about the diamond 3.and of course there is 878 miles between perimeter and new york and of course mickey mouse will be president after obama.
Jonathan J. Dickau wrote on Jul. 28, 2011 @ 15:23 GMT
I wanted to ask, does this construction explain varying decay rates, cyclical with variations in Earth-Sun distance and the Sun's rotation. Originally; I saw this written up for yearly variations by Jenkins and Fischbach, and I saw a similar result from a Russian scientist using other data, but now I read they have observed a 33 day cycle - which corresponds with the Sun's rotation.
Jenkins' team have asserted it could be neutrinos, but this appears to be ruled out now, and they are looking for a missing particle. Could it be geometry instead? Alex Mayer thinks it plays an important role. And Joy's description of the 7-sphere's properties, and the part played by geometric algebra, appear to highlight a similar connection between microscale and macroscale observables.
One could describe the Earth and Sun as a massively entangled system. It is certain that the two objects each possess a significant amount of matter content which once resided, or will reside, with the other. However; one could explain this more simply as a case where geometric relations are felt both locally and at a distance.
In "Chromodynamics War" on pages 415-416 I address the varying decay rates, cyclical with variation in Earth-Sun distance. At the time that I requested permission to use their data, they had no explanation. My model suggested the neutrino explanation. I would be curious to know how neutrinos have been ruled out.
Edwin Eugene Klingman replied on Aug. 2, 2011 @ 17:31 GMT
Jonathan,
Thank you very much for these links. I haven't yet studied the last paper, but the slashdot entry did answer the key question I had.
I think I agree with one of the commenters who said:
"This experiment covered only the decay of Gold-198; The ones that were found to be changing were exhibiting electron capture decays, a completely different mechanism. ... Neutrinos also oscillate forms; perhaps the emitted form doesn't interact the same way."
The other comments are also interesting. The result seems not fully established.
I made some comments earlier with minor errors and never received a proper response, so I am correcting those errors and reposting those ideas. Joy said that the devil is in the details, and yet some of those details bother me.
Joy is working with a parallelizable and potentially-stable 7-sphere, but he also has these weird statistics that continuously range from negative one (an anti-symmetric fermion wave-function) to positive one (a symmetric boson wave-function). This looks like the real projection of Anyonic statistics with phases of exp(i*theta), where theta ranges from zero to 2*pi. Anyons are quantum particles on 2-dimensional surfaces that don’t behave exactly like fermions or bosons (and may thus be a good place to start in an effort to unify quantum statistics into a TOE). Some examples of possibly important 2-D surfaces are the M2 Blackbrane and the effectively 2-D Graphene lattice of Holographic Theory.
Now suppose that the potentially-stable 7-sphere were to spontaneously decay into an M2 Blackbrane, its dual NS5-brane, and an eighth dimension of time. The M2-brane could explain the occurrence of Anyonic statistics, while the NS5-brane explains why the five-fold Pentagon color graph (see Florin’s Color Me Surprised post with the Kochen-Specker Theorem) is a minimal model for quantum behavior.
The devil may be in the details, but these details seem consistent with M-Theory…
Steve Dufourny replied on Jul. 30, 2011 @ 18:07 GMT
M theory now, Mr Baez is in you or what, or is it still a patriotic american pub.....strings are just a pure joke where only perhaps 1 per cent, and i am nice, is interesting(oscillations, spherical and still the convergences must be deterministic) the rest is sciences fiction like time travel or exotic particles, bizare or decoherences.....
the rotations of entangled spheres are proportional with mass....the physicality possesses its laws, intrinsic.
No but you dream in fact , you are comics in fact, with your extradimensions,
Steve Dufourny replied on Jul. 31, 2011 @ 13:49 GMT
the truth is the thruth, the business decreases the velocity of evolution.You can be a kind of team, that won't change. If your country is in this state and if the hour is serious, it's just due to that. The republican must understand that the world is not to them.The monney , the power and the vanity aklways like main parameters of this chaos. And they insist furthermore, just because they fear to loose their investments. It's not important, they are humans like all.Equals then of course the evidence appears easily. With or without their approvements, the world will change. Obama I am with you, yes all is possible with a simple evidence, the united of good people.....If it exists problems, these problems must disappear. Mr The president , you musty stabilize all that for a correct evolutive and harmonious future of this earth.If those persons continue to imply these chaotics series, never the world will be on the good and quiet road. GOOD OR BAD GOVERNANCES all is there......with UNIVERSALITY OF COURSE.
Edwin Eugene Klingman wrote on Jul. 31, 2011 @ 03:08 GMT
Joy,
It's great to see your new work. You say, "I feel that it is not appropriate to try to fit my framework in any pre-existing conceptual box, not the least because it uses the unusual tools of Geometric Algebra."
I think this is an extremely important point. Let us consider two incompatible theories A and B, both of which are reasonably effective in their respective realms of application (say A=QM, B=GR). We desire a new theory, C. We may reasonably require that both A and B "fit" into C's conceptual box. We should *not* require that C fit into A or B's box(es).
Joy Christian replied on Jul. 31, 2011 @ 15:55 GMT
Hi Edwin Eugene,
Thank you for your comments. Needless to say, I fully agree with your point about the incompatible theories. My main concern about Florin’s attempt to reinterpret my work is very similar.
Steve Dufourny replied on Aug. 1, 2011 @ 20:15 GMT
EPR VS COPENAGHEN now , well without me ,oh my god, sciences are lost in an ocean of ironical things. and for what always the same parameters(monney,vanity,power, differences, borders and frontiers....)what a bizare and stupid world. A scientist must act , the rest is vain...
SPHERICALLY YOURS
:)
A little experiment, calculate the number of x where the word sphere is utilized on this platform and all correlations.You shall see the date of my inscription, you shall see the exponential since this date ahahah and now they use all the word sphere.No but we dream, I dream , a sphere here , a ball there, and a theory here, and what after the spherical toe also and the spherical nobel prize, no but I dream. I want continue to beleive in human nature, but frankly sometimes i am so disgusted, trickled. It's sad simply.It's not a bohrian complementarity or a reinterpretation that, but just a kind of packaging.
I find your paper Disproof of Bell's Theorem by Clifford Algebra Valued Local Variables technically correct, but I have a different view of the interpretation you gave to the result. More precisely, I think that equation (19) is in fact a restatement of equation (4). Apparently, equation (4) involves a finite sum, and (19) an integral, but if we recall that the singlet state (1) is spherically symmetric, we realize that we can change the direction n in (1) as we wish and obtain the same singlet state. So, we can average over all possible directions n, and put (4) in an integral form too. The prediction of quantum mechanics, encoded in (4), follows from the non-commutativity of the spin observables (Pauli's Clifford algebra), in the same way as (19) does.
In my opinion, it is an illusion that (19) is obtained so that the local variable corresponding to a ignores the state of b and conversely. The correlations are in fact implicit in using the Clifford product, which is non-commutative. Therefore, for each pair a and b in the integral (19), the correlation between them is included.
So, I would not count this as a disproof of Bell's theorem. But I think your paper introduces something very interesting: the expectation values (4) can be obtained by a straight generalization of classical correlations (equations 7,9) to Pauli's algebra, via (19). I like this feature, because it suggests that quantum mechanics is connected to classical mechanics in a deeper way than the canonical quantization allows us to see (at least for the particular case of two 1/2 spin particles). I would speculate that it worth investigating whether (19) can be a gateway to a theory of non-commutative probabilities which reveals better the connection between classical and quantum, eventually enriching our understanding of quantum mechanics.
Joy Christian replied on Jul. 31, 2011 @ 15:10 GMT
Hi Cristi,
Eqs. (4) and (19) of the paper you cite are two ontologically different representations of one and the same correlation observed in nature. As is well known, the correlation described by Eq.(4) cannot be interpreted locally, whereas that described by Eq.(19) result from an integral over two manifestly local and realistic variables. Bell claimed that such a thing was impossible. In any case, the paper I much prefer is this one. It makes the same basic ontological point much more succinctly---namely that entanglement and non-locality are illusions.
Cristi Stoica replied on Jul. 31, 2011 @ 18:26 GMT
Hi Joy,
Thank you for your answer. You say that there is a difference between the ontologies. My current understanding is that the two ontologies are the same, and equations (4) and (19) are equivalent, being different only formally. If I am wrong, I'd like to go beyond this. Could you please explain the ontology you proposed? More precisely, how does your hidden variable predict the outcome of a measurement?
For example, could you provide a description of the EPR-Bohm experiment, from the viewpoint of the ontology you proposed? Say that a spin-0 particle decayed into two spin-1/2 particles. Say that Alice measures the spin of one of them, and Bob of the other, at a time t. What would be an example of the values of the hidden variables just prior to the time t, and how would they determine the outcome?
Joy Christian replied on Jul. 31, 2011 @ 19:08 GMT
Hi Cristi,
I have described my approach to the EPR experiments in great detail in these two preprints: this one and this one. I hope you find the answers to your questions in them. If not, then the full list of my papers on the subject can be found here.
Thank you for pointing me to the references. About the article arXiv:1106.0748. May I ask you about the local variables / bivectors A and B defined in equations (27) and (28), page 6. I understand that they are the elements of reality. Are they contextual? (it seems to me that they are, because they depend on the orientation of the measurement devices.)
No, the variables A and B are not contextual. They do refer to the orientations of the measurement devices (as they must), but the measurement results themselves (+1 or -1) are determined entirely by the orientation (i.e., handedness) of the 3-sphere (i.e., by the hidden variable “mu”).
Thank you for the quick answer. If I understand well, the bivectors A and B represent the states obtained by the measurements, while the correlation is encoded in the choice of the orientation mu.
What if we take A and B as representing independent particles, which don't form a singlet state, it seems to me that from equations (32) and (33) from arXiv:1106.0748 we obtain the same correlation -cos 2(alpha - beta) (even though they may have different orientations mu). Probably I am missing something, because otherwise it seems that any two particles are correlated like this.
Thank you for the patience, it seems that I have many questions.
For two independent particles not forming a singlet state the random variables A and B would represent two independent events. Therefore the product (32) would no longer be meaningful. This is because A and B, as bivectors, would then belong to two entirely different spaces. Moreover, the joint expectation value of A and B would then be, not equal to E(AB), but equal to E(A)E(B). As a result the correlation between A and B would be much weaker than –cos 2(alpha – beta).
You were too kind and answered me with patience, but I still have many questions. I will try not to monopolize you for a while, while I will digest the information. Here are some of the questions that I am trying to make sense:
Why it is important whether the pair of particles is singlet or not, given that in your theory entanglement is an illusion? I understand that before the measurement, the two particles are in the same space, being a singlet. If the devices of Alice and Bob are not parallel, then after the measurement the two particles become independent, so they are no longer in the singlet state, or in the same space. It is like the measurement destroys something that looks very much like the entanglement.
If one of the particles from the singlet changes the orientation of its spin with a value which can be made no matter how small, does the space S3 split into S2xS2? Is this change continuous?
How can the bivector formula for correlation be extended to more general states, containing any case between singlet and totally independent particles?
Edwin Eugene Klingman wrote on Aug. 1, 2011 @ 19:35 GMT
Cristi,
You ask above, "How does your hidden variable predict the outcome of a measurement?"
I do not pretend to speak for Joy, but John Bell made a few remarks worth noting. In his discussion of EPR (on p.143 in 'Speakable...') Bell says, -- [I use asterisks for italics]:
"It is important to note that, to the limited degree to which *determinism* plays a role in the EPR argument, it is not assumed but *inferred*. What is held sacred is the principle of 'local causality' - or 'no action at a distance'. ...mere *correlation* between distant events does not by itself imply action at a distance..."
Further, he states:
"It is remarkably difficult to get this point across, that determinism is not a presupposition of the analysis. There is a widespread and erroneous conviction that for Einstein determinism was always *the* sacred principle."
Later Bell points out that
"It was only in the context of perfect correlation...that *determinism* could be inferred for the relation of observation results to pre-existing particle properties... [and] it is a preoccupation with determinism that creates the problem."
He then proceeds to argue while pointedly making no mention of determinism.
Cristi, I believe that focus on local realism leaves the door open for conscious (willed) behavior or chaotic (random) behavior, neither of which is incompatible with local realism, but both of which are problematical with strict determinism.
Indeed, as far as I know, not only Bell, but also Bohm clarified that he was interested in causal interpretations of QM, and not necessarily in determinism. And indeed, the attacks against the EPR argument on the basis that Einstein believed in determinism, IMO, came from the belief that quantum mechanics introduced for the first time genuine randomness in physics, and by this, allowed the free-will. It is still generally believed that a necessary condition for free-will is the indeterminism of physical law. My own view on quantum mechanics happens to be deterministic (but not a la Bohm), and yet compatible with randomness and free-will, as I tried to explain here.
I reviewed your question and I think that maybe the first time I missed the point. When I asked "How does your hidden variable predict the outcome of a measurement?", the reason was to understand the ontology, and not to ask for determinism. If the purpose of a hidden variable theory is to complete quantum mechanics, I understand that it has to give a better prediction of the results than the Born rule, and by this, to explain the correlations.
Steve Dufourny replied on Aug. 2, 2011 @ 15:16 GMT
A hidden variable if it exists, is and will rest proprotional and deterministic in 3D and a pure constant duration implied by rotations.
In fact people confounds all , it is not posssible.You confound the limits due to our young age at the universal scale and the research of some hidden things bizares or irrationals defianting our laws. That has no sense for things which are axiomatics,universally speaking.
We complete QM by rational equations, not pseudos irrationalities. The rest is vain, it's that a deterministic axiom, we see the universal laws in all with a pure complexity and simplicity. So many time lost for nothing.....for some people who doesn't see the whole.
Edwin Eugene Klingman replied on Aug. 2, 2011 @ 16:06 GMT
Cristi,
My comment above, in response to your question, was based upon my own model of quantum mechanics. I do not understand enough about Joy's model to remark upon it.
My model, based on 'particle PLUS wave' is local realistic but indeterminate. Behavior is not strictly determined because we do not, and, I suspect, cannot know the relevant phase angle of the wave function.
For this reason I wanted to draw attention to the fact that the issue of local realism is not joined-at-the-hip with the issue of determinism.
I have just read your "Flowing with a Frozen River" in which you state "the probabilistic character appears from the undetermined initial condition, but the evolution is deterministic." Our models seem similar in that fashion. I will need to read your "Smooth Quantum Mechanics" before I say more.
There are other issues in 'Frozen River' that I find interesting, but this is probably not the place to explore these.
I agree with Cristi. The issue is not philosophical (free will vs. determinism). The physical issue is whether nonlocal effects determine local outcomes.
Going back to Einstein's definition of "physically real" " ... independent in its physical properties, having a physical effect but not itself influenced by physical conditions ..." classical physics is all local. Communication among...
I agree with Cristi. The issue is not philosophical (free will vs. determinism). The physical issue is whether nonlocal effects determine local outcomes.
Going back to Einstein's definition of "physically real" " ... independent in its physical properties, having a physical effect but not itself influenced by physical conditions ..." classical physics is all local. Communication among bodies is restricted by relativistic limits. "Local realism," then, applies to isolated systems -- and because Einstein knew (from Mach's principle) that there are no such isolated systems in the universe as a whole, general relativity describes a universe that is finite in time and unbounded in space.
As I understand it, the Joy Christian model is entirely consistent with GR's "finite but unbounded" result; i.e., the division algebras in 2, 4, 8 dimensions incorporating, respectively, the closed algebra of R, quaternion algebra (noncommutative) and octonion algebra (noncommutative and nonassociative), allow recurrence (i.e., finite, or bounded, time) by confining measured events to manifolds of parallelizable spheres S^7, S^3, S^1 (where "parallelizable" is a topological term describing spheres S^1 of 2 dimensions, S^3 of 4 dimensions and S^7 of 8 dimensions -- all smooth manifolds incorporating vector fields). So Christian foresees local field correlation of tangent vector properties in the same general way that Einstein did; i.e., finite in time and unbounded in space. He has exchanged the relativistic limit in the mathematical language of PDEs for a topological limit in the language of geometric algebra.
Joy's result may indeed subsume Bell's theorem (not "disprove" it); I reserve my opinion. Even on this basis, it is a truly great achievement.
However, I differ -- ironically, by using many of the same principles as Joy -- in the conclusion that local realism can be successfully described as finite in time and unbounded in space. I find the converse -- local realism is finite in space and unbounded in time.
Joy's among others' results aim to obviate quantum theory, and I don't see how that can work. After all, if Planck's constant were zero, we would have an ontologically classical world. As it is, we live with "fuzzy" measurement and nonlocal influence insofar as t = T = 1 (normalization). What must be established as "physically real" in a quantum mechanical model that is finite in space and unbounded in time, is information loss. We can then maintain "finite but unbounded" classical parameters, without losing any of the measurement characteristics of either classical or quantum mechanics. Such quantum-classical deterministic models are already reflected in the work of Gerard 't Hooft, Ted Jacobson and Erik Verlinde. Information loss, however slight, IS a nonlocal effect and "physically real."
In the next few days, I plan to post my own results, extended from my ICCS 2006 paper and "On breaking the time barrier" preprint.
Edwin Eugene Klingman replied on Aug. 2, 2011 @ 16:44 GMT
Tom,
Instead of "the issue is not", it might be more appropriate to say "my issue is not"...
Just because you are not interested does not make it not an issue.
But, as I've remarked to Cristi above, the issue I was trying to highlight was not 'free will', but the separability of the issues of local realism from the issue of determinism. You've many times stated that quantum mechanics is "incoherent without nonlocality". I don't believe that to be true, but we've failed to communicate on this issue often enough that it makes no sense to argue it.
You say that "Joy's among others' results aim to obviate quantum theory". It is not clear to me that that is his aim. He appears rather to confirm the quantum mechanical results, while claiming that Bell's calculation is incorrect. I too feel that Bell's calculation is incorrect but for different reasons than Joy.
Of course "if Planck's constant were zero, we would have an ontologically classical world."
But you claim that "What must be established as "physically real" in a quantum mechanical model that is finite in space and unbounded in time, is information loss" and "Information loss, however slight, IS a nonlocal effect and "physically real."
This appears to assume that one accepts information as ontologically real, which I do not. Nevertheless, I look forward to your posting your ideas in the next few days. I would like to understand you.
Finally, I have asked Florin several times, but he may have missed my question. My question is this:
Is it correct to say that "violation of Bell's inequality is *the* basis for the rejection of local realism in physics"?
It's not my personal issue. It's a question of objectivity -- one cannot impose philosophical/religious ideals on a scientific theory without sacrificing factual clarity and often, facts themselves.
Nevertheless, thanks for clarifying your perceived separation of local realism from determinism. I don't see how one can do that, and preserve either concept. "Locally real" classical theories obviate hidden variables, so that all dependent results are causally determined by independent variables. I agree with Florin that Joy stretches the meaning of "locality" in that he actually constructs a hidden variables theory, although he does a capital job of correlating his variables to the orientation-dependent results. I do think his method is mathematically superior, and have said that I can be convinced that it subsumes Bell's result(though not yet).
You misunderstand Joy vis a vis Bell's Inequality. He does not say Bell's mathematical result is incorrect ("disproof" is a truly unfortunate choice of words)-- he says that Bell's starting assumptions are inferior to his (Joy's) own, and he may be right. Look at it this way: say something in English is untranslatable to Urdu; then English would be the superior language to explain the point, though it is still possible to insert the English phrase into the Urdu translation.
You are correct that I assume in my (own) mathematical theory, that the world is made of information alone. Of course, I am not the only one who holds with this assumption, nor even the only one who identifies information with time. Having seen the criticism that Joy is encountering, I decided to delete every bit of reference to physics from the paper I am working on and present the mathematical theory alone -- this has precedence; e.g., Claude Shannon's classic paper that became "information entropy" and quickly found physical applications. He didn't try to beg the quesiton, and neither will I. The working title is: "Applications of number theory to information, time and geometry."
You ask, "Is it correct to say that 'violation of Bell's inequality is *the* basis for the rejection of local realism in physics'?"
I wouldn't put it that way. I would say that Bell's result is a sufficient but not necessary condition to reject local realism (there are many more ways in which quantum mechanics is incoherent without nonlocality). By the same logic I would say that Joy's result is a necessary but not sufficient reason to _accept_ local realism -- as Florin makes a point of asking, what does "local" really mean in Joy Christian's theory? Not, to be sure, what we accept as classical physics.
Edwin Eugene Klingman replied on Aug. 2, 2011 @ 20:18 GMT
Tom,
Whether "free will" versus "determinism" is an objective issue or not is debatable. As I understand it, the current view of consciousness is that it is an artifact that can (presumably) be explained as emerging from the structure of Lego blocks or conceptual equivalents. In my mind a fully deterministic physics precludes free will of any meaningful kind. Nevertheless, I have no...
Whether "free will" versus "determinism" is an objective issue or not is debatable. As I understand it, the current view of consciousness is that it is an artifact that can (presumably) be explained as emerging from the structure of Lego blocks or conceptual equivalents. In my mind a fully deterministic physics precludes free will of any meaningful kind. Nevertheless, I have no interest in pursuing these issues here. I repeat that I was focusing on the separability of local realism and determinism.
I know that you don't understand this separation, but your opposition in the past has helped me to understand it better. In fact I am currently in process of organizing the quantum mechanical aspects and implications of the C-field theory. Many of the comments and conversations of the last essay contest stimulated me to both ask and answer issues that I had not previously gotten around to. My earlier work was on the cosmological implications of the C-field and on the generation of all of the KNOWN particles of physics. I had not looked deeply into the question of how the C-field ties into quantum mechanics. I have now done so, and believe my results are important.
You say "You misunderstand Joy vis a vis Bell's Inequality. He does not say Bell's mathematical result is incorrect ("disproof" is a truly unfortunate choice of words)-- he says Bell's starting assumptions are inferior to his (Joy's) own, and he may be right."
I agree with you that "disproof" is a truly unfortunate choice of words. But I do not misunderstand Joy. I did not mean (or mean to imply by the word 'calculation') that Bell's mathematics were wrong, although this does seem to confuse some on these threads. Bell's physics is wrong, not his math. It has nothing to do with Urdu vs English.
I can see why you would delete all references to physics from a "mathematical theory", based on your belief "that the world is made of information alone." I have no objection to such mathematical theories of multiverses, strings, extra dimensions, etc., and I will be very interested in your work. But physical theories are different. They cannot fore-go connection to the 'real' world. [Yes, I recall your views about 'reality'.]
Your analogy with Shannon is good, and I do not argue that you may find very useful applications for your theory, despite the fact that I do not think 'information' has any ontological reality. Shannon could have just as easily called his work "A theory on the transmission and reception of coding formats" and it would have been just as useful, while more explicitly acknowledging the fact that his 'information' in every case depends upon the arrangement of some 'pattern' applied to some 'carrier' (i.e., physical medium). The pattern itself is not a physical entity.
Thank you for answering my question about "the basis for the rejection of local realism in physics". You see it as sufficient but not necessary, because you believe that "there are many more ways in which quantum mechanics is incoherent without nonlocality." I may in the future ask you to spell some of these out for me, because I believe it to be the sole physical basis for the rejection of local realism. The fact that you find QM incoherent without nonlocality I consider to be your shortcoming, not a physics reason. But, as I say, I may ask for clarification at some later time. This is a very important question, since I believe that, if Bell is wrong, then all such rejection is false.
There have been a number of very interesting statements made, by Joy, by Florin, by you, and others. I hope to doggedly try to consider these statements, one by one, and see what agreement we can all find.
I don't know whose "current view of consciousness" you take as your standard, but my own is akin to that described by Kafatos and Nadeau in _The Conscious Universe_. It isn't made of Lego blocks.
Regarding free will, I am satisfied to leave that question to theologians and philosophers.
If Bell's physics is wrong, so is his math. A physical model that doesn't describe a 1 - 1 correspondence of theory to result is invalid.
You wrote, " ... the fact that his (Shannon's) 'information' in every case depends upon the arrangement of some 'pattern' applied to some 'carrier' (i.e., physical medium). The pattern itself is not a physical entity."
D-O-G isn't a four legged creature that chases cats, either, but one wouldn't communicate that physical entity as a pattern of bones and flesh. The morphing of one such creature into a separate species is demarcated by information contained in the one that does not smoothly map to the other. That bit of information is sufficient, to communicate species changing in time on a continuum of common ancestry. The naive "warm little pond" narrative of evolution, however, has long been found lacking, supplemented by more progressive and sophisticated theories such as punctuated equilibria (Gould/Eldrege) to restore connectedness while acknowledging and explaining gaps of information.
Shannon's theory is related to physics only by using the mathematical model of physical entropy. It is applied to communication, not to a physical medium. So it useful to explain the evolution of matter, without assuming matter -- only, like biological evolution -- a common ancestry.
Edwin Eugene Klingman replied on Aug. 3, 2011 @ 23:58 GMT
Tom,
I take the consensus as the current view of consciousness, which I interpret to be that consciousness is emergent, hence an artifact. 'Lego blocks' is my shorthand intended to illustrate the ludicrousness of this perspective, in my opinion. Does your 'conscious universe' pre-exist the physical universe, co-exist with the universe, or emerge from the universe?
I'm happy you're satisfied to leave free will to others. That you have certain beliefs about consciousness and information, but not about free will is of no concern to me. It does generally relate to the fact that our discussions tend to end in "you believe vs. I believe" dead ends. We simply see things differently.
What seems ever more evident to me is that some think inside the box, and some out. This doesn't imply that either is correct, but it does affect communication. As I remarked above, if C (a new theory) is a super-set of A and B (old, failed theories) then it is not necessary that C fit into A or B. Yet believers in A and B seem to demand this. This is not necessarily unreasonable of them, yet neither is it very productive.
You wrote, "Does your 'conscious universe' pre-exist the physical universe, co-exist with the universe, or emerge from the universe?"
You forgot "None of the above." I told you my reference, and it wasn't an anonymous "consensus" which in any case plays no role in science. In the Kafatos universe, consciousness is integral.
We're not on the same page. If you want to have a technical discussion, don't you think it would be more productive if we cite our sources? If you want to have a philosophical discussion, I am truly not interested.
Much has been made out of a possible demonstration of the validity of my arguments by means of a computer simulation. It has been suggested that if my ideas are correct, then one can write a computer program modelling them and obtain the Tsirelson bounds. While such a demonstration would indeed be sociologically important (especially considering...
Much has been made out of a possible demonstration of the validity of my arguments by means of a computer simulation. It has been suggested that if my ideas are correct, then one can write a computer program modelling them and obtain the Tsirelson bounds. While such a demonstration would indeed be sociologically important (especially considering the fact that Geometric Algebra remains an unfamiliar language for many), it is irrelevant as far as the logic of the EPR debate on physical reality is concerned. An analytical model such as mine cannot possibly be proved or disproved by its numerical simulation. A simulation of a model is a mere implementation of its analytical details, not an experiment that can either prove or disprove its validity. If reality can always be so simply simulated then there would be no need for the staggeringly expensive actual experiments. Reality is mathematically far richer and profounder than some of us are able to fathom, let alone a computer software. The EPR correlations are observed in nature in the actual, real-life experiments, not on a dead computer. I have produced impeccable analytical arguments to demonstrate that Bell’s theorem is wrong, both in its input and output. Moreover, I have produced impeccable and explicit analytical models to explain the correlations observed in the actual, real-life optical experiments performed at both Orsay and Innsbruck (cf. arXiv:1106.0748). Furthermore, I have proposed an actual real-life experiment that can indeed falsify my model (cf. arxiv:0806.3078). Therefore the additional demand of producing a computer simulation of my model is like demanding a flight-simulation from the Wright Brothers when they have in fact produced an actual, real-life flying machine!
There are also more fundamental reasons why the whole fashion of a computer simulation with regard to EPR correlations is completely wrong headed. It is based on a serious misconception of the true physical and mathematical reasons for the existence of the EPR correlations in nature. In all real-life demonstrations of the correlations, Alice and Bob always observe truly random outcomes of their measurements---A = +1 or -1, and B = +1 or -1. Therefore, any correlation between A and B themselves cannot possibly reproduce the observed quantum correlation, unless the topological non-trivialities of the physical space itself are also correctly simulated. In the language of my model this means that one has to model the physical space, not in terms of the R^3 points alone, but in terms of all of the subspaces of R^3 (namely, points, lines, areas, and volumes) within the even sub-algebra of the physical space (as conceived by Grassmann some 167 years ago). However, what I have seen so far in attempts to simulate the EPR correlations is a completely wrong headed approach. What is usually tried is based on an implicit assumption that the numbers A and B are only apparently, but not truly random, and if only we can somehow discover the correct functional dependence of A and B on the disposition of the apparatus and the hidden variables then the right correlation between A and B would emerge. I repeat: this is a completely wrong headed approach. One can never ever reproduce the EPR correlations this way. For the EPR correlations are what they are because of the topological non-trivialities of our physical space itself, NOT because of some hidden order in the randomness of the variables A and B.
Florin Moldoveanu replied on Aug. 5, 2011 @ 04:57 GMT
Dear Joy,
You state: "An analytical model such as mine cannot possibly be proved or disproved by its numerical simulation. A simulation of a model is a mere implementation of its analytical details, not an experiment that can either prove or disprove its validity. If reality can always be so simply simulated then there would be no need for the staggeringly expensive actual experiments....
You state: "An analytical model such as mine cannot possibly be proved or disproved by its numerical simulation. A simulation of a model is a mere implementation of its analytical details, not an experiment that can either prove or disprove its validity. If reality can always be so simply simulated then there would be no need for the staggeringly expensive actual experiments. Reality is mathematically far richer and profounder than some of us are able to fathom, let alone a computer software."
Also: "In the language of my model this means that one has to model the physical space, not in terms of the R^3 points alone, but in terms of all of the subspaces of R^3 (namely, points, lines, areas, and volumes) within the even sub-algebra of the physical space (as conceived by Grassmann some 167 years ago). "
Let me start with the second quote. This is absolutely no problem for a computer simulation. For my thesis I did a numerical simulation of optical pulse propagation in an optical fiber equivalent to a cable from US to Japan. The equation used was a nonlinear Schrodinger equation and then I had to find the minima of a function with 10^6 variables. This was done 12 years ago on a PC 10,000 times slower than a typical PC today and a run took under 10 minutes. Numerical modeling is a mature, sophisticated domain and people can do much harder tasks that this, accurately simulating chaotic systems with runaway error accumulation.
About: "An analytical model such as mine cannot possibly be proved or disproved by its numerical simulation." this is not true. I know several examples of analytical models which were first investigated by computer modeling and later on the theoretical work was performed. Staying in the realm of nonlinear partial differential equations, this domain is much harder than ordinary differential equations and the solving method is called inverse scattering, a generalization of Fourier transforms (inverse scattering because one actually solves a QM scattering problem backwards starting with the scattering result and solving for the potential). However, before the solving method was discovered, computer simulations convinced people that there was something very strange and totally unexpected going on there.
About "A simulation of a model is a mere implementation of its analytical details, not an experiment that can either prove or disprove its validity." Here I agree. However, the point is not to prove your math wrong, I think I made clear that I agree with it, but to clarify the interpretation. (I will come back to this point in another post where you gave more details)
About: "If reality can always be so simply simulated then there would be no need for the staggeringly expensive actual experiments." this is incorrect. The biggest issue in computer modeling is how to keep errors under control. Some models are inherently stable, others have exponential growth (like chaotic systems). There are appropriate techniques for each case. If the model is known, it is a matter of cost/benefit analasys to decide which way to go:simulation, or experiment. For your theory we know the model: your theory, and all that remains to do is to pick the appropriate numerical method.
About: "Reality is mathematically far richer and profounder than some of us are able to fathom, let alone a computer software." True, but irrelevant here. See point above. The model is known, and we are not trying to redescover it by computer. The goal is to validate an assertion with modeling: achieve Tsirelson bound by using only local operations, or not.
Steve Dufourny replied on Aug. 5, 2011 @ 10:15 GMT
Your models to both of you are so weaks, your simulations about quantization of mass is then weaks also.Then your future simulations shall be falses and weaks simply. Grassman and tirelson, yes of course.You are going to simulate nothing yes, then dear investors , be rational. An isntitute is just an institute. THEY TRY THAT IS ALL.
ahahahah
SPHERICALLY YOURS.AND YES ONE THING EUREKA FROM BELGIUM FRUSTRATING NO,
I find myself in agreement with Joy Christian on the computer simulation question.
Looking over that criticism on the web we were talking about elsewhere, the critic said or implied something to the effect that Joy admits he can't write a single line of computer code, so he can't possibly know what he's talking about. That's a telling, and profoundly stupid, statement, demonstrating that the critic cannot tell the difference between computation theory and programming.
Joy Christian's theory depends on continuous functions throughout. That is the characteristic that keeps it true to classical physics and therefore to EPR criteria. Differential equations can be machine modeled to arbitrary accuracy by substituting difference equations, and error correction can be written in. The problem is in preventing the multiplication of errors over time; i.e., replicating results. Gregory Chaitin has dramatically demonstrated arithmetic randomness -- calculating the value of Omega by the same algorithm in different languages produces different numerical results as random as a single coin toss. (I wrote a nontechnical treatment of the consequences of Omega for ICCS 2007.)
A machine model of Joy Christian's theory would have to be networked to control for random output, so that correlations between input and output results at an arbitrary time can distinguish between pseudorandom (continuous) phenomena in which input and output are correlated by continuous function (i.e., analytical) criteria, and random (discrete) output. There would never be a way to correlate input data to output data even in a nonlinear algorithm that faithfully replicates results time after time.
The upshot is that Christian's theory is time-dependent, as are all classical models of continuous spacetime events.
Considering the challenges to networking computations to simulate continuous real world events, a true real world experiment would indeed seem to be much less complicated and less costly.
Steve Dufourny replied on Aug. 5, 2011 @ 11:27 GMT
correlations, how many are trues????
The algorythms must be realistics and precises, the evolutive mass and its polarization of evolution is specific with a pure duration correlated with this constant of time.
"Gregory Chaitin has dramatically demonstrated arithmetic randomness -- calculating the value of Omega by the same algorithm in different languages produces different numerical results as random as a single coin toss."
Well and of course you are going to say that a time barrier exists and we can travel in time because the time is not dependent of events of evolution.You are a rationalist or a pseudo rationalist? Do you really understand what is a quantization of mass and a polarization of evolution between hv/m on a pure entropical and thermodynamical arrow of time.You do not understand what is the distribution of numbers inside this universal 3D sphere.You aren't general simply.
Regarding the real-life experiment Tom mentioned above, I would like to add that (as far as I know) a classical EPR experiment has never been done before. Here again is my proposal for such a classical experiment: arxiv:0806.3078. If this experiment is performed in real-life, then I claim that we would see the EPR correlations purely classically. I have consulted the distinguished experimentalist David Wineland about this and he thinks that the experiment is doable. It is also noteworthy that both Bell's theorem and quantum theory predict linear correlations for this experiment (because of decoherence effects and the fact that the system is prepared in a manifestly product state); whereas my model predicts cosine correlations. So this would be an excellent test not only of my model, but also of quantum theory itself, not to mention it would also test whether we live in a space that respects 2pi rotation as a null operation or 4pi. A computer simulation is not capable of doing any of these things.
Steve Dufourny replied on Aug. 8, 2011 @ 14:23 GMT
It exists experiments more urgent in a pure global and rational humanistic and universal point of vue. Are you going to test an experiment just for a lost of monney. Any sense. The sciences are there to imporve and optimize the quality of humanity and all creations. The rest is vain. This kind of experiment is simply not useless at this moment.It exists priorities in ecology, economy,energy.....a sceintist is there to help humanity. The rest is vain.
Florin Moldoveanu replied on Aug. 8, 2011 @ 21:48 GMT
Joy,
I agree that an experiment can settle this question as well. However, I strongly doubt that the experiment proposed in http://arxiv.org/PS_cache/arxiv/pdf/0806/0806.3078v2.pdf would contradict Bell's limit. Peres has analysed this experiment from the classical point of view in http://www.fisica.net/quantica/Peres%20-%20Quantum%20Theory% 20Concepts%20and%20Methods.pdf page 176 and the correlation is clearly -1 + 2 theta/pi I could not find any mistakes in Peres' elementary analasys.
In the paper I mention above I discuss Peres's mistake at some length (cf. my equations (6) and (7)). His mistake is the same as Bell's original mistake. Namely, he uses a wrong co-domain for the maps A and B. Instead of a 3-sphere, he takes the co-domain of A and B to be a 0-sphere. But a discrete union of 0-spheres is a poor topological substitute for the compact, simply-connected 3-sphere. A discrete union of 0-spheres can at most be homeomorphic to R^3, but not to S^3. Both R^3 and S^3 are parallelized topological spaces, but they differ by a point at infinity. More importantly, there is no torsion in R^3, whereas it is the torsion within S^3 that is responsible for the EPR correlations (I have discussed all these things at great length in my papers). Thus Peres's calculation is as naive and incorrect as Bell's original calculation. Moreover, all simulation attempts I have seen so far seem to make the same basic mistake. They all start out with 0-sphere as the co-domain of the maps A and B, whereas they should start out with a compact, simply-connected space S^3 as the co-domain. It is then not surprising why they never get anything beyond linear correlations. As they say: garbage in, garbage out.
This is an incredibly interesting discussion. I have no side in this. I am grateful to be able to view the sides in such detail. There is no question that this ongoing discussion about Joy's work is the best discussion I have seen occur here.
Florin Moldoveanu replied on Aug. 9, 2011 @ 05:52 GMT
Dear Joy,
Unlike in the case of hidden variables for QM where you have full freedom to define the elements of reality anyway you see fit, in this case the elements of reality are fixed: the rotation of the "bomb" fragments. Assuming the rotation direction is randomly distributed with equal probability on S2, Peres' analyses stands as is (and the argument is rather elementary).
Regardless of their perceived deficiencies, in this experiment there is no freedom to define the elements of reality any other way: they are the "bomb" fragment angular momentum. As this angular momentum is randomly distributed on the surface of the S2 sphere, all that remains to compute is the surface area for which the two measuring directions "a" and "b" detects the same or opposite rotations.
Computer simulation, or macroscopic experiments will yield the same result: Bell's limit. Please disagree with me on the proper analysis, but let the experiment decide. I have 100% confidence I will be proven right by your proposed experiment.
Indeed. Let the experiment decide. That is precisely what I have been arguing for the past four years. I too am 100% confident that the proposed experiment will prove me right. Unfortunately, your comments here show that----despite your great efforts (for which I am truly grateful to you)---you have not really understood the essence of my argument. For me EPR correlations are nothing but a vestige of the geometrical and topological properties of our physical space. Accordingly, in my view Peres's analysis is fundamentally flawed from the very start. What is missed by Peres (and Bell before him) is the fundamental property of our physical space known as the "orientation entanglement." One does not have to frame my argument in terms of the elements of reality to appreciate the importance of this property. All one needs to appreciate is that the bomb fragments in the experiment would be rotating, not as isolated objects, but in tandem, in the presence of each other. The full argument of why mere presence of the other fragment is important in the analysis is given in my paper, but the neglect of this elementary fact invalidates Peres's analysis. Consequently, if the experiment is done, you will see the cosine correlations I have predicted. It will prove that neither Peres nor Bell really understood the correct physics of the problem before they made a funny theorem out of it. Ironically, the correct physics of the problem was well understood by mathematicians like Hamilton, Grassmann, and Clifford some 100 years before Bell.
I did not phrase my argument clearly enough in the previous post. All I am saying is that Peres has modelled the physics of the problem pretty badly. More precisely, both Peres and Bell represent the angular momentum in their local models by an ordinary vector, which is simply wrong, as I have discussed in several of my papers. When the angular momentum is modelled correctly as a bivector (as, for example, done in this paper), it becomes abundantly clear that the correct classical correlation between the bomb fragments can only be the cosine correlation.
I congratulate you on work which should unlock the truths of nature. I have cited your earlier papers in my own because your thesis is essential to allow mine, as outlined in a finalist essay in the competition here. It is conceptual not mathematical, but I would greatly appreciate your reading it to see if you can conceive the local reality derived, providing a quantum mechanism for the SR postulates and principles. (courtesy of Chandrasekhara Raman's much ignored Nobel prize work, and learning from Bohr's lesson to VH about knowing how lenses work).
A number of other more detailed jointly authored papers on various aspects are on the way now, but they may all be simply written off at page 1 if Bells theorem remains as misunderstood as it has been.
I an not qualified to comment on the details or mathematics of yours so can only agree with the approach, principles and, importantly, results, which allow the unified field theory of the 'Discrete Field' Model (DFM) described; http://fqxi.org/community/forum/topic/803 I believe the maths need to develop in the direction of yours as well as using 'time stepping' techniques.
Note there are a number of errors in the essay, (now corrected in the papers), it is raw and very limited in scope, but describes a dynamic conceptual construction which resolves many issues. (direct Email on P1). One simple way to perceive it not (referred) is that on considering Doppler shift and constancy of c is; c = d/t, EM signals do not react to an observer until they reach him, and when they do both f and wavelength lambda change equally on frame transformation to maintain local c, in c = fLambda, and also conserve E = fLambda.
As Lorentz said, "Science cannot progress without changes that may at first appear alarming." I greatly look forward to any comments.
Peter Jackson replied on Aug. 18, 2011 @ 12:52 GMT
Wil.
I'm disappointed Joy either missed my post or didn't respond, but thanks for your continued interest. As you know, I don't have a website or intend to have one, but do have a few papers on Phil's viXra. I'll send you a link with anything new, which is a specialist paper I'm working on for my own institutes monthly notices, plus a major joint work, which may first see light as an Ebook. So obviously I'm flat out on these!
I've derived an interesting result for the domain limitation of geometric algebra which I must catch up with Joy's papers on. It say's we can't have two times. i.e. if we use it with Descartres system we can't then add it back again in space time, but rather than question the latter the DFM shows that the former is the mistake. Very interesting stuff emerges.
Joy Christian replied on Aug. 18, 2011 @ 13:27 GMT
Dear Peter,
Thank you for your kind words and for citing my papers. I am sorry to have missed your message earlier, but there were some technical issues being raised by various people (including Florin) which required my immediate attention. In any case, I will have a look at your work when I get a chance.
Peter Jackson replied on Aug. 18, 2011 @ 17:47 GMT
Joy
Many thanks. I'm still trying to fully understand your work, but seem have found an equivalent result from a different route. This is a different language, but..
If local reality was also entirely contextual, i.e. subject to observer frame, and only measurably accurate (real) from one frame, would that not somehow remove a lot of assumed limits? I did not refer to Proper Time in my essay but have since found it central in testing for a Discrete Field Model. We seem to assume we can measure without checking we're using Proper Time, and it seems therein lies a major problem, which I believe has helped create the divide in current physics.
Also, do you model motion in geometrical algebra? How would you look at the concept of removing it from Descartes basic geometric system and then considering it, just once, in the Minkowski metric. I hope that may make some sense to you.
Wilhelmus de Wilde de Wilde replied on Aug. 19, 2011 @ 16:35 GMT
Hi Peter,
Joy's answer does not touch the essence of your question I think, first I am also now putting up with geopmetric algebra, and as as far as i understand it untill now there is no time in it.
Your perception of subjective reality is a clear one , like in your essay it exolains the faster than light paradoxes and far more, I think if you continue to travel this way you will arrive at a simple (very important) and logic theory, go on please, I like very much this approach.
Peter Jackson replied on Aug. 24, 2011 @ 15:27 GMT
Wilhelmus
To be fair Joy hasn't considered that yet, but has promised to do so. But yes, a simple and logical theory has already emerged which better describes nature, without the paradox but with a Quantum Mechanism, and it is consistent with Joy's proof.
Geometric algebra and time proves part of the problem. Treating Cartesain co-ordinate value changes as vectors means time has already been used in the equations, because there can be no motion without time. So then adding it in again as a space-time dimension would be as invalid as an extra x co-ordinate. However, and this takes some thinking about, Minkowski space time is essentially fine, It turned out that was the first assumption that was wrong!
When Descartes and Einstein considered co-ordinates terms like "rigidly attached to A BODY" and "BODY of reference" were used. The solution which works in terms of describing nature without paradox proves we should have taken that more literally and used mutually exclusive local inertial frames or "infinitely many 'spaces' in motion relatively" (AE 1952), not the ethereal overlapping ones we assume are right. It's also all about only using 'Proper Time.' It seems Charles Dodgson was correct. The answer also better meets the SR postulates, and proves his previously paradoxical 'box s within box S' conception logically.
But even with a few of us now working full time on it I still estimate 2020 as the earliest this will be perceived by most. It's just too fundamentally different, and however much people fool themselves science, including maths, is really almost all 'belief' based.
Wilhelmus de Wilde de Wilde replied on Aug. 25, 2011 @ 16:13 GMT
dear Peter,
paralel free thinking is easier with you indeed as with others, the thing I do not understand is that our view is much simpler and yet people are hiding behind the abacadabra of their formula's (that appears intelligent), in this way they go deeper and deeper into their own black hole, not knowing that they cannot escape any more, but peter i am positive , I think it will change in the coming 3 years (also because of the results of the LHC); it is OCCAMS razor that we are going to apply.
Peter Jackson replied on Aug. 25, 2011 @ 23:03 GMT
Wilhelmus
A good analogy. It seems both a great strength and the biggest weakness of the human race that we have such diverse viewpoints and ways of thinking.
I like your optimism, and faith in humanity, and appreciate your excellent conceptual dynamic perception, and support. I promise I'll pass you a link soon, It's quite exciting and a little overwhelming, with new aspects and solutions now emerging from every angle. Which areas are you most interested in?
In fact I can give you a link to a very limited 'Intuitive Physics' essay I did a while ago on the 'sailing' viewpoint and lessons for Nature's elements, inertial frames, superposed waves and Fourier transforms. It's Occam to a tee! http://vixra.org/abs/1106.0013 I think the link has ceased to be 'entangled' for some reason, but just paste in into Google.(I hope you haven't already seen that one. - let me know).
Very best regards
Peter
PS; Did you know Lorentz said in 1913; "...the daring assertion that one can never observe velocities larger than the velocity of light contains a hypothetical restriction of what is accessible to us, a restriction which cannot be accepted without some reservation."
also in 1906; "...we can make no progress without some hypothesis that looks somewhat startling at first sight, we must be careful not to rashly reject a new idea…"
Peter, What a coincidence that I used Occams Razor (your last (25th) theorem) , the messages are clear , however I have to reread them calmly again, I just was curiuos and then "consumed" the article in 10 minutes, I fully agree with you, only I do not understand why it is not directly achievable in Vixra, you should ask our friend Gibbs.
You asked my interests, well you also read my essay, here I touch all my main interests, by the way it was the first time that I wrote something down in this area and I was very happy that it was accepted by FQXi, after the prizes were given, my essay was mentioned for about a month under Forum Updates (you were there during the contest) and that Peter was for me a bigger prize as money, it is also published in the Scientific God Journal from Dr. Huping Hu 5he publishes also the "Prespacetime Journal" your text would be very good in their view I think (first I asked to publish me there but HU thought (because of the Total Simultaneity 5I am not a believer peter!!!) that it was more apt for his SGJ), Huping Hu is very symphatetic and working close with Philip Gibbs from Vixra.
keep on following your intuitions Peter and keep me informed.
Eckard Blumschein wrote on Aug. 4, 2011 @ 12:45 GMT
Dear Joy Christian,
The last in alphabet but certainly not the least FQXi member is Zeh. He wrote a paper "Quantum discreteness is an illusion" arXiv0809.2904v7, to be published in Foundations of Physics (DOI 10.1007/s10701-009-9383-9). The published version can be found at www.springerlink.com. Via FQXi I got the file NoDiscreteness.pdf.
Did you deal with Zeh's view? I recall you illustrating in a figure the plurality of possible future parts of a world-line. Did you also take into account something like half-life, i.e., ending or ramifying world-lines?
Perhaps I should briefly explain my own reasoning: I see the future not observable and therefore any integration over time from minus infinity to plus infinity with arbitrarily chosen t=0 inadequate for a description of an open to unseen influences physical reality, which I understand as the ultimate basis of abstraction.
Eckard Blumschein replied on Aug. 5, 2011 @ 17:03 GMT
Alternatively goto http://www.zeh-hd.de Quantum theory, and the offered download of the paper "Quantum discreteness is an illusion". Prof. em Zeh belongs to the advisory board of FQXi.
Eckard Blumschein replied on Aug. 10, 2011 @ 14:51 GMT
Dear all,
Is NoDiscreteness.pdf irrelevant? Or does Zeh not deserve our attention?
Incidentally, I wonder why Tom wrote "random (discrete)". Well, computers generate random (discrete) numbers. However, I understood random as without a definite plan or pattern. Shouldn't this also include irrational numbers?
Joy Christian replied on Aug. 10, 2011 @ 16:09 GMT
Hi Eckard,
Sorry, I should have replied earlier. Zeh's argument is different from mine. It is important too, of course, but with very different philosophical implications for the interpretation of quantum theory. I am arguing more in line with Einstein, who believed quantum theory to be an incomplete description of nature. This was the basis of the EPR argument. In my view the EPR argument stands as tall today as it did in 1935 (because of my work). If only the followers of Bell are able to see this!
Thanks for the link to Dieter Zeh's site. I appreciate his recent Physics Today letter that addresses the frequent abuse of the term "quantum information" and sets straight the proper context for unitarity:
"Although I personally prefer the assumption that unitary dynamics is universal, I agree that some stochastic dynamics has to be used somewhere along the chain of interactions that ends at the observer. It does not matter whether you describe this observed indeterminism in terms of a collapse or a branching of a universal wavefunction into dynamically autonomous components (unlike the collapse, this branching does not require any new dynamical postulate; it is a consequence of the Schrödinger equation with local interactions). Such a real or apparent collapse is an important part of the effective dynamics of 'our quantum world' -- our 'branch,' if you like -- that should be carefully analyzed rather than being used ad hoc in a pragmatic and confusing manner. In neither case would it describe a mere increase of information about an initially incompletely known quantum state of the involved systems; the indeterminism is described by a change of a state which is known to be different from an ensemble of potential states."
I think this point relates rather directly to Joy's distinction of random events in quantum configuration space from pair correlations in topological space. Information correlated at a distance depends only on the initial condition and the topology, just as Joy has it.
Eckard Blumschein replied on Aug. 11, 2011 @ 11:07 GMT
Dear Joy,
Aren't "very different philosophical implications for the interpretation of quantum theory" a challenge to look for possible mistakes and maybe even of importance in practice? Where do you see weaknesses in the approach by Zeh and by youself?
Dear Tom,
Should we trust an the presently mandatory topology that cannot even perform a symmetrical cut between R+ and R- without any remnant. Every child can, in principle, cut a sheet of paper in the middle without a vestige.
Eckard Blumschein replied on Aug. 15, 2011 @ 15:42 GMT
Dear Tom,
More than a hundred years ago, the good old Euclidean notion of number as a measure was replaced by the point on a yardstick that indicates its distance from zero. While sets of points can discontinuously approximate measures of any physical dimension with any desired resolution, logic demands to choose between either the cutting property of a dimensionless point or the subject cut by it.
I got aware of this calamity when nobody was able to provide a convincing answer to my request how to deal with the point zero between R+ and R-. I offered a solution in my last essay 833, and I also discussed the matter with David Joyce, a professor of mathematics, who was aware of the serious change to the notion of number I mentioned above. Being not a mathematician myself, I feel nonetheless obliged to blame this arbitrary but currently mandatory notion of number imprudent and responsible for mistakes that affect physics, including EPR.
Eckard Blumschein replied on Aug. 15, 2011 @ 22:22 GMT
Sorry Tom, What were you not able or not willing to accept? Of course, a point is given in a line by one measure, in an plane by two, and in a volume by three measures. My hint refers to something else: Any point has the measure zero. In other words: It is zero-dimensional. Euclid: A point is something that has no parts.
How accurate or how unique is a real number? I see no limitation to its accuracy and therefore no chance to exactly address it. Given I did cheat myself as usually do mathematicians who feel entitled to "well-define" anything and declare a particular point removed from R. Could this unfeasible definition have any noticeable effect?
Real numbers make only sense as a different from rational numbers quality if they are considered constituting a continuum every part of which has parts. Neither the finite Hilbert space nor EPR did take this logical necessity into account. Dogmatic mathematicians do not even accept |sign(x)|=1 without an exception for x=0. At least physicists should have preserved their ability for more sound reasoning.
I'm not grasping your problem. Zero is defined axiomatically as a number that is the successor of no other number. In the complex plane, where points have two parts, the point [0,0] is a line of measure zero.
Eckard Blumschein replied on Aug. 16, 2011 @ 21:21 GMT
Tom,
No"where points have two parts". The "point [0.0]" is a sloppy denotation for the point located at the coordinates [0,0].
While it might be reasonable to consider the number zero as a line with zero measure, the arbitrary description of zero as "a number that is the successor of no other number" is bewildering. Within the integers, zero is the successor of minus one. Within the rational as well as the real numbers, no number has an immediate successor. While I do not trust in axioms on demand, definitions and axioms by Euclid and Peirce have proven still reliable:
A point is something that does not have parts.
A (rational) number is a multiple (or a fraction) of the unit measure one.
A continuum is something every part of which has parts.
Do not call the imperfection of currently mandatory mathematics and its interpretation e.g. by EPR my problem. I understood and resolved it by means of reasoning that does not require training in mathematical terminology, just willingness to use the notion point as an abstractum described by Euclid, see above.
In the uncountable continuum of all real numbers of a line, the distance between two points is a measure, no matter whether a rational, an irrational or even a transcendental one. Even the tiniest piece of the line cannot be resolved in singular points. In case of a step function or the like, the limit from the left and the limit from the right are different at the same point. This is, however, no problem at all because the measure always refers to just one side. Let's return to Euclid for the benefit at least of physics.
Eckard Blumschein replied on Aug. 20, 2011 @ 10:50 GMT
Dear all,
Invention of the theory of point sets arose from intention to combine abstractions with beliefs. Already the change from interpretation of the notion number from a physical measure to a point led into an unresolvable contradiction: Because a point has no extension, it cannot be part of but only border between two mutually excluding measures. We must define functions accordingly. Any objection?
Eckard Blumschein replied on Aug. 24, 2011 @ 00:01 GMT
Hi Joy,
Thank you for your reply. I accept that you took the argumentation by EPR for granted. I would just like to ask you whether or not I explained my somewhat heretical mathematical view understandable enough to you and if so, whether you see a possibility to refute it.
Incidentally, what might be wrong with Zeh's argumentation? Do you know someone who criticized it? Often, at best one of two mutually excluding theories can be correct.
Your work has given rise to the best conversation that I think has occurred here. I do not know where it is going to end nor whether or not I will understanding and recognize that ending, but I hope it continues for now, especially among those who are professionally qualified.
Steve Dufourny replied on Aug. 4, 2011 @ 22:25 GMT
and the winner is elected by Yoda, Joy because it is like that amen .
Professional, that doesn't mean they are trues.I know professionals in all domains who are not skillings. Qualified to ponder or qualified by an university, it's different.We retrun about the real understanding of the generality. Yoda stop also to make the nice baby with a politness of pseudo recognizing, already that you do not undertand what is this universal sphere and the rotations then don't insist really.A time for all , it exists philosophical platform, me I am rationalist and I have invented equationas and a pure genral and rational model, then of course I am not here to laugh. the end you say , yes of course you shall be invited aahahah the force is with you, a debate no but frankly, a cyclic debate yes. don't be offensed but the transparence and the truth is essential and of course the short distance between 2 points is the line of course.
Author Frank Martin DiMeglio wrote on Aug. 8, 2011 @ 16:05 GMT
"Science cannot progress without changes that may at first appear alarming." -- The greatest truths often go ignored and unrealized. Witness my work.
True and fundamental inertial and gravitational equivalency involves instantaneity and balanced attraction and repulsion. Space then manifests as gravitational/inertial/electromagnetic energy. I proved this.
I apologize, but I have some questions about the macroscopic experiment proposed by you in arxiv:0806.3078, page 4.
I understand that the experiment takes place in two steps:
STEP 1: Explode non-rotating spheres. Measure and record the rotation axes of the resulting half-spheres. "The interfaced computers can then record this data, in the form of a 3D map of all such directions."
The output of the first step is therefore a pair of lists of (pseudo)vectors, so that a vector is on a list if and only if the opposite vector is on the other list.
STEP 2: "the two computers are instructed to randomly choose the reference directions, a for one station and b for the other station - from within their already existing 3D maps of data - and then calculate the corresponding dynamical variables sign (Lj · a) and sign (-Lj · b)". Then it is calculated the correlation function, and then "this result, which would give purely local correlations, should then be compared (in N -> infinite limit) with the predictions (3) and (15)."
QUESTION 1 (about step 1): After a large number of such explosions, will each of the two 3D maps consist in uniformly distributed directions on the sphere? If not, can you provide the probability distribution?
QUESTION 2 (about step 2): Is there a reason why, when the computers randomly choose the directions a and b, it has to be "from within their already existing 3D maps of data"? (Peres seems to allow equally any possible direction.)
Answer to your question (1): I do not think the directions would be uniformly distributed, because angular momenta obey rather non-linear equations (as in equations (3) and (4) of my 1-page paper). I also cannot provide a probability distribution for the directions (for the same reason). If that was possible, Bell's theorem would have been forgotten a long time ago.
Answer to your question (2): I do not mean the directions a and b have to be two of those recorded directions of angular momenta. The added requirement is simply to mimic what is done in the actual EPR experiments. There, the directions are randomly chosen while the particles are already in-flight to ensure that there is no communication of any kind between Alice and Bob. What I am allowing is a possibility of choosing the reference directions months after the data is collected, so that one can be sure there was no communication between the two sides of the experiment.
Florin Moldoveanu replied on Aug. 9, 2011 @ 16:34 GMT
Dear Cristi,
I know I cannot convince Joy, but maybe I can convince you. Peres' analasys is really easy: (http://www.fisica.net/quantica/Peres%20-%20Quantum%20Theory %
20Concepts%20and%20Methods.pdf page 176)
Assume that the rotation direction is randomly distributed with equal weight on the sphere. We know each pair of fragments is perfectly anticorrelated from angular momentim conservation. Pick 2 arbitrary directions a and b and project the angular momentum of a fragment on those 2 directions. Half will spin in one direction and the other the opposite way. It all depends on which semi-sphere the angular momentum points. The semi-sphere is bounded by the plane perpendicular to a or b. The two planes cut the sphere in 4 segments with alternating signs for the projection for both a and b. The area for plus or minus is proportional with the angle between the vectors and you recover the standard Bell answer.
So to your question 1, the answer is yes. Assuming uniform distribution and random measuring a and b directions, Bell's result is a straightforward trivial mathematical consequnce.
In this case the elements of reality are the actusl angular momenta of the fragments. There is no freedom to redefine them for whatever reasons; they are set in stone by the measurement procedure for this experiment. The random distribution is also set in stone by the proposed preparation procedure of the experiment.
This is where Joy's analasys goes bad. He is confusing this experiment with the hidden variable case where one is indeed free to choose the elements of reality anyway one sees fit, provided that the QM results are recovered in the end. Once the experiment is proposed, there is no such freedom anymore. Joy thinks his mathematical model apply here, and I say (and Peres' elementary analasys proves) it does not. If needed, I can break the proof into simple elementary steps and arrive at Bell's result in the end (and each step would be completely and totally non-objectionable).
Florin Moldoveanu replied on Aug. 9, 2011 @ 16:40 GMT
Cristi, and Joy,
Apparently I was writing my reply at the same time Joy was writing his. Now Joy claims something interesting: the distribution is not uniform. In this case it will be possible to generate correlations different from Bell, but I need to think a bit about this before I will reply. (I highly suspect the correlations will be under Bell's limit).
Florin, you don't need to convince me, I understand what Peres and Bell say, but I want be sure what Joy saids about this experiment.
It seems to me that what Joy said is that there is an unknown probability distribution which ensures that E(a,b)=-a·b. Joy, please correct me if I misunderstood you.
"It seems to me that what Joy said is that there is an unknown probability distribution which ensures that E(a,b) = -a·b."
This is essentially correct. The correct local model for the experiment is given in my 1-page paper. Both Bell's and Peres's analyses are incorrect becausse they represent angular momenta by ordinary vectors. This is simply bad physics. The correct mathematical object that can represent angular momentum is a bivector. That is what I use in my papers. Bivectors respect non-linear equations, as in my equations (3) and (4). As a result, probability distributions are not so easy to predict. One must go through the analysis I go through in my papers to make the correct prediction, which is E(a, b) = -a.b for the experiemnt discussed by Peres.
Steve Dufourny replied on Aug. 9, 2011 @ 23:38 GMT
Well , what are your real convergences, and what are the real correct predictions. At my opinion, your probabilities are just falses and just a kind of maths play, a game of superimposings simply,Joy you aren't general you know, where is the cause of mass??? If you want an answer, forget your vanity and respect the rotations in 3D and then the proportions with mass. What are for you the form of a particle,answer.....
You can answer also christi .
The distribution of your probabilities are just a parallelization of some irrationalities. I have reread your posts, it is not foundamental simply but it's well made, the form, the politness, the equations.
But you are a good scientist. You confound many things but you are interesting. I don't understand why you focus on a disproof of a thing which is an anti axiom, an "not useless thing" to disproof in fact, all rationalist knows already that these stupidities are for the second part of the sciences community. Why you want disproof that, I have several explainations but here are the main, you are not general, or you have time to loose.
I repeat what are for you the form in 3D of a particle? you have several days to answer.
You can speak about probabilities of course but please make it well and with rationalism and generalism please. Where are the thermodynamics, the real maths methods, the pure gravitation, the real proportions, answer ....anywhere.
You are better than that Joy, then please ponder better things.
Florin Moldoveanu replied on Aug. 10, 2011 @ 04:57 GMT
Joy and Cristi,
If I understood correctly, Eq 3 and 4 represent the bivector multiplication rule. As such it has no relevance to Peres' analasys because it is an additional fact which is not used (or needed to be used).
Let me quote from Joy's paper: "A small lump of density much grater than the density of the ball is attached on the inner surface of each shell at a random location, so that, when the ball pops open, not only would the two shells propagate with equal and opposite linear momenta orthogonal to their common plane, but would also rotate with equal and opposite spin momenta about a random axis in space."
The key parts are: "A small lump of density much grater than the density of the ball is attached on the inner surface of each shell at a random location" and "would also rotate with equal and opposite spin momenta about a random axis in space"
Therefore the axis of rotation of the fragments is randomly distributed around S2 with equal probability contrary to Joy's earlier claim from above: " I do not think the directions would be uniformly distributed"
The equally distribution is a consequence of the experimental preparation (how the small lump is attached), and not a consequence of the bivector algebra. I hope we are in agreement that equal distribution does yield Bell's limit so I'll not present the rest of Peres analasys here.
If the lump is attached randomly, then all radial directions in S2 are equiprobable from the symmetry of S2: there is no prefered direction with an accumulation of lump distribution near it. Therefore the axis of rotation is random as well on S2.
Linking the algebraic product with the experimental procedure is not only bad handwaving, it is logocally illegal.
If you do not trust my analysis, here is the logical contradiction in its most basic form: "about a random axis in space" and "I do not think the directions would be uniformly distributed"
Cristi Stoica replied on Aug. 10, 2011 @ 06:30 GMT
Florin,
I already disproved mathematically the possibility that such a collection of lambdas as Joy needs may exist. Can you comment about it?
As for Joy's explanation:
"Peres's analysis is naive and wrong. Angular momentum is not a vector. The issue is as simple as that."
it is easy to answer:
The Hodge duality establishes an isomorphism between the vectors and the pseudovectors.
The key word here is "isomorphism". Because of this, you can easily replace anywhere in Peres's argument "vectors" by "pseudovectors", and get the same result.
Joy Christian replied on Aug. 10, 2011 @ 06:35 GMT
Florin,
You are avoiding the real devastating flaw in Peres's analysis and instead basing your argument on something I wrote in response to Cristi's question out of context. The real issue is that Peres's analysis is fundamentally flawed from the very start and hence it cannot possibly give the correct prediction for the experiment. His analysis, in fact, is an embarrassingly bad physics. No conclusion about the distribution of measurement results can be drawn from bad physics. As I mentioned before, angular momentum is not a vector. And yet Peres has modelled the physics of his experiment by treating angular momenta as vectors. The correct analysis of and the correct prediction for the experiment are given in the two of my papers I mentioned before.
You have confused two separate parts of my argument in these papers. The first part is the correct theoretical analysis of the problem and the corresponding correct prediction---which is E(a, b)=-a.b. The second part is the experimental procedure which can be used in practice to test this prediction. In actual practice one can indeed use ordinary vectors, and this *does not* contradict the bivectors used in the theoretical analysis. If you read my paper carefully, I have shown how the bivectors constructed in my papers are operationally identical to the vector-based observables used by Peres. My arguments are therefore entirely coherent, consistent, and correct, because they use correct physics and mathematics. Peres's analysis on the other hand (and hence his prediction) is as wrong as 2=5. If the experiment is performed, you will see the cosine correlations as I have predicted. You and Peres will be proven wrong.
Cristi Stoica replied on Aug. 10, 2011 @ 06:38 GMT
Florin,
"The equally distribution is a consequence of the experimental preparation (how the small lump is attached), and not a consequence of the bivector algebra."
Your wrote to Joy, "If you do not trust my analysis, here is the logical contradiction in its most basic form: 'about a random axis in space' and 'I do not think the directions would be uniformly distributed'"
One of the more stunning aspects of Joy's theory is its ability to obviate paradoxes, at least one of which is the cosmological horizon problem.
As I explained in my post in this forum 9 Aug 20:16 GMT, correlations of pair functions at a distance is independent of the counting function on R. In other words, there is no relevance to probability distributions in space, only to pair correlations in time.
I explain (4.11 et seq in the draft paper referenced in the 9 Aug post) how pairs of properties are correlated at any distance using the case of prime pairs (modulo 2). Joy has made me realize that it doesn't matter whether we speak of prime number pairs or particle pairs, true (i.e., irreducible) pair correlations incorporate 100% of the information contained in the system's initial condition. This is, of course, completely compatible with Bell's theorem and the Aspect experiments, where each of a pair of particles is 50% of the total information of the measured system.
The deeper story, which I now believe that Joy has gotten right, is that we were looking for the wrong thing all along. I will put this in terms of mathematics and information theory, which I understand, rather than the physics which I don't:
If I take a pair of P(mod 2) correlated prime integers [P_1,P_2], I don't mean that the distance between them is zero, unless the pair are twins. So we have this null result in the case of twin primes, and all other odd prime pairs can be irreducibly correlated by modular arithmetic regardless of the magnitude that separates them. There are a whole lot of non-correlated pairs of integers, right? -- but we are not interested in that decoherence. We want correlations that cohere not with fragments of the information in the initial condition, but which total to unity without regard for distance. In other words, while Bell's theorem gives us system unity for a fraction of the cosmological initial condition (and the principle of superposition then gives us superunity, so to speak) -- Joy's result promises to reveal pair correlation for ANY initial condition, including the cosmological.
So there's no logical contradiction between random axes of rotation and the single axis on which true irreducible properties are correlated. Probability distribution in space plays no role. Spatial magnitude between particles plays no role. Reduction to complexity, i.e., true and irreducible pair correlations containing 100% knowledge of the initial condition, demarcate random decoherence from knowledge of "the bomb" in its pre-exploded state.
Joy Christian replied on Aug. 10, 2011 @ 13:05 GMT
Well done Tom!
Just as you don't quite understand my language of physics, I also don't quite understand your language of information theory. But you seem to have got the essence of my argument absolutely right. Only two things really matter---the initial condition and the topology of the 3-sphere (more generally, that of a 7-sphere). All the rest is the unnecessary baggage that we are stuck with because of the chequered history of Bell's theorem. I thought my arguments are going over people's heads, but at least you seem to have understood what I am going on about. That's a relief!
Whew! I feel like Thomas Hobbes, who upon being exposed to a proof of the Pythagoras Theorem, exclaimed, "Bye Gawd, this is impossible!"
Joy, you've really taken me back to some geometrical/topological principles as fundamental as the P.T., and then brought it all up to date in a quite compelling package.
I hope we get a chance to do something toegther sometime.
Steve Dufourny replied on Aug. 10, 2011 @ 17:36 GMT
Vectors by pseudos vectors??? Christi you must rethink your line of reasoning about what is a vector or a bivector, a duality you say.And an isomorphism. Well well well we have not the same foundmantal books of maths. But it is just a suggestion.
A pseudo vector, a pseudo dimension, a pseudo particle.and a pseudo free thinking also...in fact you confound dear irrationalists what is a deterministic law and on the other side some plays of maths.
And you Tom you are the specialist, I d say even you are the expert of irrationals superpositions. The principle of superimposing, and after what? a pseudo post of pseudo sciences also No?
Cristi mentioned replacing 'vectors' with 'pseudovectors', and you misunderstood him.
In quaternion mathematics, we have 'scalars' and 'pseudoscalars' (still a scalar-like quantity, but with different parity properties - a classic physical example is the pion). Cristi is using the terminology of 'vector' and 'pseudovector' for vector-like quantities with different parity properties. Personally, I am more familiar with the use of 'polar vectors' (Cristi's vectors) and 'axial vectors' (pseudovectors). The origin of the parity properties of the axial vector (pseudovector) is the familiar non-commutative property of vector cross-products: a x b = -b x a. A simple example is the angular momentum vector L = r x p. If you were to flip a spinning sphere, it would also flip the direction of the angular momentum vector, and require a net torque to effect this change. When I taught Sophomore Physics, I would flip a spinning bicycle wheel while I was sitting on a bar stool that was free to spin. By doing so, I could cause myself to spin or not.
Steve Dufourny replied on Aug. 10, 2011 @ 23:10 GMT
Ray quaternions and octonions are a pure joke where people bad interprets the relativity, general and special.
In fact it is an ocean of decoherences and irrationalities.
Ray Ray Ray, the spheres in rotations are proportional with mass....do you understand what is this meaning. That must rest in 3D for a real evolution and polarization between mass and light. The number must be finite and the fusion apppears. For that the 3D is essential ,and the rotations of these spherical volumes are the key .If the hv, m and space possesses the same number for the uniqueness and if the cosmological number is the same also, it's relevant correlated with my constant. mass of the spheres m,velocity linear of the sphere c or l,the velocity orbital of the sphere o, the velocity spinal of the sphere s, and the volume V =COSNTANT. MORE E=(c²o²s²)m space without rotation, light in one sense, the mass in the other main sense,3 main gauges with the same number, even 4 with the cosmological scale. MASS POLIRIZES LIGHT AND SPACE.....the thermodynamics are essental pression, density, rotations, spheres, volumes,mass,......all is unified in this logic of 3D SPHERIZATION. Everywhere in our universe, these laws are a reality.They turn then they are Ray, the mass is proportional with these rotations of these spheres, quantics and cosmologicals. Ray say hello to Dr Coda :) , I like his works, the gravitational spherical waves and their superimposings in 3d are fascinatings, I am persuaded that Dr Corda will find many relevances about the gravitation. He respects the old school, it's so important.The mass curves Ray in 3D , it's essential for a real understanding of the rotations of all these spheres.Furthermore due to evolution and this fusion mass light , mass increases and then the pression and density.....the rotations and volumes are correlated then...
LET'S BE RATIONAL
Steve
ROTATIONS AND SPHERES EXPLAIN ALL IN 3D AND A PURE DURATION LIKE TIME COSNTANT.
I gave you a simple Sophomore Physics example of how angular momentum can be an axial vector (pseudovector using Cristi's terminology):
L = r x p = -p x r, and you completely denied its truth. How can you build a theory on spinning spheres when you do not even understand angular momentum?
Florin Moldoveanu replied on Aug. 11, 2011 @ 04:48 GMT
Dear Joy,
You state: "basing your argument on something I wrote in response to Cristi's question out of context."
Now who is gasping for straws? The discussion is about http://arxiv.org/PS_cache/arxiv/pdf/0806/0806.3078v2.pdf. One quote is from the paper, and another is from your answer to Cristi's question:
"STEP 1: Explode non-rotating spheres. Measure and record the rotation axes of the resulting half-spheres. "The interfaced computers can then record this data, in the form of a 3D map of all such directions."
[...]
QUESTION 1 (about step 1): After a large number of such explosions, will each of the two 3D maps consist in uniformly distributed directions on the sphere? If not, can you provide the probability distribution?"
and your answer was:
"Answer to your question (1): I do not think the directions would be uniformly distributed, because angular momenta obey rather non-linear equations (as in equations (3) and (4) of my 1-page paper)."
Your answer to Cristi directly contradicts what you wrote in the paper: "when the ball pops open, not only would the two shells propagate with equal and opposite linear momenta orthogonal to their common plane, but would also rotate with equal and opposite spin momenta about a random axis in space"
So in one instance you claim uniform distribution and in another you state the exact opposite. How can you claim any out of context defense on this? The context is your proposed experiment and the contradictory statements are about the uniform distribution or not for your experiment.
Florin Moldoveanu replied on Aug. 11, 2011 @ 05:04 GMT
Dear Tom,
Just a curiosity: did you read Peres's analyses: (http://www.fisica.net/quantica/Peres%20-%20Quantum%20Theory %20Concepts%20and%20Methods.pdf page 176) to see the opposing point of view as well?
I think is fair to compare both points of view before passing judgement.
If you did, what did you find objectionable in Peres' analyses? If needed, I can explain this analyses in really easy elementary and trivial steps and the only pre-requisite is simple high school trigonometry and geometry (no fancy topological spaces, fibrations, or quaternions).
Joy Christian replied on Aug. 11, 2011 @ 06:50 GMT
Dear Florin,
I see absolutely no contradiction in what I said in response to Cristi's question and what I write in my paper. The two quotations have little overlap, and in any case they are from two completely different textual contexts (and therefore they should be respected as such). Cristi (who seems to have no understanding of the physics of the problem) has been trying to trap me in his bizarre and convoluted logic. But let us leave that aside. More important is the fact that you are missing several crucial points: (1) To fully understand my argument my paper should be read as a whole, not in bits and pieces; (2) When it is read properly, you will find that there are two parts in the paper, first a theoretical analysis, and second an experimental (or operational) procedure---these two parts, and the concepts used within them, should not be mixed up and confused as you and Cristi are doing; (3) Finally, and most importantly, as I have emphasized several times before, Peres's analysis is fundamentally and embarrassingly flawed, because it is based on wrong physical and mathematical concepts. The correct theoretical and mathematical analysis of the physical problem at hand can be found in two of my papers I have cited before. This correct theoretical analysis should not be confused with the experimental (or operational) procedure I have suggested for recording and analyzing the data. The correct theoretical prediction for the problem is E(a, b) = -a.b and not what Peres has predicted. If you properly follow the operational procedure I have suggested in my paper, then you will see confirmation of my prediction and refutation of Peres's. I am sorry to see that you are unable to see the holes in Peres's analysis. They are as big as the ones in my Swiss cheese.
Steev Dufourny replied on Aug. 11, 2011 @ 11:49 GMT
A business school Ray it is that. Ahahaha you do not understand what is the mass and the rotations of spheres. You aren't a good teacher in fact.
In fact you do not understand what are the real proportionalities. Ray you say thesame than in physics forum ahahaha well tried , of course I am laughing so much. Ahaahah
You need to be less jaleous and less in the business with your friends, in fact you have lost in live, but of course you can kill me also.It will be easier you know, because there frankly with your pseudos maths and your pseudos return at shool, I know.If yoy knew hom many persons have tried to copy my revolutionary theory. Ahhahqaha they fall down all, naturally .Why because it is not my theory Ray, but THE THEORY of God .You can critic and even you can make all you want with me, be sure, if you knew my faith....let's me laugh Ray. You are just a hater jaleous now, touched by belgian truths.
Angular momment ahahah well tried .
and after what the inertial also NO.
PS Even without doctorate due to my coma at the age of 20,I know better my foundamentals than you and your friend. Why just because I haver good books and I like studying all days.Ahahah quaternions and octonions, yes of course and a nobel prize also ahahah RETURN AT SHOOL WITH YOUR FRIENDS AND STUDY IN BELGIUM?INDEED WE HAVE GOOD UNIVERSITIES. You want a course of thermodynamics still in live.
Just a copy about my proportions about the rotations of spheres and mass.Well and after what ??? Let's me laugh. I am not the only one who laughs I am supposing.
STUDY MY EQUATIONS AT THE BELGIAN SHOOLS. Ahahah Solvay you want soon , ok I am going to contact them for a team with me.You want that dear scientists of business.
Just a band of extradimensionalists loving monney.You have lost. Even if your vanity eats you and even if your very hater against me, you have lost. The only solution is to kill me.Perhaps there you shall win my prizes. My ^prizes are for the international humanistic sciences center and what I can't help also perhaps no? Let's me laugh....
Please, let's try to keep this dialogue collegial.
Florin,
When you first exposed me to Joy's work, I reacted in knee jerk fashion to his claim that "Bell got the topology wrong," by saying something to the effect that "So what? He wasn't doing topology." What Bell didn't get wrong was the classical assumption that point particles, like points of R, are correlated by simple...
Please, let's try to keep this dialogue collegial.
Florin,
When you first exposed me to Joy's work, I reacted in knee jerk fashion to his claim that "Bell got the topology wrong," by saying something to the effect that "So what? He wasn't doing topology." What Bell didn't get wrong was the classical assumption that point particles, like points of R, are correlated by simple arithmetic functions, implying by extension that algebraic geometry is sufficient to model all functions in quantum configuration space.
So when you tell me that " ... I can explain this analyses in really easy elementary and trivial steps and the only pre-requisite is simple high school trigonometry and geometry ..." I reply:
So can I. By the same criterion I applied to my answer to Joy, however, I again say, "So what?" We aren't doing algebraic geometry. It's irrelevant to the case in point.
I'm familiar enough with Asher Peres to know that he is very particular to describe quantum mechanics in terms of its own domain, and extract meaning from "the experiment not done." This alone sets any analysis he might make outside the domain of Joy's experimental criteria.
There is no argument to be made, or that can be made, that Bell's quantum configuration space does not map to physical space without a nonlocal model. A theorem is a theorem (which is the reason I strongly disapprove of Joy's use of the term "disproof").
Joy goes a step beyond -- he asks in effect, if physical space is the reality and spacetime is physically real (as so described by Einstein in terms of Riemannian geometry) then why try to describe probability distributions in space with no reference to continuous time? It's clearly impossible -- every measure "at a time" is in an artifical configuration space which merely correlates properties assumed as part of the quantum state at that moment and assigns no reality to measurements not made.
A true pair correlation of properties at arbitrary distance from the initial condition, on the other hand, is consistent with a physical spacetime continuum. Einstein's conundrum was how to avoid the singularity (the boundary condition for time) in order to get a complete *physical* theory from general relativity, which is only mathematically complete (i.e., it renders a closed judgment from first principles in an entirely self consistent way). Quantum mechanics is physically complete (i.e., it completely corresponds to the elementary measurement criteria you referenced above) yet *mathematically* incomplete, because its measurement criteria are preceded by the physical phenomenon (two-slit experiment).
Joy takes physical space on its own terms, and finds a way to use the continuous functions which suppot classical physics to obviate isolated "at a time" spatial measures in favor of pair correlations separated by arbitrary disance in time. While that can't be done in either the discrete method of algebraic geometry, nor in the continuous method of metric tensor calculus, it can theoretically be done in topological analysis, where "distance" has a different meaning than in the less general geometry we're most familiar with.
I don't mean to be self promoting here; however, in my 2008 "time barrier" preprint, 2.12 -- 3.2, I describe "nonlocal measure criteria" based on the desire that Joy, I and Einstein share for a singularity free, nonperturbative theory of creation. Sure, I still disagree with Joy over what "local realism" means, yet that's just philosophy. I recognize that an assumption of "reality" is simply not a scientifically useful assumption. It's enough to know what "local" means.
Steve Dufourny replied on Aug. 11, 2011 @ 14:30 GMT
Points particules you say, yes of course a stringly point AND A TIME TRAVEL WITH YOUR PSEUDO TIME BARRIER OF NOTHING FOR NOTHING also.Well you aren't determinsitic, neither rational, nor universal, nor foundamental. And you insist furthermore with a kind of pseudos maths and pseudos words. That won't change your irrational road and falses conclusions. Just sciences fiction.Where have you studied your maths dear Tom. An advice, don't say us its name of this university, it is bette for your credibility.
You say "While that can't be done in either the discrete method of algebraic geometry, nor in the continuous method of metric tensor calculus, it can theoretically be done in topological analysis, where "distance" has a different meaning than in the less general geometry we're most familiar with." just an ocean of pseudos sciences and confusions.
A theoren is a theorem, no but we dream in live there. If bell's theorem is a theorem then I suspect a real problem at the global scale, and it is not about sciences. But about the business.
A complete theory ahahah if einstein was here, he will laugh with me be sure.And you insist furthermore on a kind of axiomatic road, a pure joke of confusions yes. You describe nothing with your decoherences and non continuity. You aren't really scientists it's not possible, you are just like player in sciences , like just a game. You aren't on the good road, sciences aren't that.
Riemanian geometry and the zeta function you know , well now apply it to thermodynamics and let's laugh together in live.
A quantum space and a QM and after a time barrier, and what also you know einstein, in fact it's ironic you do not understand really the relativity, special and general where the mass curves in 3D and the evolution with c makes the rest with a coded gravity. You confound all in fact, you think really that you understand the relativity , let me laugh Tom, you do not understand what is the realtivity and the universality nor the spherization in 3D. Then don't insist to be a kind of teacher in relativity.You understand nothing about the realtivity.The only thing which interests you, it is the sciences fiction of this relativity , just because you do not understand it really. Then why you insist about a thing totally unknown for you.
Pass the message to your pseudo relativists.You need to study all sciences and perhaps you shall see the whole and the generality but frankly I doubt.
Steve Dufourny replied on Aug. 11, 2011 @ 17:14 GMT
For the sake of casual reader, yes of course.It is that.Of course. Your paper is an ocean of confusions. The problem is your lack of whole point of vue,you confound too much things to be a kind of teacher. I laugh indeed about time travel but you are not far of that with all your decoherences and non continuity.
Let's return at the Riemann zeta functions and the QM and the thermodynamics and the rotations of 3D entangled spheres with their specific volumes.is it possible to speak with real specialists yes or no?
Let's begin pi² cos and pi exp 4 sorry for my maths writing i haven't a program to write.Now insert fourier series ok Tom and with setting x and pi now show me what are your real foundamentals knowledges in live. what is the harmonious series....You have several minutes.
Steve Dufourny replied on Aug. 28, 2011 @ 14:48 GMT
Come on APS linkedin, we shall discuss together with Riccardo Melchiori, David Menard,Narendra Nath, Jim Harlow, Stanislav Sykora,.....we shall see where are your reals rationalities in total transparence. Mer I want well but frankly let's be serious now.
Steve Dufourny replied on Aug. 9, 2011 @ 16:42 GMT
Well the team seems more important than I thoughts.How many are you in fact, me I am alone and just like that I eat your pseudos sceinces, you imagine if I had a tealm also with me, kill me really before.ahahah yes I am crazzy and already dead ahahah do you listen me during your nights, and beforze your dreams, be sure I will be there to say you my theory.Yopur last strategy is to be nice with me or to kill me.Meditate on that.You are very bad fallen.
Ray, when you speak with your friends, say them that it is time to be in the universal reason. But it is just a suggestion. The patriotism is just a human invention, we are all humans, brothers without borders, you can see the universality in this simple evidence.The complexity always returns to simplicity. To be or not to be , That is the question ray.In the past, I thought you shall be in my team in the future, I know now where you go and why you go.
Currently, I am primarily corresponding with Jonathan Dickau and Owen Cunningham. Of the three of us, I think that Jon is the best writer, I have the broadest physics background, and Owen is the best programmer - we each have our strengths and contributions to the group. Every once in a while, we bounce an idea off of Lawrence Crowell - whom I think is corresponding with Christian Corda. I think that Tom Ray has some interesting ideas, but we have not yet worked together. In our last paper, Jon and I studied the websites of some physics mavericks like Tony Smith and Doug Sweetser. I bounce an occasional idea off of Lubos Motl, but try not to overextend my welcome because he is the 'star' of his blog site, and he will cut some people short. Garrett Lisi defriended me on Facebook - we have not had any contact in about a year. To my knowledge, I have not had any direct contact with John Baez. And I mailed Lee Smolin a copy of my book three years ago, but I have never heard from him.
The funny thing is I have not met any of these people. Just like you and me, we all have our own ideas as to what should comprise a TOE, and we may not necessarily agree with everything that the other is doing.
As a Floridian, I am isolated from most of these people. Tony Smith lives about 500 km from me, but he occasionally does business in Valdosta - which is only about 150 km away. That is a reasonable day trip in my opinion.
As a Belgian, you are also isolated from most of these people. Probably the closest regular FQXi bloggers are your Dutch neighbors: Wilhelmus de Wilde and Peter van Gaalen.
I do not appreciate being called a liar. Nor do I have anything to discuss with you. Your ideas are just too far off of 'the normal physics grid'. I suggest that you correspond with Sridattadev Kancharla - who seems to have similar concerns for the origin of consciousness. Or you might want to get together with your fellow Baltimorean, John Merryman.
Steve Dufourny replied on Aug. 9, 2011 @ 22:44 GMT
Lubos is just a vanitious scientist like all scientists. A star , ahaha a sphere then .In the spherrical crackpot index then.ahaha
Ray ,You are I think perhaps the only one who is not in this team then. Smolin tries with Ex of lisi, they just try to make a kind of mathematical packaging. I am laughing , it is so ironic in fact all that Ray, just for this monney. It's so sad. Sciences aren't there for that.
And of course My theory of Spherization has nothing to do with the toe of peter, paul or jacques. My theory is general, respect that.
Author Frank Martin DiMeglio wrote on Aug. 9, 2011 @ 17:20 GMT
Our origins trace back to the center of the human body.
There is no true difference between inanimate and animate in keeping with the fact that being and experience and thought are ultimately inseparable and interactive.
You physicists here at FQXi.org are in the Stone Ages compared to me because you refuse to admit to the fundamentally integrated and interactive nature of being, experience, and thought.
This is, in fact, too much for you all to handle -- both emotionally and thoughtfully -- but I'm not finished with your lessons boys.
Reality/truth/nature just doesn't go away, however -- not without a fight.
You better start seriously examining what (including the effects of) you are doing here.
Have you ever noticed that the invisible eye/body seamlessly adjoins invisible/visible space? Now take this together with the visible body adjoining the visible ground.
What does this mean to you weirdos here who cannot think? I really don't care, but it proves how lost you all are.
Let's assume that there is such a probability distribution like that predicted by you: so that the correlations it provides depend only on a·b. I will call such a thing "Joy probability distribution" or JPD. I will present a succession of steps leading from this hypothesis to a contradiction.
#1. The dot product is invariant under rotations: we can apply a rotation to a and b and we get the same a·b. It follows that the rotation of a JPD is also a JPD.
#2. From equation (16) in arxiv:0806.3078, page 4, we can easily see that if two sets of directions satisfy JPD, their union also satisfy it. Therefore, the arithmetic mean of some JPDs having the same N is again a JPD.
#3. Let us take all rotations of a JPD. By #1, they are also JPD's. By #2, their arithmetic mean is also a JPD. Of course, we will have to take the limit and instead of summing, integrate over all possible rotations of the initial JPD, with respect to the uniform spherical measure which gives the area of the sphere 1, and we obtain again a Joy probability distribution.
#4. But the Joy probability distribution from #3 is nothing but the uniform spherical distribution. This means that the uniform spherical distribution is a JPD.
#5. The uniform spherical distribution leads to a correlation linear in the angle, and not at -a·b, contradicting thus #4.
Hence, unless you point a mistake in my reasoning, the hypothesis that there is a JPD (a probability distribution so that the correlations it provides depend only on a·b) is incorrect.
what I proved above is that if a probability distribution of the lambdas is such that the correlations depend only on a·b, for example E(a,b)=f(a·b), then f(a·b) has to be the same as for the uniform spherical distribution.
Your mistake is that you insist on talking about probability distributions. You will not find any mention of probabilities in my papers, and for good reasons. I deal directly with measurement results for individual physical systems, and so do Einstein, Bell, and Peres. It is well known that factorized probabilites cannot lead to correlations stronger than linear. So why bother with such a useless concept? The goal is to make a correct prediction for the experiemnt at hand using correct physics. Probabilites are not physics. They may be useful elsewhere, but not for the problem at hand. You will find the correct physics and mathematics for the problem at hand in my papers.
I have in the course of a couple of weeks gone from being a complete skeptic to a near convert to Joy Christian's theory.
The qualification "near" is only by way of saying that I still want to quibble over what "locally real" means. There is no doubt in my mind now, though, that Joy's measurement schema hold over arbitrarily far distance. As my ICCS 2006 paper (see esp. sections 2.0 and 4.0) explains, an extension of self similar points of S^0 is self-limiting and infinitely orientable over S^n. The ideas are further explored in this rough draft of a work in progress that I posted elsewhere.
This is pure mathematics. I don't have Joy's talent for physics nor the courage to publish it if I did.
I do grasp the geometrical and topological landscape of Joy's model, however, and I think it's beautiful. I found, in researching the 2006 paper, that correlation of pair functions at a distance is independent of the counting function on R. Take Euclid's fifth ("parallel") postulate that concerns the two right angles formed by a single line through a point external to the base of the angles. We can easily think of these angles as left and right hand correlated, and the line as a null result. So in keeping with our conventional view of numerical results as positive, negative or zero, we would find that all right angles are positively correlated or negatively correlated. I explain the significance of the sign change in the 2006 paper, as a Popper-falsifiable criterion supporting a proof of the Goldbach Conjecture. I provide an existence proof, though with Joy's experiment, it might well be converted to a constructive proof.
By topological criteria, "local" is expansive indeed, and "real" hardly seems to matter.
Cristi Stoica replied on Aug. 10, 2011 @ 07:12 GMT
Tom,
In the paper arxiv:0806.3078, page 4, Joy proposes an interesting experiment, which has two parts. After the first part is done, two data sets result. Then, these data sets are plugged into equation (16) of the same article, to calculate E(a,b). Joy predicts that E(a,b) = -a·b.
You're begging the question, Cristi. You can't write a constructive impossibility proof for Joy's prediction without knowing what pair correlation means in Joy's theory.
What you've done is assume impossibility of a correlation that doesn't exist in Joy's formulation.
Cristi Stoica replied on Aug. 10, 2011 @ 18:28 GMT
Tom,
Please tell me which of the following statements is/are false according to you, and why. They all are about Joy's paper arxiv:0806.3078v2.
1) In that paper, Joy proposes an experiment from which a list of angular momenta results.
2) Joy said that this list of angular momenta can be stored in a computer.
3) When applying equation (16) to these angular momenta and two random directions a and b, a number is obtained.
4) Equation (16) is clear, and all the mathematical operations involved in it are defined. These are the regular sum of real numbers, division of real numbers, dot product, the function sign, product between real numbers.
5) Joy said that a computer can calculate the result of equation (16).
6) Joy said in the paper that if he is right, the number resulting from (16) will approach -a·b for large number N.
7) Joy said that the number resulting from (16) will not approach the number given by (3), (which Peres claims to be).
I would appreciate if you would say clearly which is true and which is false, and for the false ones, if you explain precisely why.
Steve Dufourny replied on Aug. 10, 2011 @ 18:43 GMT
Humbly me I have found how really to encode mass and with its pure reals numbers and spheres and their specific volumes...the rotations are proportionals with mass.
ANGULAR MOMMENT......ROTATIONS OF SPHERES.
MASS ...ROTATIONS OF SPHERES
And our UNIVERSE IS A BEAUTIFUL UNIQUE SPHERE IN ENTROPICAL EVOLUTION.
ALL POSSESSES A CENTER.....OUR UNIVERSE ALSO? THE BIGGEST VOLUME
OUR PARTICLES ARE IN THE SAME LOGIC LIKE A FOTO OF OUR UNIVERSAL SPHERE !!!!!THAT IS WHY WE NEED A SPECIFIC NUMBER FOR THE SERIE OF UNIQUENESS.
They're all true, Cristi. Or else, they're all false. What you're missing is the difference between probability distributions in quantum configuration space, and pair correlations at arbitrary distances in physical space.
The former, we associate with a pair of quantum measurements that are correlated "at a time." The latter, we associate with classical measurements that are time dependent and modeled by continuous functions.
Your model of quantum configuration space is always changing the initial condition by fiat. Joy's initial condition is augmented by correlations of pair characteristics which always existed, up to the cosmological limit. This is because the topological space in which he is working obviates the classical notion of "distance" and by implication (due to the physical reality of spacetime) the notion of the completeness of "at a time" measurement.
One must remember that even so-called quantum formulations such as Bell's are based on classical parameters. (Peres explains this, in fact.)
Cristi Stoica replied on Aug. 11, 2011 @ 11:36 GMT
Tom,
"You proof may be correct (I haven't checked it.)"
I don't know other kind of rejection of a proof.
You see, many people reject Joy's theory without trying to understand it, because they are sure that Bell's theorem is true. By contrary, I spent the last two weeks on his papers, and I gave some physical solid arguments, a mathematical proof, and a computer program which can allow Joy or you to introduce a list which you think will give the correlations predicted by Joy. I did not reject Joy on the basis that I am a fan of Bell. I analyzed Joy's work with the same considerations I analyzed Bell's.
Please don't do to my proof what they are doing to Joy's theory. I expect that, if you declare that my proof is guilty of petitio principii, to be able to show this in my proof, not to derive from speculations, without checking my proof.
I don't ask you to believe me. I ask you to read carefully my proofs before claiming that they are wrong.
Joy Christian replied on Aug. 11, 2011 @ 14:32 GMT
Cristi,
You are not listening to us. Whether or not your "proof" is correct is irrelevant, because you have not understood my argument. As I have said before, you are confusing operationally relevant quantities like lambdas in my equation (16) with the mathematically and conceptually relevant quantities in my argument. If you treat my lambdas as Bell's or Peres's lambdas, then it is trivial to show that the linear limit on correlations can never be exceeded. The lambdas in my equation (16) are not hidden variables or angular momenta in a physically meaningful sense. They are simply stooges for the operational procedure. Moreover, the observed numbers +1 and -1 are in fact occurring on the 3-sphere according to my argument. But I don't see anything remotely resembling a 3-sphere in your "proof." This is because you are starting from the wrong end of my argument.
Steve Dufourny replied on Aug. 11, 2011 @ 18:00 GMT
Oh my god, how could you encode correctly if you do not insert the evolution and the rotations of my spheres. It is purelly not possible, a real quantization is essential.The predictions must be in 3D and muts rest in 3D, but if you haven't a cause for this mass, here my rotating spheres with their volumes entangled. It is not possible. The fact that space, mass and light are the same in a kind of BEC, implies that the rotations become fascinatings when the number, finite is respected.
The determinism, it is that, we have real proportions in a pure 3D and a time constant.Dear Albert, it is not only the angles but several things which are not understood in its pure generality.
A real programm and its algorythms must be precise and rational respecting the entropical evolution, where the mass polarizes the light in a space evolving also. The thermodynamics take all its sense of reasoning. The entropy always....they turn then they are...The real question is this one, fusion and increasing of mass volumes or "binar systems"..you see the informations I suppose and the sorting and synchro by volumes, velocities of rotations spinals and orbitals......and the mass ??? all is there about the E and the m and the hv.....identic but not when they turn....
I am one of those who believe that Bell's theorem is true. It wouldn't be a theorem if it weren't. If the Stoica theorem of Bell-like quantum correlations reproduces those results, I'll gladly accept it as true as well, and if it got different results, I'd look for an error. I just wouldn't be *surprised* that it's true, any more than I would be surprised by one more Bell-Aspect...
I am one of those who believe that Bell's theorem is true. It wouldn't be a theorem if it weren't. If the Stoica theorem of Bell-like quantum correlations reproduces those results, I'll gladly accept it as true as well, and if it got different results, I'd look for an error. I just wouldn't be *surprised* that it's true, any more than I would be surprised by one more Bell-Aspect type demonstration of nonlocality in quantum configuration space. I know that the theory of quantum mechanics is incoherent without nonlocality -- really, I get it.
What informs me that Joy's theory is unrelated to quantum theory (and is not even a Bohm-like alternative formulation of QM, as I've seen some claim) is its dependence on analysis (i.e., continuous functions). This is a purely classical scheme, which deprives us of a great many mathematical tools we are comfortable with (e.g., central limit theorem, equally-likely hypothesis, axiom of choice, double negation proof methods), because we can't force a conclusion on physical space. Bell's theorem tells us that much.
Computers don't do analysis. Computers implement programs. Were it not so, quantum configuration space and physical space would be identical. Again, though, Bell's theorem tells us otherwise -- it's still a very important theorem, and will remain so, for mathematics as well as physics.
Joy says, let physical space do analysis, by experiment. In that case -- and once more, due to Bell's theorem -- either physical space subsumes quantum configuration space as the theorem assumes, and in which we conventionally assign meaning to "the experiment not done" as Peres puts it (implying that God really does play dice with the universe, as Einstein put it), OR:
Quantum nonlocality and superpositions are calculational artifacts without physical meaning. Joy aims to show, in other words, that pair correlations of properties in physical space (i.e., spacetime in the conventional sense of general relativity) are *independent* of quantum configuration space. As a consequence, any pair-correlated properties at the initial condition hold at any arbitrary time thereafter -- and NOT in an abitrarily chosen configuration space (where t = T = 1, by convention). The greater point is that spacetime is a physically real object, just as Einstein described it, and not a mathematical artifact.
I tried to make clear the point that these correlations defy uniform distribution (and therefore obviate general application of the equally likely hypothesis and the central limit theorem) by showing that correlation of irreducible pairs of prime integers [P_1, P_2] is independent of the magnitude separating the integers. Same with physical properties -- the information carried from the initial condition is 100% correlated, rather than 50% as with an arbitrary choice of configuration space.
There really are profound implications here. Experimental confirmation would give us the same advantage that the theory of evolution has in biology. That is, evolution is an observed physical fact that Darwin's theory of common ancestry explains -- even though we cannot do comprehensive experiments on evolution in real time. By the same token, observed pair correlation of physical properties in spacetime would give us the basis for a comprehensive theory of the evolution of spacetime.
Steve Dufourny replied on Aug. 11, 2011 @ 19:31 GMT
Frankly I think people confounds a proof in its pure reality of demonstartion.And their proofs without sense.In fact they want to proof to who, not to rationalists in all case!!!
You said "Your mistake is that you insist on talking about probability distributions. You will not find any mention of probabilities in my papers, and for good reasons."
I can obtain the same conclusion without mentioning "probabilities", as you did in your papers. You predicted that for large numbers the correlation (whatever "correlation" is) is E(a,b) = -a·b (*).
#1. The dot product is invariant under rotations: we can apply a rotation to a and b and we get the same a·b. It follows that if for a set of lambdas (*) holds, it also holds for a rotation of this set.
#2. From equation (16) in arxiv:0806.3078, page 4, we can easily see that if two sets of directions satisfy (*), their union also satisfy it. Therefore, the arithmetic mean of some such sets having the same N satisfies again (*).
#3. Let us take all rotations of a set of lamdas which satisfies (*). By #1, these rotations also satisfy it. By #2, their arithmetic mean also satisfy it. Of course, we will have to take the limit and instead of summing, integrate over all possible rotations of the initial set of lambdas, with respect to the uniform spherical measure which gives the area of the sphere 1, and we obtain again a set of lambdas satisfying (*).
#4. But the set of lambdas from from #3 is uniformly distributed on the sphere.
#5. But such a set of lambdas as in #3 leads to a correlation linear in the angle, and not at -a·b, contradicting thus the hypothesis that such a set of lambdas satisfying (*) which you predicted exists.
Author/expert Frank Martin DiMeglio wrote on Aug. 9, 2011 @ 20:24 GMT
Nature and life prefer LOW ENERGY, not high energy, FQXi.org. Again, you really need to, and you are going to, stop lying.
True/fundamental gravitational and inertial equivalency fundamentally balances attaction and repulsion and combines and includes larger and smaller space in conjunction with low energy and instantaneity.
I demonstrated all of this, and more, in/as dream experience FQXi.org.
FQXi.org, your credibility is ruined. How do you think that it will be salvaged?
The first part of the experiment consists in exploding balls in a particular way and collect the resulting angular momenta.
The second part of his experiment is done by a computer, which calculates the correlations according to equation (19) from Joy's paper. To perform the second part of the experiment, you need the list of angular momenta from the first part.
I created an application which does precisely the second part of the experiment. You can paste a list of angular momenta which is produced by the first part of Joy's experiment, and then test it as in Joy's article (unfortunatelly it will not work in Internet Explorer, but feel free to use Mozilla, Chrome, or Opera).
Of course, I do not require anyone to actually do the experiment, YOU CAN PRODUCE THE LIST OF ANGULAR MOMENTA BY ANY MEANS YOU WANT. You can calculate such a list, assuming that Joy's theory provides the means. Use any Geometric Algebra and any Hopf fibrations you wish, if you believe that only they can provide the correct results.
In my application you can also see what correlations a random list of angular momenta can provide. The randomly generated data looks like it is predicted. You can use it to exemplify Bell's theorem.
If you don't trust me, you can ask your browser to show you the source code and check it yourself (this is why I implemented it in JavaScript).
In a comment above I proved mathematically that Joy's prediction is impossible, and that the only correlations depending only on the angle between a and b are those linear in the angle.
If you disagree with my proof but are unable to find a mistake, please produce a counterexample, and you are free to test it in my application.
Cristi Stoica replied on Aug. 11, 2011 @ 09:47 GMT
Hi Joy,
If it is your word against mine, I have no chance here, and you know it. So I ask you to precisely point the mistake in my proof. Also, please point what is wrong with my algorithm, because it does exactly the second part of the experiment you wrote in your paper.
Please read carefully. I DID NOT MADE A SIMULATION OF YOUR EXPERIMENT, as you said. I made the program which does precisely THE SECOND PART OF YOUR EXPERIMENT. It just takes a list of angular momenta and calculates your equation (19).
The only thing you should provide to my program is the outcome of the first part of your experiment - the list of angular momenta.
I already gave a proof that this list cannot provide the correlations you claim it does. But if you can produce the list, by any means you want, you can just paste it in my application.
I did the application to help you, but if you don't like, please provide the code you consider correct for the second part of your experiment. This way, you will allow other people to test various sets of angular momenta, and see if anyone can obtain your prediction.
Joy Christian replied on Aug. 11, 2011 @ 10:39 GMT
Cristi,
I am not trying to stamp my authority on you. I am simply pointing out that you have completely missed the point of my proposed experiment. Both your "proof" and your simulation are totally irrelevant. What I have proposed in the experiment is to test the actual physical behaviour of the two angular momenta in tendem. The correct prediction of the correlation, based on solid mathematical and physical reasoning, is given in the first part of my paper. The second part of the paper, which you claim to have simulated, is only the operational procedure for recording the actual observations, and then calculating the correlations from these actual observations. You have no idea what the actual observations of the numbers +1 and -1 will be, so you have guessed the behaviour according to your own questionable reasoning. Why should this have any relevance for the *physics* I am proposing to test? I do appreciate your efforts, but I find your whole approach a complete waste of time.
Joy Christian replied on Aug. 11, 2011 @ 11:50 GMT
Hi Cristi,
What you have written is absolutely clear and absolutely irrelevant. As I have said before, no one can supply you the correct list of angular momenta but Nature. That is why an actual experiment is inevitable. I am afraid you are still not getting my point.
Cristi Stoica replied on Aug. 11, 2011 @ 12:05 GMT
Dear Joy,
When you will perform the experiment, please remember me and paste the results in my application. I hope that then you will not find it irrelevant :-)
Of course, I have that mathematical proof which shows that not even God can supply the list which will vindicate your prediction.
I have an idea: I am sure that you know some students who know well mathematical optimization. Maybe they can find a list like that you need. Mathematical optimization is doing precisely this kind of stuff.
I mean, if blind Nature can produce such a list, maybe they can too. Then they can check their results with my simple program.
Joy Christian replied on Aug. 11, 2011 @ 12:25 GMT
Sure Cristi. I will remember you. And some day I will also show you a mathematical proof that proves that not even God can fly heavier-than-air flying machines.
Ray study here now, how could intergrate correctly if you haven't a finite number, and also how could calculate the total system of rotations if you haven't a specific serie,finite also for the quantum number and its uniquneess.In fact DISCRETE AND CONTUNITY ARE IN THE SMAE RELATIVISTIC LOGIC. IN 3 DIMENSIONS FOR A REAL RESPECT OF ALL PROPORTIONS.
SPHERES AND ITS ROTATIONS SPINALS AND ORBITALS AND THEIR SPECIFIC VOLUMES EXPLAIN ALL IF AND ONLY IF THE SERIE,UNIVERSAL IS RESPECTED AND ITS FINITE NUMBER ALSO.
MEDITATE ON THIS REVOLUTION RAY.and study of course.
Dear Florin, and anyone else who knows math and/or at least elementary computer programming
I need your help.
1) Please check my mathematical proof that any list of angular momenta which provide E(a,b) depending exclusively on the angle between a and b, when introduced in equation (19) of arxiv:0806.3078v2, page 4, provides the same correlation as a list of angular momenta uniformly distributed in all directions. This means that any such correlation is linear, and not -cos, as Joy claims.
2) Please check whether the script I created actually does the second part of Joy's experiment.
Then, please post the results of your verifications. If you find a mistake, please state it clearly. If not, please write that you did not find any mistake. Please do not fill the space with pure speculations of why Joy or me cannot be right, but be precise.
After all, my arguments reduce just to simple math operations, and a simple implementation of the algorithms calculating them, as it is described in Joy's paper, so it should not be so hard for you guys.
Albert Jan Wonnink replied on Aug. 11, 2011 @ 17:28 GMT
Correct me when I'm wrong, but one of the problems might be your angle calculation between a and b: you take both a and b as random 3d unit vectors, and use the angle between them. This doesn't correspond to the normal angle difference in a 2d plane between Alice's and Bobs filter setting.
Cristi Stoica replied on Aug. 11, 2011 @ 17:54 GMT
Well, this is not the experiment with photons polarizations. It is the experiment described in Joy's paper, which is in fact the thought experiment from Peres's book, and it allows all directions in space. Anyway, before making it public, I tried what you say: to have the photons in just one plane, along one line, and other constraints. You can simply replace the z axis with 0 in the javascript code and get what you say.
You are free to try any rules you think may help constructing the correlations predicted by Joy.
Cristi Stoica replied on Aug. 11, 2011 @ 19:39 GMT
What is "Cristi's scheme"?
I just provided a proof that there is no such list of angular momenta as you claim your experiment can produce. You claimed that you can produce such a list here.
"We know this since 1964"
From whom? From Bell? I thought you have proven Bell's theorem wrong...
I attach an annotated version of page 4 from Joy's article. I draw on it what part my program does. It does not "simulate" Joy's complete experiment, as Joy misunderstood. His experiment has two parts. Part 1 outputs a list of angular momenta. Part 2 is done by computer: generate random pairs a and b, and applies equation (16) to the list of angular momenta generated by the first part.
My program receives as input a list of angular momenta. Then it just generate the a and b pairs, and calculates (16), as described in Joy's paper. This can be done as well with pen and paper.
My program waits Joy or anyone else to provide the list of angular momenta, and to plot the results.
Until then, you can use it to generate random lists of angular momenta and see what happens.
Or you can try to guess a list of angular momenta which will make the results be along the -cos curve, rather than along the line segment.
Joy Christian replied on Aug. 11, 2011 @ 19:19 GMT
No one can provide Cristi the list of angular momenta he demands. No list of angular momenta within Cristi's scheme can generate the cosine curve. We know this since 1964.
Somewhere in all this, has the basic constitution of reality been lost?
In very simple terms: 'something exists independently of us, and we experience it, individually'.
In more words:
While it has to be assumed that understanding of our existence involves presuppositions and limitations, for the scientific process that is irrelevant. Because, as it is not possible to transcend our existence, we cannot experience anything beyond its confines. So, since the possible state of ‘not-existence’ is unknowable, by definition we can deem experience of our existence a valid closed system. For the scientific process then, the task is to investigate reality as experienced by us, and not conjecture about the unknowable.
Evidence shows that reality exists independently of experience, which is effected at the individual level. The information from reality which we experience is, in the initial phases of the entire process of knowledge acquisition, enabled by different media. So for every existent event in reality, there exist sensory representations thereof. The reality we experience, individually, is a reality of sensory representations. We do not ‘know’ reality directly. Optical images, sound, vibration, etc, are all the result of real physical phenomena, instigated by an independent reality.
This reality can only ever be approximated, by a process of extrapolation, from those individual sensory experiences. The aim of that process being to identify, and then eliminate, any aspect of the outcome which is a function of the process itself. However, at the practical level, it is unlikely that we are able to experience all types of phenomena. Therefore, in order to avoid the loss of potential knowledge, the criteria for what can be accepted as reality must be extended to include entities whose existence can only be determined logically from other validated experiences. Albeit their status remains that of a hypothetical reality, until proven otherwise.
Florin Moldoveanu wrote on Aug. 11, 2011 @ 20:53 GMT
Cristi,
It is too complicated to navigate around this website, and I am starting a new thread here. You asked for my help in checking your proof and source code. I will be happy to. Please do me a favor though:
Can you please copy paste it in a file and attach them to a reply to this post? For the code, please do not add any HTML formatting and just put the Java script functions?
Thanks,
Florin
PS: I accepted your linked in invitation. It's a small world. I see that you know Stupariu Sorin. He did a PhD in geometry in Switzerland I think. I was coleague with him for 4 years in high school and we even sat next to each other for a year or so. He was the best in math in our class.
Cristi Stoica replied on Aug. 11, 2011 @ 23:23 GMT
Florin,
Thank you.
I attach a document with almost no html formatting. I kept it minimal: there is the text area where the user can introduce the angular momenta, and three buttons. I used JSXGraph. Maybe I will LaTeX the proof, so that I can add the equations, which are anyway those from Joy's paper. Anyway, Joy said that it is impossible to construct a list like that, except by his experiment. And that it is irrelevant if my proof is correct anyway.
Florin Moldoveanu replied on Aug. 12, 2011 @ 04:38 GMT
Great work Cristi,
I checked your source code and it is perfect.
About the proof, there are a few things I did not get at first in what you posted so far. Forget about LaTeX. My advice is to make it 100% self consistent and with clear references to whatever you define. For example in #2 you state:
"It follows that if for a set of lambdas (*) holds" What lambdas are you talking about? It comes out of nowhere (in the context of the proof) and they are ill-defined. I am not criticizing the correctness of your proof. The point is to make the proof as understandable as possible and that the reader should not have to do any mental gymnastics to get it. (I think I do get your proof and where you disagree with Joy).
If you are interested, I can collaborate with you to polish its presentation. We can do it on line publicly right here, or off line (my email is fmoldove@gmail.com), whatever you like.
Florin Moldoveanu replied on Aug. 12, 2011 @ 19:09 GMT
Cristi,
Oops, I did find a mistake after playing with you code,
Your function RandomDirection() does not generate a uniform distribution. Here is the corrected code:
function RandomDirection()
{
var ret = new Array(3);
ret[0] = 2*(Math.random()-0.5);
ret[1] = 2*(Math.random()-0.5);
ret[2] = 2*(Math.random()-0.5);
if(GetNorm(ret) > 1)
return RandomDirection();
return Normalize(ret);
};
Your function was generated a randomed filled 3D cube which does not traslate to a uniform S2 distribution. In the fixed version I exclude the values outside the inscribed sphere. With this change now when running your program for large enough data points the points converge to the straight line.
"You are not kidding anyone. Why do you keep uploading just the last page out of context I wonder?"
Please count how many times I gave the link to your full paper (9 times), versus how many times I provided the link to the last page with my annotations (3 times). These are cold, impartial numbers. Someone may think that you are trying to misrepresent my position...
I linked to the page 4 when I wanted to show something which was there: your proposed experiment. Because you misunderstood my program as being a simulation of your full experiment, I annotated on the copy of your page 4 to show which part of your experiment is done by my program, and that it is not a simulation.
So many brilliant ideas are rejected just because are not mainstream, without being given a good reason for this. I think that it is the duty of the reviewers and critics to actually explain where a particular "impossible" theory goes wrong, not to refute it "without opening it", just on the basis of a no-go theorem.
This is why I invested with pleasure two weeks in studying your papers, with the intention to help you, with the little I can. The help can come as blindly acceptance, but also can come as constructive criticism. It also came as a modest computer program which does the second part of your experiment.
I feel that my help is not welcome and the pleasure was not reciprocal. I regret that my good intentions are perceived as aggression on your theory. It's fine, I am busy these days, and I cannot continue to provide you my unsolicited help.
I have anyway the feeling that you are about to understand what I was trying to communicate to you.
I don't want to get sucked into a flame war, but I don't think that Joy Christian lacks any understanding of what you're trying to do, Cristi. It just doesn't have relevance to his theory.
Did I not explain in sufficient detail the difference between quantum configuration space (the space investigated both in the Bell-Aspect experiments and in any computer program relating to quantum nonlocality) and physical spacetime? We're all busy, and none of us are getting paid for this.
Joy Christian replied on Aug. 12, 2011 @ 11:01 GMT
Cristi,
I appreciate your trying to help me (and I take your word for your good intentions), but sadly you have completely missed the point of my proposed experiment. Both your "proof" and your "simulation" are totally irrelevant for my argument. What I have proposed in the experiment is to test the actual physical behaviour of the two angular momenta in tandem. By starting at the output end rather than the input end of the physical problem you have confused operationally relevant quantities with the physically relevant quantities in my argument. In statistical terms, you have confused raw scores with standard scores in my argument. To fully understand my argument it should be read as a whole, not as two separate pieces. Better still, it should be read in conjunction with my latest papers, which explains it more fully. If you do that, then you might understand way what you are doing is completely irrelevant for my argument.
OK, so this comes from 'left of field', BUT has anybody taken a few minutes to relate all this maths, etc to existent reality? The reality we inhabit exists independently of us. So, many of the concepts that underpin QM do not exist. The point is we only know reality through experienceable representations thereof (sight, hearing, etc). For example, an observation is a light based representation of reality. The problems we have in understanding reality at the particle level are purely a function of the process of detection, they do not reflect inherent characteristics of reality. Reality is not indeterminate, it does not exist in 'various' forms until we experience it, etc, etc. Objective and subjective knowledge, as used in QM, relate to knowledge of the 'system'. But that is all it is, knowledge. Real objectivity is concerned with whether any given entity alluded to actually exists, independently of us, not as a concept.
What I am saying is, perhaps investigating any given theorm is a 'red herring' because the fundamental flaw lies in the assumption in QM as to how we relate to reality, which is incorrect.
Joy Christian replied on Aug. 12, 2011 @ 14:58 GMT
Paul,
I am not sure what your background is, but the problems we are concerned with here revolve around a very specific criterion or reality put forward by Einstein, Podolsky, and Rosen (EPR) in 1935. I, for one, take for granted that anyone interested in the issues raised by Bell's theorem is familiar with the history of this notion of reality presumed by EPR. You, however, do not seem to be familiar with this history, which is intimately tied with the history of quantum mechanics.
Now I will go away and try to understand this particular point, because that demonstates a common courtesy. But on the other hand, I don't really need to in order to make my point. If the rules of reality are X,Y,Z, then I do not need to understand any particular theorm , or indeed an attempt to refute it. All I need to do is test whether it complies with X,Y,Z, if not then it is not science but a metaphysical construct.
One point for now, Joy. How does one have a "very specific reality", or "notion of reality"? There is one reality. It exists independently of us. Our experience of it does not create it or alter it in any way whatsoever. That is, of course, given the constraints of our existence. But since we cannot transcend those constraints, other than making that correct logical point, that is irrelevant.
Well, at one level that took 5 minutes. Whether EPR is a paradox or counter to the 'uncertainty principle', etc, is irrelevant. Because all such concepts contravene the nature of the reality we live in. It does not matter whether they are elephants, flowers or quarks. ANY existent matter obeys the same laws. It exists, it is in one form. It is independent of us. What is happening here, and indeed happened in SR (anybody ever wondered why c occurred in the equations?) is that reality is being conflated with the observation of reality. In this case, a light based representation, ie SEEING. If we cannot detect two variables, it is because we cannot detect them. ANY existent entity MUST have a spatial position and velocity at any given point in time. We should not be attributing the failure of our process of detecting reality as a an innate feature of it.
Steve Dufourny replied on Aug. 14, 2011 @ 15:10 GMT
Well for all readers, My theory of spherization, you know this revolutionary theory has nothing to do with the works of Joy or others like extradimensionalists or "higgs fans" or this or that. I am not in the metaphysics me,I don't say that Joy is in this line of reasoning of course,but I must say that my works have nothing to do with the works of all these people. well I observe, I shut up, I contemplate, I recalculate, I make some correlations, I reshut up, I reobserve, I remake links, I contemplate, I reshut up, I recalculate with the corrects deterministic series, I reshut up, I recontemplate and I make my conclusion of spherization, with quantum spheres turning in 3D and with cosmological spheres turning in 3D and an unique universal sphere and its center. They rotate then they are, it is simply a general contemplation of spheres.
Not need of advices after all. We need just rationalists and a pure determinism.
The rest is vain.I am not here to laugh. The courtesy is a important thing depending of many parameters. It is simple in fact the universality.
Whilst it's preferable to get positive responses, engagement is good. After all, I might be wrong, but I am making a serious, but simple, fundamental point. I was thinking of a suitable analogy this morning. How about: Let us assume that all current knowledge indicates that elephants must be grey. Now, without understanding an elephant, if someone presents me with an animal which is red and says it is an elephant, then I know it is not. Though, of course, one always allows for the possibility of new information. But that debate would be about 'not-grey'. It would not be about yellow or blue. But this is what is happening here. The whole debate is about whether one compensatory theory is better than another compensatory theory to patch over the consequence of an original mistake. And it is completely divorced from reality. Reality is constituted as X. Any theory which concerns reality and contravenes that, is null and void. In a sentence, the essential point (X) about reality is: Within the constraints of our existence, which we cannot transcend, reality exists independently, in one form, which we then experience, individually, through sensory representations thereof.
Here's another thought. Schrodinger's Cat. Just assume the QM 'logic'. Then the cat will 'cause' the wave-form collapse and hence 'reality'. A human opening the box will be looking at it post-event!! Ah, I hear, the sensory capabilities of a cat (or indeed any other animal) don't count, only humans can experience, and hence 'create' reality!!!!
Having had an electrical problem fixed on my (camper) van, I am now going off back on holiday for a couple of weeks. But as Arnie said, I will be back.
Steve Dufourny replied on Aug. 15, 2011 @ 17:26 GMT
Paul,
It is a beautiful philosophical interpretation about "how to consider" our pure observations and their irreversibles laws. Now of course the relativity of the schrodinger cat must be taken with this biggest "said" relativity. All is there about the real understanding of what is the evolution, relativistic, of our universal sphere,
and then the understanding of what is really the dynamic of spacetime. The relativity is a tool.
Not need of bizares things, let's accept the 3D....
Okay, so long as we're focusing on only that last page of Joy's proposed experiment (actually, it's a sketch of experimental protocol), why don't we talk about the meaning of a statement that you didn't comment on:
"(mu.n)are elements of two different grades in the algebra Cl3,0 (one is a scalar and the other a bivector), physically they represent one and the same rotor quantity [2]."
I'm seeing that the chief difficulty Joy is having in communicating his intent is truly the reviewer's unfamiliarity with the mathematical terms. It's clear to me that the dimensionless magnitude represented by the scalar coupled to a one dimension channel represented by the bivector implies pair correlation of differently weighted quantities at arbitrary distance from the origin that contains 100% information of the initial condition. (I tried to illustrate this independently of Joy's theory by showing a correlated pair of irreducible prime integers [P_1,P_2] that remain correlated regardless of the difference in magnitude between the primes, i.e., the distance separating them on R.)
Just previously, Joy had made the point that the derivations of (lambda.n) and (mu.n) are operationally identical. So there's no point in plugging a computer-generated list of lambdas which obviously do not convey 100% information of the initial condition into the pair correlation that does. Just as Joy said, the lambdas are a calculational artifact.
I was composing my post to Cristi conccurently with Joy's last post. Mine was not intended as a followup to Joy's, but it's gratifying to see we agree in principle. I do hope we can get the terms clear and move forward on this significant work.
I am not sure what your background is, but the problems we are concerned with here revolve around a very specific criterion or reality put forward by Einstein, Podolsky, and Rosen (EPR) in 1935. I, for one, take for granted that anyone interested in the issues raised by Bell's theorem is familiar with the history of this notion of reality presumed by EPR. You, however, do not seem to be familiar with this history, which is intimately tied with the history of quantum mechanics.
Joy
This illuminates the problem. Worrying about the correctness of EPR, Bell, etc is irrelevant. Because the problem lies in a fundamental premise of QM, as to how we interact with reality. Take the projector Joy uses in the video. If we brought the entire human race AND all animal life forms into the room (the latter is important because most arguments presume reality is a human preserve), then EVERY SINGLE organism would recognise its existence. The animals would sit, walk/swim round it, etc. The differences in describing the reality of projector would be due to sensory capability, culture, etc. In other words, the differences are a function of the PROCESS of experiencing reality, not reality itself. Within the constraints of our existence, which we cannot transcend, reality exists, in one form, independently, of all living life forms capable of experiencing it.
Now, until proven otherwise, there is no reason whatsoever to presume that elementary particles behave in any form of 'irrational' way when compared to more composite entities. As stated some 100 years ago, studying them is certainly a different, and problematic, enterprise. But those practical issues must not be reified and attributed to inherent characteristics of the reality of elementary particles. Neither should the way in which we actually intereact with reality be contravened, because we are considering elementary particles rather than elephants. Even if the simple fault has been disguised by a whole range of complex sounding concepts such as uncertainty, complementarity, entanglement, superposition, waveform collapse, local reality, hidden variables, etc, etc.
Just put your pens down for 5 minutes and think about it.
For me, the question of whether Joy's theory is true or not, is settled. It is.
Knowing that in the larger world it will probably be controversial for a while longer, however, I'd like to get a dialogue started along the line that "If Joy Christian is right, these consequences follow ..."
Having found my "lost notebook" as I mentioned in Florin's blog "To be or not to be ..." I...
For me, the question of whether Joy's theory is true or not, is settled. It is.
Knowing that in the larger world it will probably be controversial for a while longer, however, I'd like to get a dialogue started along the line that "If Joy Christian is right, these consequences follow ..."
Having found my "lost notebook" as I mentioned in Florin's blog "To be or not to be ..." I realize why I laid it aside a year ago. The conclusions seemed just too "out there." Now, though, Joy has shined considerable light on the paths of some leading edge problems. The most important, in my opinion, is Einstein's singularity problem; i.e., the inability to model physics with continuous functions in a relativistic domain without arbitrarily specifying boundary conditions ("Did Nature have a choice ...?")
In my notebook beginning 9 Aug 2010, I wrote the heading: "Kissing curves of S^n implies physical string dynamics."
Then I followed with the known definition of hyperbolic space (the space where string theory originates): "H^n is a maximally symmetric, simply connected n-dimensional Riemannian manifold with constant sectional curvature - 1."
The text:
1.0 The most fundamental aspect of string theory is the substitution of objects of nonzero length for point particles. More recent advances (ref Witten) favor 2-dimensional objects (branes) that imply a nonperturbative theory in 11 dimensions.
A background independent nonperturbative theory of this kind that unites quantum mechanics with general relativity is necessarily a continuous field theory -- i.e, the geometry of the field that includes a time continuum is smoothly connected to infinity.
The problem is finding the zero points. If particles are not described as points, but rather oscillating ends of hyperdimensional strings or branes, what does "zero" mean?
In standard particle physics, we understand the role of vacuum energy; virtual particles give us a zero place of origin -- the price, however, is a statistical inference that obviates time and requires infinite spatial extent. We renormalize to 1, when we record observations, but this "by hand" technique is unsatisfactory to most. Why should Nature demand a "screen" of sorts, between reality we can describe and an inaccessible singularity that jumps all over eternity until we ask where it is and how fast it is traveling?
Time dependence implies scale invariance(I have brackets around this statement with a big question mark, but I now believe the statement is true). And our time dependent measures are always local, so we shouldn't be surprised that solutions are infinite and that renormalization works.
The "screen" is a scale invariant field of infinitely self similar random fields. The localized measure, being time-dependent, is the least moment in which this complex network can match point for point between observer and point in the field.
(There is a figure of two superimposed quadrangles, the background object is labeled C*, and just inside the superimposed object a point is labeled P "hyperbolic projection" with a double headed arrow extending past the boundary of C* to a dot labeled "0" and the callout "R^n")
There is reference to Zaslow in Tim Gowers' Princeton Companion of Mathematics, p.163: "Every complex manifold of (complex) dimension n is also a real manifold of (real) dimension M = 2n." Also, pp. 163-164, "Complex manifolds always have real orientation." R_ij = 0.
[There's a lot more, but I am going to end my notebook text here, for now.]
It should be apparent that Joy's model fully accommodates pair correlation by orientation to all points of S^3. Why is this important? -- because it allows non-arbitrary boundary conditions for general relativity, in which "all physics is local." Joy's "Pacman screen" metaphor of two interchangeable antipodal points could never apply to Minkowski space-time which is finite in time and bounded in space. It does apply however, to a model which is finite in space and unbounded in time. Remarkably, this conversion does no damage to general relativity at all! -- it does give us access to antipodal points, however, that never disappear and at which paired events are correlated at arbitrarily far distance. As I showed in my remarks in Florin's "To Be or not to be ..." blog, the 4pi revolution in Joy's topological space vice the 2pi revolution in quantum configuration space (another Joy Christian result) orients all events to real (i.e., Lebesgue) measure between the two edges of.the "Pacman screen" which are imaginary.
As I implied, this formulation could very well open the door to real world string theory experiments.
My concern is that Equation 8 of paper 11060748 leads Joy to an answer of ±1 and Joy interprets this as the spin of the photon – either up or down. On my first read-through of his paper, I interpreted this as the wavefunction symmetry, and a full solution should include all complex phases exp(iθ)(Anyons) between −1 (Fermions with θ=π) and +1 (Bosons with θ=0,2π).
Anyons exist on a 2-D membrane, have continuous symmetry characteristics ranging from Fermion to Boson, and MAY also be tachyons. If Joy is accidentally using tachyons (and is interpreting it differently) then this completely negates any conclusions about locality vs. non-locality because theoretical tachyons of imaginary mass always travel faster than the speed of
light.
Thus far, my comments have been ignored. Am I 'crazzy', or am I looking at it wrong? Regardless - no one has responded to my concerns.
Furthermore, Cristi and Delta Kilo have expressed concerns. I know that Cristi is tired of being teamed-up on (and this is part of why I have been somewhat quiet), and I haven't seen an answer to D.K's concerns.
Even if Joy's math is 100% correct (and I am concerned about a potential fault for not including all complex solutions, and D.K. is concerned about a possibly inconsistent use of scalars, vectors and tensors), we must be sure that his interpretations are 100% correct.
Another interesting thing in that notebook. I found a longhand message to Lev Goldfarb in a forum that Brendan had set aside titled "Limits of mathematics in cosmology" for the sole purpose of discussing Lev's ETS program (colloquially speaking, numberless computing). Lev and I have been going around about this for several years. Insofar as Lev and I share many opinions on computing and information theory (including the role of time independent of space), one wonders if Lev's "pairs of primitives" correspond to pair correlations in Joy's theory. I'll leave that judgment to others. The dialoque is in the thread "Lev Goldfarb wrote on Aug. 23, 2010 @ 14:48 GMT" "T H Ray replied on Aug. 26, 2010 @ 16:58 GMT"
Joy Christian replied on Aug. 16, 2011 @ 17:38 GMT
Ray,
Yours was one of the first questions I answered and you seem to be happy with my answer. As to your present note, both Bell's theorem and quantum correlations are concerned mainly with binary results, +1 and -1, not with wave-functions of any kind. You are indeed reading my paper quite incorrectly. As for Cristi's and Delta Kilo's concerns, I have repeatedly explained that what Cristi has done is completely irrelevant to my proposed experiment. I have also explained that Delta Kilo's objections are based on his total lack of understanding of basic statistics, as well as of the language of geometric algebra. Florin has also pointed out Delta Kilo's errors. Unless you know the latter language and well-versed in the literature on Bell's theorem, you are likely to misunderstand my work. It is also important to note that mine is not a theory, but a local-realistic framework, whose main purpose is to reproduce all quantum mechanical expectation values in a local and realistic manner. As a comprehensive program towards this end, my work is spread out in some eight papers. You seem to have read only one of my papers, however.
"Think classically?" We are talking about QUANTUM correlations, but Anyons have continuous (classical-like) wavefunction phases. Problem solved, but it doesn't say anything about locality vs. non-locality because Anyons are the most non-local thing that you can imagine...
Dear Joy,
I read a couple of your papers. But in the above-mentioned paper, if Equation 8 requires complex solutions (and reducing a 3-sphere down to 2-spheres *SHOULD* introduce an continuous circle of solutions, not simply plus or minus unity), then Equation 11 and so on are defective. Furthermore, I think that the paragraph between Equations 12 and 13 is an interpretation that may or may not be correct (and a different solution for Eq 8 will lead to a different interpretation). From our early questions and responses, we seemed to be on different pages. I honestly have not had the time to try to tear your paper apart (Lawrence Crowell would understand my points, but he has also been busy), and I apologize if I sound like sour grapes.
I do agree that octonion-like 7-spheres and quaternion-like 3-spheres should be important. Close-packing of 7-spheres builds up an E8 Gosset lattice. And close-packing of 3-spheres builds up an F4 24-cell lattice.
Joy Christian replied on Aug. 16, 2011 @ 18:55 GMT
Ray,
There are no complex numbers or complex solutions in geometric algebra. And Bell's theorem is about local-realistic (or "classical") theories, not quantum theory.
Did you get that last from Joy, Ray? It took me a while to get it, too. You are talking about statistical particle behavior, which has nothing to do with Joy's continuous function model. And it's really quite nice mathematicallly, where complex calculations produce real measure. ("All real functions are continuous.")
There are no complex numbers or complex solutions in geometric algebra. And Bell's theorem is about local-realistic (or "classical") theories, not quantum theory.
I agree that if we stay on the surface of an imaginary 7-sphere or an imaginary 3-sphere, then all points on the surface are real/space-like (all radii are imaginary/time-like), but you still require a phase between 0 and 2 pi to define a point on the circle of 2-spheres intersecting a 3-sphere (each 'point' on the 3-sphere surface requires 4 coordinates, which can be reduced down to the phase within a 3-D plane). I don't see a simple plus or minus unity solution.
Bell's Theorem seems to contradict some quantum postulates, but a complete proof must include some quantum concepts. I think that a particularly quantum property that needs to be considered is wavefunction symmetry. Why are Bosons and Fermions so different? Why do antisymmetric Fermions obey the Pauli Exclusion Principle, but symmetric Bosons do not? Classical physics cannot explain these phenomena. Have you accomplished anything if you use purely classical operators to prove a classical concept? Have you proven locality vs. non-locality if your solution necessitates non-local Anyonic tachyons?
I'm not interested in a long-term debate. I just wanted to say my 'nickel's worth'.
Joy Christian replied on Aug. 16, 2011 @ 20:17 GMT
Ray,
I appreciate your questions and concerns. The numbers +1 and -1 appear in my formalism as limiting cases of the general multivectors (see, e.g., eq. (19) and the discussion that follows). These limiting cases behave exactly as the measurement results considered by Bell in his first paper. There is no question of looking for solutions of the kind you are suggesting. Bell's theorem concerns only about coming up with a correct set of Bell-like functions that reproduce the quantum correlations in a local-realistic manner. In particular, Bell's theorem is not about quantum theory at all, and Bell's proof does not employ a single postulate of quantum theory. I recommend going through Bell's original paper and his proof. I am afraid you have fundamentally misunderstood what Bell's theorem is all about. What I have to show to counter Bell's theorem (and what I have indeed shown) is that I can reproduce any quantum mechanical correlation (i.e., any quantum mechanical expectation value) purely local-realistically. That is all one has to do to counter Bell's theorem (in fact one has to do much less, but let me be generous to Bell).
I understand that Bell's original inequality is based on classical statistics, and Tom is the one who says "think classically", but if you really want to settle the local vs. non-local question, you need to include QUANTUM entanglement, and you can't accidentally include NON-LOCAL Anyons.
A 3-sphere could decompose into a circle of 2-spheres, not a two-valued bivector of 2-spheres. I think that you have artificially collapsed the 3rd spatial dimension, and this confusion has led to further confusion in your interpretation of spin-up and spin-down photons (how would a longitudinal Z boson behave in your scenario?).
Perhaps we are on different wavelengths, and need to "agree to disagree" for now. I did not come here to "kick sand in your face" on your blog thread. I was simply disagreeing with Tom's opinion that this question is "settled".
Joy Christian replied on Aug. 16, 2011 @ 22:04 GMT
Ray,
We are indeed on different wavelengths. Local vs. non-local question is decisively settled in my papers. I have shown quantum entanglement and quantum non-locality to be illusions. At least Tom seems to have understood this.
Thanks for your questions and comments in any case.
For the record, I said that for me, the question is settled. I well understand, and I think Joy also understands, that for a generation brought up on statmech and its quantum mechanical extension, quantum configuration space is identical to physical spacetime.
Joy intends to prove by experiment that that identity does not hold. So it's proper that he refers to "a...
For the record, I said that for me, the question is settled. I well understand, and I think Joy also understands, that for a generation brought up on statmech and its quantum mechanical extension, quantum configuration space is identical to physical spacetime.
Joy intends to prove by experiment that that identity does not hold. So it's proper that he refers to "a local-realistic framework" of continuous functions that subsumes quantum mechanical predictions. I.e., while quantum mechanics simply does not work without a nonlocal model, and no reality is assigned to "the experiment not performed," a locally realistic model has no boundaries between theory and result. Observer and observed are thus entangled in continous function measure, rather than simple discrete outcomes that assume a third observer (the experimenter). This is why Joy can refer to "quantum entanglement and quantum non-locality" as "illusions." The quantum configuration space where the measurement terminates and nonlocality begins is independent of the physical spacetime -- and while we've always known that Bell's theorem is formulated within classical parameters, to Joy the parameters have to disappear and be absorbed by classical measure without boundaries; IOW, the parameters (adjustable variables) are identical to the physical spacetime. Why? **Because spacetime is physically real.** (I think Hawking almost got there with his "no boundaries" proposal years ago but stopped short of the prize.)
I have gotten past any skepticism I had in the beginning about Joy's method, especially after I realized that he was using S^7 only to orient the observables on S^3. I still disagree, however, with some of his choices of natural language terms -- I've already spoken up about "disproof" and I have no more to say about that. In the same vein, the use of the term "illusion" for entanglement and quantum nonlocality bothers me -- it implies that we are deluding ourselves in our formulation of quantum event space, yet that isn't the case; we are simply applying statistical methods to a domain that doesn't map to spacetime, because with quantum mechanics we aren't modeling a time dependent system.
In the dialogue with Cristi about the operational identity between (lambda.n) and (mu.n), Joy referred to the lambdas that Cristi was misusing as "stooges" for calculational purposes. He might better have referred to them as mathematical artifacts -- the real message is that lambda and mu are correlated at arbitrary distance from the initial condition, and are not separable in the sense that Cristi was trying to do with his independent list of lambdas.
I explained the role of mathematical artifacts applied to physical models in my "time barrier" preprint (3.1 - 3.2) by the example of Einstein's famous E = mc^2. We do not need c^2 to inform us that E = m. All sorts of nonsense (particularly in this forum!) has been written on the role of c^2, which plays absolutely no part in the conclusion of special relativity other than to correlate the continuous relation of mass to energy at arbitrary points of continuous spacetime limited by relativistic time/distance. Likewise, the pair correlations of lambdas and mus in Joy's framework are in continuous spacetime and not separated by mathematical artifacts that instantiate the meaning of that relation without changing the relation. We get an inverse result, E(a,b) = -a.b for the same reason that E and m are inversely proportional to c^2 in special relativity -- and it's a reason that Joy has explained. The S^3 topology without boundary, with a Moebius like twist, correlates proportionality at antipodes, as inverse pairs. Same with E = m -- even though energy and mass are directly proportional as a linear algebraic statement, spacetime transformations describe nonlinear correlations by inverse proportionality. Again, this is because **spacetime is physically real.** So far as the real measurement result is concerned, remember that proportion and recursion are native to R. And R, unlike the space of probability functions, is continuous.
I very much appreciate Joy's use of S^7 and S^3. These directly correspond to octonion and quaternion algebras. If we consider a quaternion to consist of one 'real' coordinate (the 'scalar' component of a quaternion) and three 'hyper-complex' coordinates (the 'vector' component of a quaternion), then it is easy to translate this into a 3-sphere with 3 space-like (or time-like depending on overall phase) and 1 time-like (or space-like depending on the aforementioned phase) radius. The exact same idea applies to octonions and S^7, but now we have one 'real' coordinate (a time-like radius) and seven 'hyper-complex' coordinates (a space-like hyper-surface).
S^7 and S^3 (as well as the 'complex-like' S^1 and the 'real-like' S^0) are parallelizable and thus stable against the Hairy Ball Theorem, and close-packing of these hyper-spheres leads directly to the E8 Gosset lattice (for an octonion-like S^7) and the F4 24-cell lattice (for a quaternion-like S^3).
In our last paper, Jonathan Dickau and I defended the use of quaternions and octonions in physics. Jon and I have reasons to expect S^3 to be more stable than S^7, and I feel that Joy's use of S^3 can certainly be justified. I just don't understand the bi-vector analysis - it seems obvious to me that an S^3 would decompose into a continuous circle of S^2's. What is the implication of this continuous choice of 'phase' from 0 to 2 pi? Are these the continuous wavefunction symmetries of Anyons - where pi = Fermions and 0 & 2 pi = Bosons? Are these the infinite number of different angle choices in a Stern-Gerlach experiment? Joy expects a bi-valued bi-vector of plus or minus one, and relates this to the spin up or spin down of a photon. But what about the Z boson? The Z boson behaves much like a 'massive photon' but it now has spin projections of plus one or minus one (the transverse modes), OR zero (the longitudinal mode) - a 'zero' option is clearly excluded by Joy's bi-vector analysis, but you cannot deny the existence of longitudinal Z bosons.
Joy Christian replied on Aug. 17, 2011 @ 16:19 GMT
Hi Ray,
The "zero" option is not excluded. In my analysis the numbers +1, -1, and 0 are answers to the experimental questions that may or may not correspond to anything physical. As I mentioned before, mine is not a physical theory but a conceptual framework in the tradition of von Neumann and Bell. The concerns of foundationalists like myself are different from those of particle physicists. Nevertheless, one can interpret the answers +1, -1, and 0 as corresponding to three spin projections you mention. In my scheme they correspond to "up" detection, "down" detection, and "null" detection, respectively. Bivectors themselves are bivalent, but the possible results extracted out of them are trivalent. Alternatively, each one of the three results can be reduced simply to yes/no answers, falling in the set {+1, -1}. I haven't done any of these things explicitly, because they are not my primary concerns. But all these things can be done. The formalism is sufficiently general to accommodate all sorts of physical systems and experiments.
So your bi-vector represents an SU(2) algebra with 3 degrees-of-freedom? Hmmm... You know I could dream up even more exotic cases (like gravitinos) if I had to.
I'm still concerned that if we collapse a 3-sphere consisting of a space-like hyper-surface and a time-like radius into a bi-vector of 2-spheres consisting of a space-like surface and a time-like radius, then we have improperly collapsed our 3rd spatial dimension into 'up', 'down' and 'null' and discarded any 'measure' along that axis.
The only way I see to get bi-vector behavior out of this is for a 3-sphere consisting of a space-like hyper-surface and a time-like radius to collapse into a bi-vector of 2-spheres consisting of a space-like surface and A SPACE-LIKE RADIUS. Such an analysis would scramble our definitions of space and time (I think it would ultimately require complex time and complex space with nothing 'purely real'), and I'm uncomfortable even mentioning this idea because I'm pretty sure it would cause more confusion than simplification - contrary to Occam's Razor.
Thankfully, Joy preempted what I was going to say about particle physics vs. classical continuous functions.
Copying from my post in Florin's "To be or not be ..." blog, 15 Aug 1715 GMT:
The y axis is always oriented on kissing equators; the x axis, always on a fixed point of a hyperbolic projection. Therefore:
(+1, -1, i)^1 = i
(+1, -1, i)^2 = 1 (1 + 1 - 1)
(+1, -1, i)^3 = 1 (1 - 1 + 1)
(+1, -1, i)^4 = 1 (1 + 1 - 1)
(+1, -1, i)^5 = i
The set of results (+1, -1, i) are the only results that live on the equator of S^3. Note that Joy finds that rotations through 4pi (vice 2pi) is necessary to return the null result (zero). That's what this ordered series of exponential operations represents -- between i and i', each complete rotation through pi returns the same set of real numbers, which are always + 1 or - 1. This is fully consistent with Euler's geometric interpretation of the complex plane generalized to S^3 and with the Lebesge measure in real analysis.
Please humor the resident Particle Physicist. The issue of locality vs. non-locality may introduce questions such as quantum entanglement or the super-luminal relay of information. It involves assumed properties of geometry and particles.
I think I understand this S^3 geometry. Are you further imposing F4 (kissing-spheres) geometry? I agree with the possible importance of the F4 24-cell, but did not read that into Joy's solution of Eq 8 at all.
Please answer these simple questions:
1) Shouldn't a 3-sphere decompose into a continuous circle of 2-spheres?
2) How does a continuous circle equate with the discrete set of (+1,0,-1)?
It looks like you are using Cayley-Dickson construction to build unit-octonions (7-spheres) out of pairs (bi-vectors) of quaternions (3-spheres). By construction (why unit radius? at least we know how to reconstruct h=1=c, there is no way to reconstruct any magnitudes or measurements here) these have the sort of quantized behavior that you were describing. I'm still having trouble grasping the connection with Joy's statements:
"Moreover, it is easy to verify that unit bivectors such as I · b simply
represent intrinsic points of a unit 2-sphere contained within the 3-sphere:
||I · b ||2 = (+I · b)(−I · b)
= −I2 b b = b b = b · b = ||b||2 = +1 . (8)
More precisely, they represent the equatorial points of a parallelized 3-sphere modeling the physical space"
"I explained the role of mathematical artifacts applied to physical models in my "time barrier" preprint (3.1 - 3.2) by the example of Einstein's famous E = mc^2. We do not need c^2 to inform us that E = m. All sorts of nonsense (particularly in this forum!) has been written on the role of c^2, which plays absolutely no part in the conclusion of special relativity other than to correlate the continuous relation of mass to energy at arbitrary points of continuous spacetime limited by relativistic time/distance. Likewise, the pair correlations of lambdas and mus in Joy's framework are in continuous spacetime and not separated by mathematical artifacts that instantiate the meaning of that relation without changing the relation. We get an inverse result, E(a,b) = -a.b for the same reason that E and m are inversely proportional to c^2 in special relativity -- and it's a reason that Joy has explained. The S^3 topology without boundary, with a Moebius like twist, correlates proportionality at antipodes, as inverse pairs. Same with E = m -- even though energy and mass are directly proportional as a linear algebraic statement, spacetime transformations describe nonlinear correlations by inverse proportionality. Again, this is because **spacetime is physically real.** So far as the real measurement result is concerned, remember that proportion and recursion are native to R. And R, unlike the space of probability functions, is continuous."
Are you using Einstein's theory as a prop to explain by comparison more about Joy's work, or, are you suggesting that Joy's work is dependent in some way on Einstein's theory being descriptive of reality? Just looking for what actually pertains to Joy's work.
This is just hyper-geometry (if it is being done and interpreted correctly...) - nothing about mass-energy equivalence here! To Tom's point, c is just a scale limit and units to provide a constant of proportionality.
The 3-sphere is a representation of a quaternion with 3 space and 1 time dimensions in which the imaginary 'i' phase of time in the Minkowski metric naturally arises. Now there is no reason to worry about 'ict' because we understand that 'i' is the quaternion mathematics, and 'c' provides the proper units. One of my concerns about what Joy and Tom are doing is that they are using these +1 and -1 signatures from a Minkowski metric, they are throwing away the constant of proportionality 'c' (we can recover this if need be), but they are ALSO throwing away the measurements (like 't' that cannot be recovered).
In my Aug. 17, 2011 @ 17:09 GMT above, I was concerned that a 3-sphere with 3 space and 1 time dimensions might be artificially collapsed into a 2-sphere with (2+1) space dimensions. Such a scenario would lead to a really messed-up concept of Time in particular and Spacetime in general.
Regardless of what may or may not be popular, I still think of Spacetime as a quaternion with an overall imaginary phase.
I understand Tom's deep committment to Relativity theory. His contributions and Joy's clarification have definitely been worthwhile reading for the purpose of understanding Joy's work. I was looking for Tom or Joy to say that Joy's work would or would not exist if Relativity theory did not yet exist. Something like that to clarify whether Tom is taking an opportunity to take shots at others in the middle of giving his view of Joy's work when it may not be an ingredient necessary for Joy's work.
"To Tom's point, c is just a scale limit and units to provide a constant of proportionality."
That is true only if Relativity theory is true. I see this concept as significant evidence that Relativity theory is wrong. I really would like to avoid mixing concepts that have no direct purpose in Joy's work with explanations of Joy's work. If analogies are being implemented, then I would benefit from having that made clear and distinguishing between what Joy is doing and unnecessary interjections that might cause confusion instead of adding to clarity.
I have read your contributions to this thread also. I appreciated having your input both previously and in the above message. Thank you for helping.
Joy Christian replied on Aug. 18, 2011 @ 06:33 GMT
Hi Ray and James,
The framework I have presented is a purely non-relativistic framework. Neither Bell's theorem, nor its variants like GHZ and Hardy theorems, nor my own work criticizing all such theorems, needs to know anything about relativity theory. Bell formulated his local-realistic framework on a meta-principle, known as a common cause principle, which does not need to know anything about relativity theory, and yet it is compatible with it. He claimed by his theorem that no local common cause---i.e., no local hidden variable---can explain the EPR correlations, where "local" simply means that two measurement results, such as A and B, are linked only by the common cause and nothing else. I have shown, however, that Bell was wrong. Not only the EPR correlations, but *all* quantum mechanical correlations can be understood as arising purely from a local common cause---namely, the local orientation of a parallelized 7-sphere (which in turn is simply a twisted bundle of 3-spheres). No relativity principle of any kind needs to be invoked to understand either Bell's work or mine. So while I have nothing against relativity theory (in fact I have generalized it in a different context), I fully agree with what James is saying. Relativity theory is not an ingredient necessary in any way to understand my work.
Don't you feel you owe it to James to explain the difference between your statement, that one " ... does not need to know anything about relativity theory ..." in order to understand your framework, which is true, and his statement, "I see this concept as significant evidence that Relativity theory is wrong," which is not true?
Time is conserved in Joy's framework. (I am happy that he refers to it as a "framework" rather than "theory," as others have labeled it, a convention I will follow from now on.)
Time is NOT conserved in my theory, which is a physical theory requiring physical information loss (Shannon entropy) by dissipation of the time metric over S^n manifolds asymptotic to length 1 in hyperspace. This loss, which I precisely calculated, is very slight but significant to local reality. The scheme requires analytical continuation over the equator of kissing spheres, as you noted. On the other hand:
I have been somewhat baffled as to why Joy is being constantly misinterpreted in his statements, which are not at all obscure, not all that challenging mathematically, and easily verifiable by conventional methods. I am guessing that it may be because we are used to thinking of the world as consisting exclusively of material particles. That being the case, the measurement criteria that we apply to what we call "physics," always rest in the domain of mass points and changes in the relationships among them.
Einstein had the tremendous insight, though, to see that time is not physically real and space is not physically real -- only spacetime is physically real (" ... independent in its physical properties, having an effect but not itself influenced by physical conditions.")
Independent of interaction with matter, physical spacetime is always "locally real," as Joy avers. That is how he can confidently say that "The formalism is sufficiently general to accommodate all sorts of physical systems and experiments." Quantum entanglement of matter states is thus an artifact of calculation in physical spacetime and not a fundamental property of reality.
Joy Christian replied on Aug. 18, 2011 @ 11:09 GMT
Hi Tom,
You are absolutely right. I should have made it clear that my work is in no way evidence against relativity theory. On the contrary, it is precisely the meta-principle of local causality underlying relativity theory that drives my entire life's work (against considerable sociological odds, if I may add).
For what it's worth, I think we'll both live to see that sociological resistance fall away, like a rotting scaffold surrounding the true and beautiful piece of art living within it.
I have an upcoming business trip and will be unavailable next week, but I wanted to make a final point.
If we think of the 7-sphere as an octonion of radius 'ict_1', and the 3-sphere as a quaternion of radius 'ict_2', then considering unit hyper-spheres seems to quantize time. I would strongly argue against such.
However, I see two possible ways out of this trap:
1) We can simply equate t_1 and t_2 and track this magnitude (it probably divides out via a geometrical property anyway), or
2) We can use a 16-D bi-octonion model where we take the inner product of a an octonion-like 7-sphere of Space-Time (with time as its radius and space as its hyper-surface) with an octonion-like 7-sphere of Energy-Momentum (with energy as its radius and momentum as its hyper-surface) such that we may have Planck-constant-sized increments of Action.
For a simple hyper-geometrical argument, option 1 may be good enough. If you want to make a more quantum-compatible argument, you might look a option 2.
Some confusion exists about Relativity. None of Einstein's postulates need to be considered here IF local reality is true, but the Minkowski metric of:
-1,+1,+1,+1 is fundamental to understanding quaternion mathematics, and a 'generalized Minkowski' metric of:
-1,+1,+1,+1,+1,+1,+1,+1 is fundamental to understanding octonion mathematics.
If you are being fully-consistent with these products of -1 and +1, then a 'null' result equates with 'nothing'. I would argue that the longitudinal mode of the Z boson is 'something'. As I implied earlier, I could always dream up a more exotic counter-example - such as massive gravitinos with spin projections of +3/2, +1/2, -1/2, -3/2.
I honestly think that a 'magnitude' or 'measurement' is being overly-simplified to unity here. I'm sure that it can be 'fixed', but I'm not sure that you see my point.
"For what it's worth, I think we'll both live to see that sociological resistance fall away, like a rotting scaffold surrounding the true and beautiful piece of art living within it."
Is a followup of this remark of yours:
"Don't you feel you owe it to James to explain the difference between your statement, that one " ... does not need to know anything about relativity theory ..." in order to understand your framework, which is true, and his statement, "I see this concept as significant evidence that Relativity theory is wrong," which is not true?"
Then I have two things to say: Why are you messing up the flow of this thread with irrelevant opinion? And, No I am not wrong, the errors that have been missed begin with the choice to make mass an indefinable property. There are others that followed. Get those errors corrected!
My interest in following Joy's work has absolutely nothing to do with what you are saying or with what I am saying about these unrelated matters. Your contributions to explaining Joy's work are appreciated.
As I read some of the responses to my blog post, I think the following four reasons may explain why my ideas are not understood by some:
(1) The first reason is my own limitations of presenting my ideas. The nine papers I have written on the subject were written in the course of four years, with the earlier papers inevitably being less clear in presentation than the latter. Ideally I would like to go back and rewrite all of the nine papers to make a single comprehensible argument out of them. But that is of course not possible for all sorts of practical reasons.
(2) The second reason is the unusual language of geometric algebra I have used in my papers. Geometric algebra is a powerful and comprehensive mathematical language, but unfortunately it is also based on rather unfamiliar ideas that require getting used to. At first sight the symbols appearing in this language may appear the same as the ones we are used to, but they are not. The physical and mathematical meanings of the symbols are quite different.
(3) The third reason is the incredible confusion that exists in the community about what exactly Bell's theorem is all about and what exactly it is supposed to say about the future theory of physics. It is ironic that for a theorem that has made such an impressive sociological impact on the community, not a single clear and universally-agreed statement exists. In most commentaries on the theorem one only finds some vague and non-rigorous ideas of the theorem, compounded by much inflated informal claims. For example, claims like: "no local and realistic theory can reproduce all of the predictions of quantum mechanics." It is of course impossible to give a rigorous proof of such a nebulous statement. Nevertheless, it is this non-rigorous statement that is believed-in by many. Worse still, the actual rigorous proof of the theorem, as it appears for example in Bell's original paper in the limited context of the EPR-Bohm correlations, is itself interpreted differently by different proponents of the theorem. This has been quite a self-serving strategy for the followers of Bell, since it allows them to obligingly move the goalpost whenever the previously held goalpost comes under attack. For a non-expert it then becomes impossible to judge who is right and who is wrong.
(4) Finally, the fourth reason for the miscomprehension of my ideas is plain and simple intellectual inertia. We are indoctrinated by Bell's theorem for the past 47 years and we understand it well. So why bother with a new perspective? It goes against the paradigm in any case, and moreover it relies on a mathematical language that is not what we were brought up with. It is not necessary to leave our mathematical and conceptual comfort zones.
Eckard Blumschein replied on Aug. 19, 2011 @ 15:15 GMT
Dear Joy Christian,
You wrote: "The physical and mathematical meanings of the symbols are quite different." Indeed.
Tom wrote: "The 1's in Joy Christian's framework are not hyperspace elements. They are results in real analysis, Lebesgue integrable."
Did you ever consider the possibility that there might be serious flaws at least in the physical interpretation of what we inherited e.g. from Dirichlet and related real analysis? For instance, I looked in vain for a compelling justification of
lim n-->oo sn(x) = ½ ((f(x + 0) + f(x − 0))
James questioned the theory of relativity. You cautiously avoided being misunderstood as a crank. I am not quite sure. On one hand, there are experimental results that seem to confirm the relativistic addition of velocities. On the other hand, neo-Lorentzian interpretation is likewise possible, and Einstein's idea requires a tense-less theory.
I tend to guess: We must not comprehend the world as a closed system. Maybe, relativity is just a simplification that fits well in Galilean mechanics. Electromagnetic fields are not likewise locally enclosed. Isn't possibly the situation similar to the linearized theory of sound. The absolute pressure of air is also restricted to positive values as is elapsed time. Isn't it?
This paragraph seems to me to be key, or at least one of the keys, to understanding your work:
"What is important to note here is that, since the eventualities A, B, etc., are pure numbers, there is no non-commutativity involved. Thus contrary to Florin’s assertions, I do not start with assumptions any different from those of Bell as far as the eventualities themselves are concerned. Moreover, as already mentioned, there is no contextuality involved either, because all local eventualities are predetermined entirely by the orientation of the 7-sphere. Only the correlations among these eventualities depend on the dispositions of various apparatus, as they must. Thus the reason for the existence of the quantum correlations is not the local variables themselves, but the global twists and turns within the 7-sphere. The local variables are, as always, purely random, and hence they by themselves cannot possibly reproduce the quantum mechanical correlations, as correctly recognized by Bell. But what Bell failed to recognize is that this conclusion depends on the topology of the co-domain of the variables A, B, etc. In my view this topology, in general, is that of a parallelized 7-sphere."
If my messages are too far off the mark, please just say so and I will return to studying what you and others are saying.
What I see under consideration are theoretical problems that result from concessions made to relativity theory with regard to quantum effects. It is not clear to me why physicists would allow one theory to interfere with the development of the other theory when the two theories seem overall to be so incompatible (my understanding).
Your approach appears to allow for the reality of a speed limit on signalling while established a physical framework that is neither subject to that restriction nor in violation of it. If my understanding is close, do you consider "...a parallelized 7-sphere." to be a 'physical framework' or would you object to that characterization? My intent here is to free myself from preconceptions that do not apply to your work.
Joy Christian replied on Aug. 23, 2011 @ 11:55 GMT
James,
I hope I am not becoming a pawn between you and Tom, but the paragraph you quote does indeed summarize the key features of my framework. However, the credit for initiating a framework within which one can formulate the meta-principle of local causality without requiring a commitment to special relativity should go to Bell himself, not me. He introduced locally causal functions, A = +1 or -1, B = +1 or -1 etc., without making any commitment to special relativity, and claimed that no such local functions can reproduce the quantum mechanical correlations. What I have shown is that they certainly can, provided the topology of their co-domain in general is taken to be that of a parallelized 7-sphere. This co-domain, however, need not be assigned any physical significance as far as the logic of my argument against Bell is concerned. On the other hand, I have arrived at the parallelized 7-sphere not by accident, but because it happens to have profound physical and mathematical significance (as I discuss in this paper). Let me put this significance in more precise but somewhat technical terms: Every single quantum mechanical correlation is what it is because the tangent bundle of the 7-sphere happens to be trivial. This elementary topological fact (which allows one to parallelize the 7-sphere by octonions), is responsible for every single quantum mechanical correlation we ever see in nature (cf. the theorem stated in my discussion above). Physically, then, the very existence of quantum correlations suggests that we live in a parallelized 7-sphere. So, to answer your question, the parallelized 7-sphere not only has logical and conceptual significance within my locally causal framework, but also has physical and mathematical significance.
My message had only to do with understanding your work. I have been re-reading your posts, and those of Florin, Tom, Christi, and Ray. The discussions between you, Florin, and Tom are great. My participation has become uncomfortable for me also. Thank you for your reply.
You wrote, "Every single quantum mechanical correlation is what it is because the tangent bundle of the 7-sphere happens to be trivial. This elementary topological fact (which allows one to parallelize the 7-sphere by octonions), is responsible for every single quantum mechanical correlation we ever see in nature (cf. the theorem stated in my discussion above). Physically, then, the very existence of quantum correlations suggests that we live in a parallelized 7-sphere."
I cannot but agree. However, I don't thnk that a retrodiction is compelling. This is precisely the predicament that string theory is in -- complete retrodiction of known physics, and no novel predictions.
Fact is, physical results from the 2-slit experiment tell us unequivocally that quantum mechanics is nonlocal. One can't simply wish it away; Bell's theorem is just one aspect of quantum theory and nothing of the theory is coherent without nonlocality.
Let's try and play our own hand instead of asking for a re-deal:
Now that you have the framework for predicting pair correlations in Bell-Aspect, take the extra step of experimentally restoring locality by continuing rotation through 4pi. What I mean is that if you are correct in your framework, i.e., if 100% of the information in an arbitrary initial condition (all the way, in fact, to the cosmological limit) is contained on the bivector axis of arbitrary endpoints -- then the 2pi rotation of Bell-Aspect correctly correlates the pairs only 50% of the time as predicted by the "at a time" measure criteria of the experiment. Continuing through 4pi shoould restore local measure by returning a null result.
What should happen is that pair correlations corresponding to Bell-Aspect that hit (1,1) or "yes," after rotation through 2pi, when carried through to 4pi should record (0,0). Bell-Aspect correlations of (0,1), or "no," are random results that return equally random answers by rotation through 4pi. The null result, however, tells us that EVERY yes answer is 100% correlated to the initial condition, such that a continuous function eliminates nonlocal solutions and creates time dependence. This supports continuous function measure without dependence on arbitrary boundary conditions.
Experimental technical details are lacking; however, I am confident that the principle is sound. Perhaps Wineland can help.
Joy Christian replied on Aug. 23, 2011 @ 14:55 GMT
Tom,
Quantum mechanics is nonlocal. This was discovered by EPR in 1935. No one is disputing this fact.
Your comments also relate to what Fred has written in another post: "Should it be clarified that Joy's counter example only possibly shows that QM is not non-local for an EPRB type of scenario. I believe that QM could be non-local due to relativistic and quantum vacuum effects at very short distances like less than the electron Compton wavelength."
But no one is trying to show that QM is NOT nonlocal. I think people have lost the perspective on what the EPR-Bell debate is all about. What I have shown is not that QM is not nonlocal, but that it is an incomplete theory of nature. My logic---which is well understood by every foundationalist I know---is as follows: EPR produced a logically impeccable argument and showed---once and for all---that QM is an incomplete theory of nature. The logic and conclusion of EPR are not in dispute. What Bell claimed, however, was that the premises of EPR are inconsistent, and therefore their conclusion cannot be relied upon. He claimed that, contrary to what EPR envisaged, one cannot complete QM and replace it with a theory that is both local and realistic. Neither Bell nor EPR disputed that QM is nonlocal. I too do not dispute that QM is nonlocal (how can anyone?). What I dispute is Bell's claim of inconsistency within the premises of EPR. What I have shown is that Bell was wrong to claim that QM cannot be completed by a theory that is both local and realistic. One can, and I have, produced a model reproducing all of the quantum mechanical correlations in a purely local and realistic manner. This means that Bell was wrong, the EPR argument is back on, and QM is an incomplete theory after all. It then does not matter if there are other types of non-localities within QM, because QM is not a fundamental theory of nature. Mere retrodiction or not, you are underestimating the significance of this fact.
Now I agree with you that retridiction is not enough. It is, however, enough for the above argument to go through. The next step of course is to come up with an actual prediction. But I have taken that step too with my proposed experiment. It is precisely the experiment that would test the 2pi versus 4pi hypothesis. It is designed for that very purpose. I recognize, however, that even that is not enough to prove my grander claim---i.e., the claim that we live in a parallelized 7-sphere. All I have so far for the grander claim is retrodiction---i.e., the existing evidence of quantum correlations.
I must be terribly naive. I hadn't imagined that anyone thinks of quantum mechanics as a complete physical theory.
I was going to reply to Fred -- I'll do it here instead. Though what he says is true, nonlocality is very much more endemic to quantum theory than what is evidenced at the microscopic scale. The mechanics that are assumed to smooth out at the classical scale are...
I must be terribly naive. I hadn't imagined that anyone thinks of quantum mechanics as a complete physical theory.
I was going to reply to Fred -- I'll do it here instead. Though what he says is true, nonlocality is very much more endemic to quantum theory than what is evidenced at the microscopic scale. The mechanics that are assumed to smooth out at the classical scale are not lost; that's why we have quantum field theory.
Since I don't know what a foundationalist is, I will have to base my opinions on what I know of analysis and the extension of analysis to topology. Analysis assumes locality in continuous functions as strongly as quantum mechanics assumes algebraic probability to support nonlocality. No question in my mind -- you've effectively obviated the conventional applications of algebraic geometry and calculus for a higher order analytical model without loss of generality.
That doesn't imply, however, that lower order models -- either analytical or algebraic -- are invalid, no more than non-Euclidean geometry replaced Euclidean geometry. They operate by different sets of axioms. And even realizing that physical science is not axiomatized, deduction from first principles still applies. So when you say that "What I have shown is that Bell was wrong to claim that QM cannot be completed by a theory that is both local and realistic," it doesn't mean a lot to me, because I see it as a distinction without a difference. So EPR were right? -- I never personally thought otherwise. QM was never complete in the sense that Einstein always used completeness; i.e., a mathematically complete theory such as relativity makes closed judgments independent of experiment. QM cannot possibly do so, since its experiment preceded it and the mathematics ("How ugly!") was built around that result. Thus quantum field theory aims to be a complete physical theory in Einstein's tradition (albeit with ugly mathematics, you and I would agree, I think) -- so I don't believe that even the most dedicated proponent of nature's unpredictability would call QM a complete theory. They would probably just say that such a theory is impossible ("cannot be both local and realistic") and even though you and I know that is not Einstein's meaning of completeness, it doesn't matter.
This prevailing view is problematic to local realism, not because you can create a local hidden variable theory and venerate the EPR philosophy, but because the quantum philosophy is simpler. It's simpler because it doesn't rely on any philosophy at all. And that's why I keep telling you that you cannot win on that battleground -- you can't make "local" and "realistic" mean what you want them to mean, with a framework that's nonlocal and a result that's realistic. Your critics are right about that (the serious ones I mean, not the one who doesn't know the difference between computation theory and programming). You'll only get what Bell already assumed about the EPR correlations.
There must be something I missed in your experimental sketch. I will have another look, because I thought it involved correlations between discrete data sets separately gathered, which I think will suffer from the same "at a time" measurement error as Bell-Aspect. What I suggested was continuous comparison of pair-correlated data from 2 pi rotation with that continued through 4 pi rotation (also discussed in my powerpoint linked earlier).
All in all, though, I remain a big fan of your motivation and your method.
Joy Christian replied on Aug. 23, 2011 @ 17:50 GMT
Tom,
You say: "you can't make "local" and "realistic" mean what you want them to mean..."
I have not made these concepts up myslef. I mean by "local", what EPR, Bell, and CHSH mean by "local." I mean by "realistic" what EPR, Bell, and CHSH mean by "realistic." I mean by "non-contextual" what Shimony and the rest of the world means by "non-contextual." My framework is completely and fully "local", "realistic", and "non-contextual" in the precise senses defined by EPR, Bell, CHSH, and Shimony. All you have to do is to read my papers to recognize this.
Of course, I've read your papers. I didn't say you were making things up. What I mean to imply is that stripped of philosophy, the Bell-Aspect result is what it is, and that your framework stripped of philosophy becomes another alternate explanation of quantum mechanics. As such, it can be marginalized, but I think it is rich enough to stand on its own.
Joy Christian replied on Aug. 23, 2011 @ 19:12 GMT
Tom,
"...your framework stripped of philosophy becomes another alternate explanation of quantum mechanics."
No it does not and it cannot. There is no superposition, entanglement, objective chance, or objective indefiniteness within my framework. You have to be quite perverse to see any sign of quantum mechanics in it. It is based purely on classical geometry and topology. Every element of physical reality (and its measurement result) has a definite value, and all eventualities are defined purely locally and non-contextually.
I apologize if I gave offense. I merely meant that it need not be positioned against Bell-Aspect, and indeed, I think that it gets damaged by association.
Joy Christian replied on Aug. 23, 2011 @ 21:30 GMT
Tom,
No apologies necessary. I too am just trying to make my viewpoint clearer. I should have written "One has to be quite perverse..." rather than "You have to be quite perverse..." Sorry about that.
You may not realize but misunderstanding, misconception, and misrepresentation of my work began from day one, some four years ago, and I have been ceaselessly fighting against them ever since, both publicly and privately, sometimes with more than one person at a time. Compared to some of my battles the exchanges we are having here are in fact quite pleasant and constructive.
Is it possible that non-locality of QM is a consequence of the spatial origin of the QM formalism (and of the whole of our present mathematics)?
I am beginning to think that what we observe is a spatial instantiation of the (new kind of) discrete representation. In that sense non-locality is an artifact, since the spatial representation is not primary but secondary.
You know I am a supporter of Popper's philosophy over Aristotle's. As always, though, you argue your case with great fervor and intellectual commitment.
Although I, like most of our generation, grew up with classical philosophy, I don't find compelling the argument for knowledge by direct experience (induction). It does not comport with the fact that most objective...
You know I am a supporter of Popper's philosophy over Aristotle's. As always, though, you argue your case with great fervor and intellectual commitment.
Although I, like most of our generation, grew up with classical philosophy, I don't find compelling the argument for knowledge by direct experience (induction). It does not comport with the fact that most objective knowledge that we have so far acquired in science is of the counterintuitive sort -- that is, the sort of knowledge that we comprehend only through our abstract models. From the time I really started (many years ago) to understand Popper's emphasis on metaphysical realism over logical positivism, I grew enchanted with the idea that science is as much art as anything else.
That being said, you also know that I am not one to dwell on philosophy for too long. While I may not agree with your motivation, your method is highly interesting. I do agree (and all the more so, having deeply investigated Joy's framework of local realism) that nonlocality is a mathematical artifact, as much as the "c^2" part of Einstein's special relativity equation is a mathematical artifact. Where I might differ with you and Joy, though, is in my opinion that we NEED these artifacts, in order to understand the deep structure of reality. Tracing the chain of Einstein's reasoning from its inception to his famous conclusion, one is hard put to see how it would have been possible to simply conclude E = m. Now certainly, it would have been possible by trial and error experimentation alone, to invent an atomic bomb and then restructure the explosion by measuring the results to find the important role played by the atomic binding energy, and thus get to the formula that way. It would seem to be a rather tedious, impractical, lengthy and inelegant process -- but possible.
Joy's research is of a similar class, i.e., demanding an artifact, a scaffolding to uphold the main idea. The construction of local realistic conditions within the limit of a metaphysical assumption in higher dimensions gives meaning to the conclusion that Einstein himself had reached: all physics is local. On the other hand, the metaphysical assumption of quantum mechanics that any measurement not made in a particular experiment is nonlocal information, also instantiates the meaning of QM. That's why I say that there is no apples-to-apples comparison between Joy's framework of continuous functions and the QM framework of probability functions. We don't need to assume "reality" to know what reality is. We only construct reality and compare it to experimental results. Stripped to essentials, that's what science is: theory and result. That's also essentially what art is: idea and creation.
Those are the characteristics of your research program I like. Do your "pairs of primitives" also correspond to local realism in a manner tractable to a continuous function model? If so, it would be a magnificent contribution to the science of computation, because it would give us a way to model the evolution of spacetime in real time -- that's trememndous predictive power!
Author Frank Martin DiMeglio wrote on Aug. 22, 2011 @ 18:53 GMT
The true unification of gravity and inertia requires instantaneity. A true and fundamental equivalency of force/energy and distance in/of space requires instantaneity. Instantaneity combines, includes, and balances larger and smaller space as the same space in keeping with this space being both (and equally) invisible and visible).
Einstein's theory of gravity entirely fails in all this regarding instantaneity. Dreams do all of this.
Again, this is why physics is so lost; and this is also why dreams unify physics.
Edwin Eugene Klingman wrote on Aug. 23, 2011 @ 16:13 GMT
Joy,
You say, "Quantum mechanics is nonlocal. This was discovered by EPR in 1935."
I interpret that as follows: Since psi^2 is the probability that a given particle is found at a certain point at a certain time, then it could happen that the same process could produce an action in two or more places on the screen. But the detection at only one place implies some kind of non-local 'action at a distance' that prevents it from being at any other point.
Is this the 'non-local' implication of quantum mechanics that EPR implied, or is there something else I'm unaware of?
Joy Christian replied on Aug. 23, 2011 @ 16:49 GMT
Edwin,
EPR produced a much stronger argument using what we now call "quantum entanglement." In a simplified version of their argument one considers entanglement between two photons polarized along two different directions. Measurement of the polarization of one of the photons along one direction then instantaneously gives information about the polarization of the second photon, regardless of the distance between the two. This is the spooky implication of quantum mechanics EPR discovered, and used it to argue against the completeness of quantum mechanics.
Edwin Eugene Klingman replied on Aug. 23, 2011 @ 17:27 GMT
Joy,
If one assumes local realism and conservation of energy and momenta, how does this imply non-locality, without a belief in superposition, which is an interpretation that is placed on top of quantum mechanics?
Edwin Eugene Klingman replied on Aug. 23, 2011 @ 18:05 GMT
Joy, that's just what I was hoping to hear. I agree that denying superposition won't get one very far, but explaining superposition may get one a little farther.
Indeed so. Following up from my earlier posts, having returned from holiday. I would just love somebody to EXPLAIN superposition (and other associated concepts) in simple emglish that does NOT contravene the logic of the reality within which we exist. It cannot be done, which is my point. This entire , seemingly scientific debate going on here is just metaphysical. It is the same as the Roman Catholic church taking issue with Protestantism over the 'true' nature of 'christianity'. There is no proof because it is outwith reality.
So how does reality exist in more than one state at any point in time, when it actually, within the confines of our existence, can only exist in one form, which is independent of our realisation of it?
I don't. It exists, for us, in one state. It's QM that assumes it exists in more than one state and we realise one of them. In simple language. Whereas, in actual fact, what one is experiencing is a medium based sensory representation of reality (a visual observation, hearing, etc). Reality is independent of us, and is neither created or altered by our experience of it. This applies to sub-atomic particles or elephants. The rules of engagement do not vary because of size.
You're wrong, Paul. Quantum theory also assumes unitarity. I.e., the equation for quantum mechanical unitarity (which I can't write in ascii here, because I've discovered that the bracket symbols disappear -- you can look it up) describes the probability in which the sum of all probabilities of all possible outcomes in a given experiment is unity. That's 1, or 100%.
That is not the same as accepting that reality only has one, independent, form. Why have any concept of probability in the first place, or indeed superposition, wave-collapse, indeterminacy, complementarity, etc, etc. Answer, because there is a confusion between reality and the observation thereof. We do not know reality directly, we experience sensory representations of it from which we can, if we understand the process, (for example how light works) extrapolate what instigated it. But a number of the difficulties that are inherent in the process of experiencing reality have been deemed to be inherent characteristics of it and there has been assumed to be a direct relationship between experience and reality instead of experience and representations of reality.
You apparently don't need anyone else to intervene in your asking and answering your own questions. I will offer, anyway, the fact that science is concerned with discovering reality, not with assuming reality. Uniformity of physical laws and unitary of observational outcomes, however, are assumptions of all physics, classical and quantum.
Only a mathematician could say "There's nothing mysterious about the principle of superposition." Someone who believes that "time" is an "n-dimension infinitely orientable metric on self-avoiding random walk." Or that "information, gravity-and time-are identical".
If you don't have such beliefs, then of course your concern about the physics of "superposition" is appropriate.
I hope, by the end of the year, to have a physics treatment that you may find interesting. Stay tuned.
Charles Francis replied on Sep. 5, 2011 @ 05:52 GMT
Eugene,
Please be aware that quantum mechanics is *not* non-local. In fact the locality condition is fundamental in qed, which is the best and truest form of quantum theory currently available.
What EPR, and Bell's theorem say, is *not* that qm is non-local, but that a classical theory which reproduced the results of qm would have to be non-local. That is a rather different statement.
This does mean that one has to revise the statement of locality. It does not mean we have to abandon it.
Indeed science should be concerned with discovering reality. That is my point. Because in this area in particular, unintentionally, it is not. At best, it's an objective review of the observation of reality, but mostly it has become an argument about different mathematical belief systems which purport, without any proof, to represent the reality.
Question: when does 'local' cease being local, after 5inches, 5 miles, and whatever the criterion is for delineating this, why is it so?
Edwin, since you have mentioned time I will make another comment. Time is an inherent quality of the reality which we inhabit. But unlike the other dimensions it is not spatial. We are aware of time because we experience change in reality, whether it be an elementary particle moving or a leaf turning brown, etc. For any sequence of change to occur, a form of 'dimension' must exist. But, reality only exists in one state at a time. It does not 'stack up' (do not confuse this with sensory representations of previous states which might be still existent). At the next point it is a different reality, etc, etc. Put the other way around, reality is, at any point in time, the last state of everything, previous states having been superceded and future ones not yet in existence. No space is required to accommodate this.
Quantum mechanics is nonlocal. This fact was discovered by EPR in 1935. Please read Bell's 1991 paper to understand how and why quantum mechancis is non local.
Just as you have recently contributed new ideas to the 1935 EPR discussion, I too hope to contribute new ideas that may lead to a new interpretation. As noted, I hope to have these written up this year, and then everyone will have an opportunity to shoot me down.
Certainly QED is "the best and truest form of quantum theory currently available." But it nevertheless has problems. For example, it is not clear that QED has properly addressed the 120 orders of magnitude decrease in vacuum energy that would seem to have implications for virtual particles. Also, QED (as part of QCD) predicted a 'strange quark' contribution to nucleons that has not been seen (possible related). And the recent discovery of a 4 percent discrepancy in the proton radius of muonic-hydrogen seems to indicate a problem with QED. My belief is that such anomalies are the best hints we have toward a 'new' physics, as will be the lack of the Higgs and SUSY, when and if confirmed.
Finally, quantum field theory, as Zee laments in "Quantum Field Theory in a Nutshell", is founded on the harmonic paradigm. He claims that "we have not been able to get away from the basic notions of oscillations and wave packets."
The problem, as I remarked to Joy earlier, is that new theories are always interpreted in the concepts of the old theory, whereas what is required is to interpret the ideas of the old, in terms of the new. This is a major problem that all new theories face, as the thinking of phycists is always in terms of the old concepts, until the new have been understood and appreciated.
Charles Francis replied on Sep. 6, 2011 @ 06:23 GMT
Hi, Edwin Eugene,
There is more than one way to skin a cat, and more than one possible approach to QED. The mathematical problems with QED have been resolved since the seventies, up to the Landau pole, although this is not widely known, probably because the maths is beyond most physicists. See, Scharf, Finite QED. I have also given a simpler treatment at http://rqgravity.net/QuantumElectrodynamics
Author Frank Martin DiMeglio wrote on Aug. 23, 2011 @ 22:43 GMT
Here's quantum gravity:
The true unification of gravity and inertia requires instantaneity. A true and fundamental equivalency of force/energy and distance in/of space requires instantaneity. Instantaneity combines, includes, and balances larger and smaller space as the same space in keeping with this space being both (and equally) invisible and visible.
Ultimately, iInertia and gravity are fundamental to physics.
Author Frank Martin DiMeglio wrote on Aug. 23, 2011 @ 22:52 GMT
The intelligibility of quantum mechanics is lacking. What is needed is the constancy/stability/sameness/cancelling/balancing of fundamental and true inertial/gravitational equivalency. Unity in variety. Complexity and order.
Space manifesting as electromagnetic/inertial/gravitational energy does the trick.
Thank you. This time I was going to print it. I am not used to using 'powerpoint(?)'. I couldn't see how to print it. Even more important, it appeared to open so that I could make changes to it. Am I off the mark or does it need some further closing?
Grrr. Still didn't preserve all my formatting, so I am going to give up. At least this time the important point I wanted to make sure of is there -- slide # 2 -- inputs of like parity on their respective axes.
James, I am the worst one to ask about computer peculiarities. :-)
Author Frank Martin DiMeglio wrote on Aug. 27, 2011 @ 18:29 GMT
The true unification of gravity and inertia requires instantaneity. A true and fundamental equivalency of force/energy and distance in/of space requires instantaneity. Instantaneity combines, includes, and balances larger and smaller space as the same space in keeping with this space being both (and equally) invisible and visible.
Ultimately, inertia and gravity are fundamental to physics.
Clearly, we see that this resolves the problem or paradox of object/frame.
All of this happens in dreams as the fundamental union of physics.
Your ever-loving father wrote on Aug. 27, 2011 @ 19:27 GMT
Sorry, the intelligibility of outer space is compromised relative to the understanding of this space -- that means comapred to dreams and typical/waking experience because being and thought and feeling and vision are ultimately and naturally balanced in a fundamental fashion.
Again boys, start with A and B before you try to leap to y and Z.
This 2009 FQXi Forum article about octonions didn't draw a very wide response. Perhaps it's time to reconsider Tevian Dray's suggestion that spacetime is not fundamental, but rather emergent in four dimensions. I don't personally agree with the conclusion (I think every odd n of S^n incorporates a spacetime of 0 + 1 description) but it does fit into the current dialogue.
I almost agree with you, but would like to emphasize the exceptions. The most important S^n are the parallelizable ones, n = 0,1,3 and 7, and these correspond directly to 1-D 0-spheres, 2-D 1-spheres, 4-D 3-spheres, and 8-D 7-spheres. The 0-spheres are an 'oddball' that we should not ignore (probably related to global transformations such as the U(1) of Electromagnetism), but close-packing of the other hyper-spheres leads directly to a G2 Graphene-like lattice, an F4 24-cell lattice, and an E8 Gosset lattice. I think it is fair to say that G2 and E8 are both very relevant in current literature. F4 may be the most under-appreciated structure...
Forget S^5, S^9, etc. - a rotating S^5 would decompose into the equivalent of a 2-brane of S^3's.
By the way, I did not ignore those papers by Dray and Manogue. Lawrence and I wrote a paper that utilized the Jordan Matrix ideas in PSTJ in 2010, and some of my latest private ideas build on a similar concept.
Scales and fractals are relevant, but I have been focusing more on Octonions lately. I am playing around with multi-dimensional models in which Spacetime *MUST* be emergent.
I probably shouldn't have inserted my own result into the post, because if I talk about it I will have to say a lot more. I do understand the limit of the algebra at S^7, but my method allows analytic continuation. That's really all I will have to say about it in this forum.
Anyway, my motive was to try and stimulate more discussion here that illustrates the differences -- both quantitative and qualitative -- between events in the space of quantum probabilities, and in physically real spacetime. Thanks for getting the ball rolling!
I think that most of us are trying to 'fit' our own results into these blogs. I don't mind you teasing us with ideas of future publications, but I *MUST* draw the line at S^5. S^7 corresponds directly with a hyperbolic octonion. Likewise, S^3, S^1 and S^0 correspond with quaternions, complex and real numbers; respectively. Coincidentally, *ALL* of these hyper-spheres are parallelizable, and *ALL* may represent normed divisor algebras. The G2, F4 and E8 Lie lattice groups that result from close-packing of S^1, S^3 and S^7, respectively, are *ALL* self-dual.
On the other hand, S^5 may be some sort of complex tri-vector, is *NOT* parallelizable (such that spinning S^5's would be unstable), and close-packing of S^5's leads to an E6 Lie group that is "NOT" self-dual. In my opinion, S^5 and E6 are 'too ugly' to be fundamental, but I know others who would argue for E6.
These dimensions and lattices are discrete in nature. I do not see how you can analytically continue the 'dimensionality' of possible Spacetimes. I agree with 'patterns', but disagree with 'continuation'.
The metric continuation is over S^n manifolds. (My method has nothing to do with discrete S^5 and S^6 groups.) Algebra ends at S^7, while analysis doesn't.
To try and steer this discussion back into Joy Christian's framework, a highly accessible outline of basic topology is contained in this excellent article by Richard Elwes.
The number of exotic spheres in dimension 4, where S^3 lives, is unknown. Now of course Joy's method does not depend on the existence, or not, of exotic spheres, because his algebra is transitive and reflexive S^7 to S^3; i.e., there is no dependence on differential topology to express the model. This underscores my point in countering Florin's counterarguments, that spaces need be only simply connected, not necessarily smooth -- to obviate probabilistic methods.
What interests me, though, is that if the number of exotic spheres in the 4 dimension Euclidean space turns out to be very large -- say, 10^500 -- might it not correspond to the number of vacua predicted by string theory? And if that is so, then the continuously changing orientation of correlated pairs on the single axis (described by my outline of experimental criteria for Joy's framework) might very well create the capacity for us to "see" those vacua as quantum fluctations. As I said to Lawrence in another thread, Joy's framework may actually be rich enough to *predict* quantum fluctuations.
Lawrence B. Crowell wrote on Sep. 5, 2011 @ 19:32 GMT
JC,
Einstein always thought quantum mechanics was incomplete. He was almost certain there must be some underlying classical-like logic to it. He said his cosmological constant was his “greatest blunder,” but I think it could be argued that this stance really turned out to be his biggest mistake.
If I am right the states of nature are given by modular forms which have an integer counting of those states as microstates in macrostates. These modular states have Borel group and parabolic group realizations. The parabolic groups give the projective geometry of light cones and the Borel groups are Heisenberg groups. There is nothing here which requires any adjustment on the logic of quantum mechanics to make it more palatable. The properties of quantum mechanics are given by projections or the span on state space, while classical logic involves unions and intersections. At the heart this is where the Bell theorem comes from.
I think what is mysterious is not quantum mechanics. Seriously, if one looks at basic QM it is a theory of linear states and a linear state space, unitary evolution, Hermitean operators and eigenvalues. What could be simpler? The existence of the macroscopic world or classical mechanics is what is mysterious. How is it that classical states of the world obtain from QM, when this theory has no contextuality? Quantum states are really in effect blind to what we call space, and only have representations of space or configuration variables. We then think of this space in a classical setting and this is what gets our panties all wedged up our butts. We orient a Stern-Gerlach apparatus according to this classical picture of space, which is what establishes the context by which we then measure eignvalues.
The counting or integer partition I indicate above pertains to black holes and AdS ~ CFT. Yet Zeh has referred to a “quantum horizon,” which might then serve a similar purpose. So maybe this might lead to an understanding of how the classical or macroscopic world emerges. The Count Rules!
Yes, I am working in the tradition of Einstein and therefore getting all these heat from all sides. I have few friends these days, intellectually speaking. It is clearly not a fashionable line of research. However, by "incomplete" Einstein did not mean "incorrect." Even Bell's theorem does not rule out a possible completion of quantum mechanics and allows, for example, a Bohm-type completion. My goal is to find out whether one can do better than Bohm. It seems to me that it is in everyone's interest to find out whether quantum mechanics is truly a complete theory of nature.
Lawrence B. Crowell replied on Sep. 5, 2011 @ 21:38 GMT
Not long ago I was reading an interview with Zeilinger about closing loopholes on Bell and KS theorems. I think that if major developments along these lines take place that experimental tests will be the deciding method. Anton said there are only a couple of loopholes left to close, and this should be decided in a few years.
Do you have a link to that interview? Or how long ago was it? Recently De Raedt et al, have blown the Weihs et al 1998 experiment (Zeilinger) out of the water. If the time window is thrown out, then the experiment produces Bell's result and does not violate the inequality. They also show Bell's theorem can't match physical reality just as Joy has shown for an EPRB type of scenario. It is back to square one for the experiments. But of course, I don't think a classical experiment has ever even been attempted. If a classical experiment violates the inequalities, then we would know for sure.
maybe this is a silly question to ask (I come from computer science, not physics), but is it not that "The quantum eraser experiment", also to a degree confirms the quantum entanglement?
Thanks. Frank
PS.: Best of luck to Mr. Christian, I truly hope you are correct.
Thank you for your question. It is not a silly question. However, nothing can really confirm quantum entanglement, because in the end all one sees in ANY experiment are correlations, not entanglement. One can have more and more confidence in the notion of quantum entanglement, but that is not the same thing. What I am trying to do is to reproduce quantum correlations without using any form of quantum entanglement.
Edwin Eugene Klingman wrote on Sep. 30, 2011 @ 19:13 GMT
Dear Joy Christian,
As you know I have been supportive of your approach to Bell's problem, although I have not felt competent to judge its correctness.
My "preference" is for a 3D plus time model of existence (4D with reservations) and I have trouble understanding a 7-dimensional reality. For example, if two 3D particles are linked or coupled by time or distance, then I can understand why the appropriate analysis would involve a 2 x (3D) plus 1 = 7 dimensional formulation, but I sense that this is not what you are suggesting.
Can you explain in simple fashion, for me and other 4D-Neanderthals who wish to better comprehend what you are up to, why 7D is required and taken as physically meaningful? That might help in 'selling' your theory. I am frustrated (as, I'm sure are you,) by the stalemate that you and Florin have reached. Tom has been a great help to you, but certainly no resolution has been reached in these FQXi blogs that would leave everyone happy.
What demands 7D? Is it the parallel transport aspect of the formulation?
I know you may prefer to stick to the math and not mess with a physics "justification", but sometimes it is useful to try to answer questions in another preferred frame of reference. One sometimes sees aspects of the problem that are not so visible in their own preferred framework.
I hope you find it worthwhile to formulate an answer for me. I hope this makes sense to you and look forward to any response.
It all boils down to this conversation that Rick and Georgina are having. If you saw my latest paper with Jonathan Dickau in PSTJ 2(6), you would see that we presented clear arguments for our observed reality being Quaternion (H) - 1) the Riemann-Sommerfeld Equation clearly puts Maxwell's Inhomogeneous Equations in a form that is fully-compatible with both Quaternion and Spacetime algebra, 2) Dirac's gamma matrices are clearly Quaternion and Spacetime 4x4 solutions (that may be Cayley-Dickson constructed from pairs of Complex Numbers - the Pauli 2x2 Spin matrices), and gamma^5 is the Quaternion Pseudoscalar, and 3) the Minkowski metric (-1,+1,+1,+1) is simply an inversion of Hamilton's original Quaternion metric (+1,-1,-1,-1) whereby we interpret the quaternion scalar as 'time' and the quaternion 3-vector as 'space'.
In the same paper, we also presented ideas for an Octonuion (O) based reality.
At the very least, we should expect Scales to require that we define both small and large, which could relate to a doubling of dimensions (coincidentally this is exactly what we expect from SUSY, so I suspect a relationship between Scales and SUSY).
If we 'twist' two (3+1)-D Quaternions together, then we can 'create' a (7+1)-D Octonion via Cayley-Dickson Construction. But please note that we have performed a 'magi-matical trick' - we have converted 6 space + 2 time dimensions (two separate 3-spheres) into 7 space and 1 time dimensions (one 7-sphere). We can perform this trick at the expense of introducing imaginary numbers. Imaginary numbers might permit faster-than-light tachyons (that is one explanation for the OPERA results that is similar to, but far less complex, than my upcoming explanation of 'superluminal' neutrinos), which are the most non-local quanta that we can imagine, and therefore cannot answer the question of 'local reality'.
These 7-spheres are 8-D (and close-packing of the 7-spheres leads directly to the 8-D E8 Gosset lattice and ties in with ideas such as Heterotic Strings and Lisi's TOE) with a 1-D time-like radius, and 7-D space-like hyper-surface dimensions. Joy claims that if you stay on the surface of the hypersphere, then every hypersurface dimension can be described by 'real' coordinates at right angles to each other. I agree with this - as long as you aren't trying to split the Octonion into two Quaternions that obey different coordinate systems.
I would like to see Joy carefully detail this decomposition of the Octonion. It is relevant to theoretical physics.
Thanks for the response. Of course you know that I already have some understanding of your model and am not buying it. What I don't know is how Joy views things. I've read most of his papers, and I don't see him pushing all of the dimensionality that you believe in, so I'm curious as to what he views as the most significant supporting argument for 7D (or more-D if he so subscribes.)
In particular, the only justification I've seen so far is the 'parallel transport' aspect of his approach. I'd like to know if this is his basis for going to 7D or if I'm missing the point.
Joy Christian replied on Sep. 30, 2011 @ 22:25 GMT
Dear Edwin,
I know you have been sympathetic to my work on Bell, and I am grateful to you for that. I am also grateful to Tom for both his strong defence of my work and his support for my wider perspective. I am grateful to Ray too, for his relentless questions, but I do not think he has understood what I am saying.
Your question is of course a very important one. Why 7D? Well, there...
I know you have been sympathetic to my work on Bell, and I am grateful to you for that. I am also grateful to Tom for both his strong defence of my work and his support for my wider perspective. I am grateful to Ray too, for his relentless questions, but I do not think he has understood what I am saying.
Your question is of course a very important one. Why 7D? Well, there are strong mathematical as well as physical reasons for 7D. In my view quantum correlations are telling us that we live in a parallelized 7-sphere. To understand this statement we must first understand what we mean by a quantum correlation. In simple terms, a quantum correlation is a correlation that is stronger than a classical correlation. That is to say, a quantum correlation is more disciplined than any classical correlation. This is what Bell discovered in 1964, and he put a precise quantitative measure on the strength of the quantum correlation in the special case of EPR---i.e., he noted that quantum correlations are the ones that exceed the bound of 2 in his inequality. Now it turns out that no quantum correlation, no matter how complicated the underlying quantum state, can exceed the upper bound of 2\/2. Thus quantum correlations are not only more disciplined than classical correlations, but they are more disciplined in a quantitatively precise manner. So the natural question is: What makes quantum correlations so precisely disciplined?
That was one of my concerns. My other concern was local causality. Following Einstein, I believe that there is no place for "non-locality" or "non-reality" in physics. I believe that a successful theory of quantum gravity will be a locally causal theory. So I asked the following question: Given realism and local causality, what does the discipline of quantum correlations point to. In other words, I searched for a mathematical structure that not only compelled quantum correlations to be as disciplined as they are, but also compelled them to be what they are because of local causality (just as general relativity is what it is because of local causality). My investigations led me to the conclusion that this mathematical structure cannot be anything but a parallelized 7-sphere. The reason for this has to do with the fact that a unit parallelized 7-sphere is homeomorphic to the set of unit octonions, which in turn forms the most general possible division algebra. Why division algebra is important? Because without a divisor there is no closed-ness under multiplication, and without that property every conceivable point of the space cannot be factorized into arbitrary number of points, and without such factorizability Bell's locality condition cannot be satisfied, and without Bell's locality condition there is no local causality. Moreover, the property of parallelizability brings about precisely the discipline exhibited by quantum correlations, with 7-sphere being one of the only four spheres that can be parallelized (with the other three, 0, 1, and 3-spheres, nested within it like Russian dolls). All these things come together in such a beautiful way in the parallelized 7-sphere that there is no doubt in my mind that we live in such a space. More precisely, I believe that quantum correlations are the evidence that we live in a parallelized 7-sphere.
In science, however, belief demands justification, support, and confirmation. Mathematical justification and support for my belief can be found in my papers. And I dream of experimental confirmation of my ideas every now and then.
Joy Christian replied on Sep. 30, 2011 @ 22:41 GMT
By the way, parallelization and parallel transport are two different things. By parallelized I mean the space is flat, with zero curvature, but the torsion may not be zero. In fact the non-zero torsion of the 7-sphere is responsible for all quantum correlations.
Thank you very much for your response. I have some immediate remarks, and may have more after I've better digested your answers.
First, I believe you and I are on the same page as far as there being no place for "non-locality" and "non-reality" in physics. I'm not sure whether you've looked at my analysis of Bell's work but I believe he made a logical error that nullifies his bound of 2 in his inequality.
Second, I do not appreciate your point about why division algebra is so important. This is my shortcoming and I will try to understand your point about closed-ness under multiplication as necessary for the correct calculation of quantum correlation. I realize this is a key point.
Finally, I would like to point out that my theory leads to de Broglie-like particle-plus-wave, but not a point particle. Instead the theory leads to toroidal particles, which have the property of being parallelizable (in the flatspace sense of zero curvature.) It is this (self-interested) fact that makes me wonder whether, if you had started with two parallelizable tori, you would have found it necessary to go to a 7-sphere. I cannot judge this point, but the torus topology is a very important aspect of my theory, without which the theory would fall apart completely. I suspect the use of toroids would complicate your analysis, but of course since I believe my model is almost certainly the correct model, I don't worry much about how much extra work you have to do!
So thanks again for your explanation. I will try to understand and appreciate your points about division algebra. You might, for your own amusement, ask yourself what the use of toroidal topology particles would do in your theory. They are, I believe, essentially a 3D Calibi-Yau manifold (Kahler, Chern class 0, Ricci-flat) and fully Yang-Mills compatible, and, according to Shing-Tung Yau, solve Einstein's gravity equations.
If you have any thoughts on this matter, I would be very interested.
Thank you for your reply. For me 7-sphere was not a matter of choice. I was reluctantly driven to it by powerful physical, mathematical, and conceptual constraints. In this paper I have explained why any locally causal theory must be based on Bell-type measurement functions whose co-domain is a parallelized 7-sphere. If a theory is not based on such functions then it is guaranteed to be non-local. For without parallelizability and a divisor the points of the co-domain (where the measurement results actually live) cannot be closed under multiplication, and without the latter there is no infinite factorizability of every conceivable element of the co-domain, and without infinite factorizability there is no local causality. Recall that even a single non-local correlation within a single physical scenario would kill local causality of any purported local theory. That is why so many claims of local-realistic models are invalid. Bell made a powerful discovery in 1964 that it is not easy to construct a locally causal theory. Although wrong, his theorem cannot be disposed off so easily.
A theory based on a parallelized 7-sphere, on the other hand, cannot be but locally causal in the strictest possible sense.
Joy Christian's model is a space of complete functions, everywhere real and continuous, over smooth manifolds. S^7 is the limit of physical space that facilitates the operations that complete both topological closure and algebraic closure over the embedded space E^3, our space of observables, where measurements are recorded.
The degenerate torus is a sphere, so I suspect that while your model may be consistent with his, yours will be incomplete, for this reason:
The parametric representation of a torus is over the half open interval, [0,2pi). A parametric representation of Joy's model would seem to me over the interval [0,4pi) and results therefore completely integrable on the closed interval [-1,+1] regardless of the orientation of the bivector measure to all points of S^3.
In other words, in a physical context, I think you might be able to recover the coin toss probability of Bell-Aspect with your model, but not the complete functions that characterize Joy's model.
I know that you have read my book, my recent papers, and you aren't 'buying' my ideas. My ideas have gotten so complex that I'm not sure that I buy all of them either - with dozens of 'dimensions'.
For this latest neutrino paper, I took a more minimalist approach, and tried to explain the necessary physics in 10-D. As such, I think that these ideas are compatible with Dray and Manogue's ideas, and easily simplify down to Joy's ideas.
My point is that Octonions and Quaternions are hypercomplex algebras, and manipulation of these algebras can introduce imaginary numbers where you did not necessarily expect them. This is not necessarily a bad thing because any any reasonable TOE model must include complex representations in order to properly represent CP violation by the Weak Force, but imaginary masses can lead to faster-than-light tachyons. Tachyons could explain the recent OPERA results, but then we must admit that 'locality' and 'causality' are weakly broken.
Your first response was directed to my question. Your last response ignores my question. I asked whether the parallelized 3D tori could replace a 7D scheme based on parallelized spheres.
Your reply that you were "reluctantly driven to [your theory] by powerfully physical, mathematical, and conceptual constraints." I can make the same statement.
What you do not say is that you considered tori, which are naturally parallelized, and found they did not work. Therefore I assume that you did not. In fact, you state in your paper that "a manifold is said to be parallelizable if it is possible to set all of its points in a smooth flowing motion at the same time, in any direction." then you say, "Rather astoundingly, this turns out to be possible only for the 0-,1-,3-, and 7-spheres."
You are mistaken in this statement-- 3D toroids are parallelizable. So when you say "parallelizability of the 3-spheres... turns out to be indispensible for respecting the completeness criterion of EPR" you have not proved that 3D tori will not work.
Because 3D tori are naturally occurring physical objects (such as smoke-rings) and a 7D sphere is not a physical object but a mathematical structure, I find your reasoning hard to accept.
You say "All of these things came together in such a beautiful way in the parallelizable 7-sphere that there is no doubt in my mind that we live in such