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T H Ray wrote on Jun. 2, 2011 @ 17:05 GMT
Suppose the disk is labeled thus, but its record is blank. To the observer (the one who plays the disk), this would differ from a disk full of information ... how?
Tom
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Eckard Blumschein replied on Jun. 4, 2011 @ 04:36 GMT
Tom,
How? Oliver Heaviside created a clever decomposition of the missing future into even and odd components as to prepare it for complex Fourier transformation. Even ones get real parts, odd ones imaginary parts. A lot of redundant symmetries arose.
Eckard
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T H Ray replied on Jun. 4, 2011 @ 14:38 GMT
It has nothing to do with past or future. It has to do with observer entanglement with the wave function. The interaction of the observer with the hypothetical CD will change history. So the ostensibly well ordered historical events recorded on the disk will not be distinguishable from random or pseudo random events at the point of interaction.
Tom
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Eckard Blumschein replied on Jun. 4, 2011 @ 15:30 GMT
Tom,
Maybe some theorist are even using the good old notion history in a sense that essentially deviates from the original one. My old fashioned dictionary tells me that history always refers to the past.
Doesn't ostensible mean not actual but alleged or pretended? The real numbers are ostensibly well ordered. However, being uncountable they do not fit on a CD.
So far nobody managed to changed history. Nothing can predict all future data for two different reasons: At first there is no known end of time, and secondly the variety of possible influences is also unlimited. Why do you refer to an entanglement of an observer with a wave function? Isn't any object under observation independent from any ideal observer? Isn't the suggested interactive CD just ridiculous?
Eckard
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Georg wrote on Jun. 2, 2011 @ 21:19 GMT
The wording "crystallizes from past" is not appropriate.
The wording for crystallisation is always that a crystal
crystallizes from liquid/melt (=less ordered) phase.
So the analogy affords to say: the past (= fixed)
crystallizes from future.
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Eckard Blumschein replied on Jun. 5, 2011 @ 10:12 GMT
Is the future a less ordered phase or does it simply not exist? I see prediction like something imagined by means of extrapolation the basis of traces.
Who feels himself crystallized from his grandchildren? Perhaps "crystallizes from the past" should be replaced by "resulting from influences", which of course belong to the past.
Eckard
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Pentcho Valev wrote on Jun. 3, 2011 @ 05:32 GMT
Kate Becker wrote: "The view that the past, the present and the future are of exactly the same physical character seems to be supported by Einstein's special theory of relativity..."
This view is DEDUCED in Einstein's special theory of relativity, and if you don't accept it, you should suggest which of the two postulates - the principle of relativity and the principle of constancy of the speed of light - is false. Any different discussion amounts to crimestop:
http://www.liferesearchuniversal.com/1984-17 George Orwell: "Crimestop means the faculty of stopping short, as though by instinct, at the threshold of any dangerous thought. It includes the power of not grasping analogies, of failing to perceive logical errors, of misunderstanding the simplest arguments if they are inimical to Ingsoc, and of being bored or repelled by any train of thought which is capable of leading in a heretical direction. Crimestop, in short, means protective stupidity."
Pentcho Valev pvalev@yahoo.com
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Pentcho Valev replied on Jun. 3, 2011 @ 06:04 GMT
Clue:
http://www.amazon.com/Relativity-Its-Roots-Banesh-Hoffm
ann/dp/0486406768
"Relativity and Its Roots" By Banesh Hoffmann
"Moreover, if light consists of particles, as Einstein had suggested in his paper submitted just thirteen weeks before this one, the second principle seems absurd: A stone thrown from a speeding train can do far more damage than one thrown from a train at rest; the speed of the particle is not independent of the motion of the object emitting it. And if we take light to consist of particles and assume that these particles obey Newton's laws, they will conform to Newtonian relativity and thus automatically account for the null result of the Michelson-Morley experiment without recourse to contracting lengths, local time, or Lorentz transformations. Yet, as we have seen, Einstein resisted the temptation to account for the null result in terms of particles of light and simple, familiar Newtonian ideas, and introduced as his second postulate something that was more or less obvious when thought of in terms of waves in an ether."
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Pentcho Valev replied on Jun. 8, 2011 @ 05:19 GMT
Another clue:
https://webspace.utexas.edu/aam829/1/m/Relativity_files
/RitzEinstein.pdf
Alberto Martinez: "In sum, Einstein rejected the emission hypothesis prior to 1905 not because of any direct empirical evidence against it, but because it seemed to involve too many theoretical and mathematical complications. By contrast, Ritz was impressed by the lack of empirical evidence against the emission hypothesis, and he was not deterred by the mathematical difficulties it involved. It seemed to Ritz far more reasonable to assume, in the interest of the "economy" of scientific concepts, that the speed of light depends on the speed of its source, like any other projectile, rather than to assume or believe, with Einstein, that its speed is independent of the motion of its source even though it is not a wave in a medium; that nothing can go faster than light; that the length and mass of any body varies with its velocity; that there exist no rigid bodies; that duration and simultaneity are relative concepts; that the basic parallelogram law for the addition of velocities is not exactly valid; and so forth. Ritz commented that "it is a curious thing, worthy of remark, that only a few years ago one would have thought it sufficient to refute a theory to show that it entails even one or another of these consequences...."
Pentcho Valev pvalev@yahoo.com
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Eckard Blumschein replied on Jun. 8, 2011 @ 16:33 GMT
Dear Pentcho,
Thank you for the link to the Physics in Perspective paper. You might be surprised, I wrote an unpublished manuscript "A still valid argument by Ritz". While you seem to entirely agree with emission theory, I merely consider Lorentz transformation and Poincaré "synchronization" most likely wrong. I was surprised that already Planck and Boltzmann disputed the issue of past and future. The latter committed suicide instead of admitting being possibly wrong. Why did not Planck or somebody else came to the conclusion to distinguish between abstracted usual time and measurable elapsed time? Do you have further information on this?
Regards,
Eckard
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Wilhelmus de Wilde de Wilde wrote on Jun. 3, 2011 @ 15:32 GMT
I like the idea of christallisation (entropy?) of reality, but in fact it is not so very much different from the many worlds theory, the difference is in my opinion that there is only ONE past, but the possibillities of the future are endless, therefore the free will is introduced, you can wonder if this "free" will is appliccable for an individual observer in one experiment or observation, there are 6,5 billion other observers around us , each of them "realising" or in this case "cristallizing" a now moment, all these together form the universe we live in, (the cd is not written by only one).
I should like to add a little thought experiment :
A photon travels in our universe at the speed of light (time is not passing), by accident it passes the border of one of the paralel universes that surround us, in this paralel universe the speed of light is higher as in ours, observers in this universe are not aware of our photon because of the little difference in constitution, our photon travels on with 2 times the speed of light , i.e.time is going back for our photon and it returns in his past being being our Universê the moment before it moved to the paralel universe, what happens ?
1. we will never observe the photon disappearing
2.our neighbours will never observe the so called black matter photon
So in both universes no one can observe anything, there is no cristalisation of any past possible.
In this thought experiment however black matter and dark energy is explained for both universes.
to be continued
Wilhelmus
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Eckard Blumschein wrote on Jun. 4, 2011 @ 04:08 GMT
When Einstein declared "the separation between past, present, and future an obstinate illusion" he made two horror mistakes at a time.
The metaphor by Ellis nicely illustrates what Claude Shannon correctly described: Past and future are fundamentally different from each other.
Einstein's denial of the separation between past and future has been a requirement for the round-trip synchronization he adopted from Poincaré.
Neither Einstein nor Ellis clarified what they meant with the notion present. The present does not at all qualify as a physical quantity because it is used in a deliberately imprecise manner as to possibly include parts of past and future at a time.
Eckard
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Pentcho Valev replied on Aug. 15, 2011 @ 11:06 GMT
Eckard Blumschein wrote: "When Einstein declared "the separation between past, present, and future an obstinate illusion" he made two horror mistakes at a time."
From a logical point of view, the mistake is only one: his 1905 constant-speed-of-light postulate is false. So one should not reject the block universe without questioning special relativity, as Ellis does. Presentists are much more straightforward:
http://philsci-archive.pitt.edu/2308/1/prese
ntism_and_qg_vp_3_dd.pdf
PRESENTISM AND QUANTUM GRAVITY, by Bradley Monton
"I am a presentist: I believe that only presently existing things exist. Contrast presentism with eternalism: the eternalist believes that past, present, and future things all exist. Assuming that there are three spatial dimensions, the eternalist believes that the universe is fourdimensional, and while there are different events in different regions of this so-called "block universe", the universe as a whole does not change. The presentist, in contrast, believes that the universe is three-dimensional. (...) The point of this paper is not to argue for presentism, but to defend presentism from a particular type of argument that is often taken to refute it. The form of the argument is as follows:
(1) Presentism is incompatible with relativity theory (usually the focus is on special relativity).
(2) Relativity theory is our most fundamental theory of physics.
(3) Presentism is incompatible with our most fundamental theory of physics. (From (1) and (2).)
(4) Presentism is false. (From (3).)
(...) But regardless of the strength of the arguments for presentism, the presentist is not required to endorse a non-traditional understanding of relativity. The presentist can simply say that presentism is incompatible with special and general relativity, and hence special and general relativity are false."
______________________________
[end of quotation]
How can special relativity be false? It is based on two postulates - the principle of relativity and the principle of constancy of the speed of light - so one of the postulates must be false. Which one? This is an absolute-crimestop question in Einsteiniana:
http://www.liferesearchuniversal.com/1984-17
George Orwell: "Crimestop means the faculty of stopping short, as though by instinct, at the threshold of any dangerous thought. It includes the power of not grasping analogies, of failing to perceive logical errors, of misunderstanding the simplest arguments if they are inimical to Ingsoc, and of being bored or repelled by any train of thought which is capable of leading in a heretical direction. Crimestop, in short, means protective stupidity."
Pentcho Valev pvalev@yahoo.com
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Eckard Blumschein replied on Aug. 16, 2011 @ 00:39 GMT
Dear Pentcho,
Is presentism the only alternative to eternalism? Because the notion presence is deliberately imprecise, I wonder why some people are using it in physics.
In reality, only traces and memories from the past are presently available or even influencing. The past is distinguished since it cannot be influenced.
To my knowledge, the speed of electromagnetic waves is limited to a constant value in vacuum as also is the speed of sound waves in a given medium. Claimed ftl propagation of signals were elusive. Electric and magnetic fields that are measurable without spatial restriction can obviously not belong to a closed local system like Galilei's boat which is the precondition for independence of velocity. For this reason, I do not exclude that Einstein's postulate of relativity is unrealistic in the real world while logically flawless on the playground of an assumed closed and tense-less system.
I got aware of those who are proponents of deBroglie's guiding wave and neo-Lorentzian relativity.
Regards,
Eckard
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John Merryman wrote on Jun. 6, 2011 @ 02:12 GMT
Very interesting article by Tony Rothman in American Scientist:
http://www.americanscientist.org/issues/pub/2011/3
/the-man-behind-the-curtain"What’s more, by resorting to a classical optics analogy of the experiment, authors are forgoing any explanation whatsoever. “Explanation” in physics generally means to find a causal mechanism for something to happen, a mechanism involving forces, but textbook optics affords no such explanation of slit experiments. Rather than describing how the light interacts with the slits, thus explaining why it behaves as it does, we merely demand that the light wave meet certain conditions at the slit edge and forget about the actual forces involved. The results agree well with observation, but the most widely used of such methods not only avoids the guts of the problem but is mathematically inconsistent. Not to mention that the measurement problem remains in full force.
Such examples abound throughout physics. Rather than pretending that they don’t exist, physics educators would do well to acknowledge when they invoke the Wizard working the levers from behind the curtain. Even towards the end of the twentieth century, physics was regarded as received Truth, a revelation of the face of God. Some physicists may still believe that, but I prefer to think of physics as a collection of models, models that map the territory, but are never the territory itself. That may smack of defeatism to many, but ultimate answers are not to be grasped by mortals. Physicists have indeed gone further than other scientists in describing the natural world; they should not confuse description with understanding."
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Edwin Eugene Klingman wrote on Jun. 10, 2011 @ 04:13 GMT
Joy Christian has written an interesting paper
Absolute Being vs Relative Becoming on this topic.
Edwin Eugene Klingman
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Eckard Blumschein replied on Jun. 10, 2011 @ 14:16 GMT
Please read my comment on it from Apr. 14 on topic 963.
Eckard
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Lawrence B. Crowell wrote on Jun. 10, 2011 @ 17:22 GMT
The block universe with a dynamic occurrence of time, or this crystallizing of time in various present periods on a spatial sheet of 3-dim, invokes a funny thing. Quantum mechanics is noncontextual in that the basis of vectors is not determined by anything in quantum mechanics. It is selected for by the experimentalist. Hence the contextual aspects of a quantum measurement are what quantum interpretations are centered upon. In the Copenhagen interpretation (CI) the cut is the classical-quantum dichotomy. Of course for this to be “absolute” you need an apparatus which is absolutely non-quantal, meaning its mass must be infinite, and you need an infinite number of experiments. That is fictional of course. The many worlds interpretation (MWI) indicates there is a splitting off of world according to eigenbases selected. The idea is then that the world continues to be quantum mechanical. However, that is still funny, for the world is split off according to the contextuality of the wave function decoherence, or equivalently by the eigen-basis chosen by the experimenter. So this too is not a complete picture.
Quantum interpretations attempt to reduce the mysterious nature of quantum mechanics to our classical understanding, which has an intuitive sensory aspect to how we perceive the world. Yet at the end if the universe is entirely quantum mechanical it is unlikely that any of these schemes can ever work completely. The hidden problem is that QM is inherently noncontextual, but how we interpret QM is contextual. This is a contradiction.
With the block universe it seems reasonable to say the progression of time involves decoherent events, or what has been called wave function collapse. Yet in a subtle way this model has the above contradiction, just as does MWI or CI. This suggests a number of things. I think the primary one is that quantum cosmology should not focus primarily on the issue at all. The question is with the equivalency between quantum entanglements and spacetime configurations. I further suspect this issue of what constitutes a present time and issues of a “flow of time” may simply not be appropriate questions to ask. This may be similar to tinkering around with aether theories and the like before 1905.
Cheers LC
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T H Ray replied on Jun. 11, 2011 @ 01:06 GMT
Yes, the fact that quantum measurement unavoidably depends on classical parameters breeds consequences that are frequently swept under the rug of metaphor.
This was the case in suggesting the history of the world on a DVD (or any finite instrument). I agree with the question of equivalence between "... quantum entanglements and spacetime configurations."
That would necessarily move the problem to n-dimension Hilbert space and the string theory extension of quantum field theory. One does not encounter the histrionic objections to "mainstream science" in physics forums outside this one. As elusive as the answers are, the basic formalisms are correct.
Tom
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Lawrence B. Crowell replied on Jun. 11, 2011 @ 03:29 GMT
The main point of a physical theory is to make predictions about measurable observables. The question on how we perceive time does far not a measurable quantity, at least at this time. We might even imagine there are intelligent life forms on other planets which perceive space and time in very different ways. If a quantum gravity theory is arrived at it might from there tell us about how it is we observe time, at it might be a dynamic block or crystallizing world. On the other hand it might not do that, but still gives answers to question or problems that have some measurable observables which can be probed.
Cheers LC
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Eckard Blumschein replied on Jun. 11, 2011 @ 10:21 GMT
LC, You wrote: "The main point of a physical theory is to make predictions about measurable observables. The question on how we perceive time does far not a measurable quantity".
I see any performed measurement of time not a question of perception but clearly related to two more or less distant events in the past.
If someone attributes traces to the past then he considers the past as part of the abstract notion time that includes both past and future. Actually measurable are only the traces of past processes. This memory of traces altogether constitutes the unchangeable reality called the past in the sense of a contextual entity of partially predictable influences.
Is it correct to attribute observability to a concrete physical quantity? Definitely yes inside a model, however definitely no in reality. Predictions are more or less uncertain.
Eckard
Because English is not my mother tongue, I wonder why you wrote "far not". May I understand "not far" as almost?
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Lawrence B. Crowell wrote on Jun. 11, 2011 @ 12:08 GMT
Eckard,
The perceptions we have of space and time are in a way mental constructions. Barbour argues that time does not exist due to the fact the ADM Hamiltonian and momentum constraints NH = 0, N^iH_i = 0 have not time content. This extends to the Wheeler DeWitt quantum version HΨ[g] = 0. The set of diffeomorphisms of the theory are removed on the moduli space, and so identification of Diff(M) with time can’t be established. However, I could equally suppose that time is a one dimensional space with a fibration of three dimensional manifolds we think of as space. I can further work out how these two pictures are in fact quantum complementarities.
In either case what we call space and time are not written in concrete at all. They are an aspect of an external degree of gauge freedom, or a coordinate choice on a frame bundle, which are chosen by the analyst or observer. They are not at all gauge covariant, and hence really do not constitute anything which can be called physically real. They are artifacts of a gauge choice, or in some sense constructed by the observer. In effect we “make them up.”
As for the “far not,” that is a mangled re-edit. The sentence “The question on how we perceive time does far not a measurable quantity, at least at this time,” probably should read “The question on how we perceive time does not so far address a measurable quantity, at least currently.”
Cheers LC
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Eckard Blumschein replied on Jun. 11, 2011 @ 23:52 GMT
LC, Now I understand your sentence. Thank you. I even understand that Lorenz gauge condition is Lorentz invariant.
However, my caveat cannot be understood within the restriction to models of reality instead reality itself. A year is a reasonable objective measure. The number of years elapsed since my birth does not depend on any arbitrarily chosen gauge. Gauge redundancy and gauge arbitrariness do not matter in reality.
I agree: We made up what we are calling time.
However, the just elapsed time is an objective and measurable positive quantity with a natural reference point: Now.
Likewise, any shortest distance between two points in space cannot be negative.
Obviously my caveat is most fundamentally at odds with a lot of non-commutative, non-abelian theories that refer to the usual abstract and arbitrarily chosen notion of time which is not immediately linked with reality: Block universe, Poincaré synchronization, Lorentz transformation, Minkowski metric, Weyl's Eichinvarianz, ...
Regards,
Eckard
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Lawrence B. Crowell replied on Jun. 13, 2011 @ 02:59 GMT
Supersymmetry is a way of interchanging internal symmetries with external symmetries. The internal symmetries are local gauge changes which introduce forces. External symmetries are the Lorentz group of boosts and rotations in spacetime. We are all familiar with the idea that internal symmetries are fictional: Take an electromagnetic vector A and add a gradient of some scalar A’ = A + gradX and we then have that the magnetic field B = -curlA’ = -curlA – curl gradX, and the last term is zero. The difference is that with the external symmetries we have a sense of them and an arrangement of objects and ourselves with respect to each other in a spatial arrangement. Yet if internal and external symmetries are interchangeable it must mean their physical statuses are equivalent.
We are all familiar with curved spacetime, after all general relativity is nearly 100 years old now, but in fact we see little immediate presence of it. The curvature of spacetime due to Earth’s gravity is 10^{-27}cm^{-2} --- tiny. By the same token we hardly have much sense that space is just a configuration variable for fields, and time is a parameterization of fields --- which are Lorentz covariant. Black hole change things a bit, for the observer outside the black hole witnesses physics according to an S matrix with a different domain than an observer who falls in with the quantum field of interest. The two observers witness the process according to entirely different representations, and yet in the end the core physics is the same. What is different is how the physical fields are “dressed,” or should we say the particular moduli used.
In analogy with the dressing of quantum states and moduli, I could tomorrow put on a suit and head out to work. I could instead try something a bit different and put on a women’s suit dress. The difference is superficial, for it is how the material folds and hangs on the underlying frame that is different --- the basic frame is the same, nothing fundamentally is different. Yet we tend to see the clothes, how the quantum states are dressed or the phase of the entanglement, as equal to the underlying quantum bits. Space and time share this property of being like the clothes.
Cheers LC
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Eckard Blumschein wrote on Jun. 14, 2011 @ 09:54 GMT
LC,
All your reasoning fits to the currently mandatory assumption of a block universe which is for instance explained in an extensive while nonetheless not convincing to me manner by Lebovitz in http://www.scholarpedia.org/article/Time%27s_arrow_and_Boltz
mann%27s_entropy
Lebovitz admits that his view is opposed to the camp of "those who regard the passage of time as an objective feature of reality, and interpret the present moment as the marker or leading edge of this advance."
Lebovitz continues: "Some members of this camp give the present ontological priority, as well, sharing Augustine's view that the past and the future are unreal". Unfortunately I did not manage to convince proponents of this view that the present is a deliberately imprecise notion.
Lebovitz adds: "Others take the view that the past is real in a way that the future is not, so that the present consists in something like the coming into being of determinate reality". I see this view in accordance with Claude Shannon and the only reasonable view. I just wonder why apparently nobody dealt seriously with it.
Isn't my reasoning extremely uncommon but a bit more consequent and compelling? We both may agree on that the usual notion of time is just a mental construct while admittedly a very successful one. However, isn't it based on experience? Experience is necessarily restricted to the belonging past. Future events evade observation and measurement. Therefore, there is NO flow of time but a steady growth of elapsed time.
Reality is not invariant under shift. Invariance, covariance etc. are based on abstraction and therefore restricted to models. Physicists should learn to correctly interpret the results of their calculations.
Elsewhere I fond the utterance: "Mathematics dictates physics." I would like to object: It does definitely not dictate reality if its essence is its freedom.
Regards,
Eckard
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Eckard Blumschein replied on Jun. 15, 2011 @ 18:32 GMT
LC,
Don't you consider Vesselin Petkov correctly stating that the timelessly existing block universe is the only one that is consistent with special relativity?
http://philsci-archive.pitt.edu/2408/
Regards,
Ecka
rd
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Lawrence B. Crowell replied on Jun. 16, 2011 @ 14:37 GMT
As a classical theory I could be disposed to this perspective. The block world in special relativity is of course the most direct. In general relativity this is a bit more complicated, but the block world is still the simplest to think about. The ADM approach to general relativity has some applicability, but I will not quibble the point here.
The problem comes with quantum mechanics. If reality is quantum mechanical all the way down, then the block world, even relational block world or crystallizing block world, becomes problematic. This depends upon some subtle issues with the foundations of quantum physics. In particular it depends upon an interpretation which has a problem with non-contextuality in QM. This puts a relational block world view in the same category as a quantum interpretation.
I suspect that quantum interpretations are in general false on some level, and this means all of them: Copenhagen, Bohm, Many Worlds, Consistent Trajectories and so forth. These quantum interpretations are also not testable, for they have no prediction of an observable consequence which can be observed to support them. They are not really theories in a proper sense.
The problem is that these interpretations are ways of trying to make quantum mechanics transparent within a classical mode of thinking. This really is a sort of intellectual security blanket or teddy bear. In order to pursue quantum gravity we are going to have to lay these things aside.
Cheers LC
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Eckard Blumschein replied on Jun. 16, 2011 @ 21:23 GMT
LC, As I understood, the Hamiltonian formalism of ADM describes spacetime as space evolving IN time, and Lee Smolin comes from Deser.
Doesn't already the word IN imply an a priori existing time alias block time? When I was confronted with Ellis' emerging block universe, I appreciated the criticism of tenseless spacetime. However, up to now I did not understand how something emerging can be an priori given block. To me the two possibilities exclude each other, and the various attempts to unite them are altogether doomed to fail.
I tend to agree with Vesselin Petkov in that, the unrealistic block universe is an indisputable precondition for SR. While I am fully aware of the consequence to be put into the drawer of many many cranks, I see no reasonable alternative as to question SR and already Lorentz transformation. I will read arguments by Lucas and by Popper who, as I was told, called Einstein a Parmenides.
What about the foundations of quantum mechanics, I already investigated what I consider improper use of complex calculus by Heisenberg/Jordan/Born, Schroedinger/Weyl, and Dirac.
Regards,
Eckard
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Lawrence B. Crowell replied on Jun. 17, 2011 @ 18:58 GMT
It is tempting to identify the foliation of spaces with a “time.” However, what ADM relativity describes are a set of spatial surfaces which are related to each other by diffeomorphism. What has not really been done, as far as I know, is to demonstrate explicitly that this is time.
Classically the block time does make sense. It does have to be realized this is a model system, it is not necessarily the universe at its foundations. When you bring quantum mechanics into the picture this model gets shaken to its core. Attempts to revise the block time picture with MWI or other state reduction schemes runs into the subtle questions I outline above.
Cheers LC
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Eckard Blumschein replied on Jun. 21, 2011 @ 15:57 GMT
LC,
Lepp pointed me to Ranzan who commented on the difference between length contraction just in the direction of motion as imagined by Lorentz and the just imagined one introduced by Poincarè and Einstein. I already read the same distinction made by Tom Van Flandern. While the mathematics of the block universe seems to be flawless, I tried to show in my essay that it does not fit reality.
You wrote: "Attempts to revise the block time picture ... runs into the subtle questions I outline above." May I replace "the subtle questions" by a fundamental contradiction?
Regards,
Eckard
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Lawrence B. Crowell replied on Jun. 22, 2011 @ 13:36 GMT
This could be an outright contradiction. A revision of the block world within a quantum mechanical setting needs to overcome the polarity between contextuality and noncontextuality. A world with a present time slice which emerges as it evolves requires some sort of context in which quantum basis vectors are selected. Without some external control this has to be done by quantum mechanics itself. However, quantum mechanics is noncontextual, and it is difficult to see how the emergence of a present space with all the field data on it according to some contextual meaning to quantum states can emerge.
There may be some subtle issue involved that escapes our attention. Quantum mechanics has a complementary logic, and contextuality and its logical complement noncontextuality have some quantum dualism. However, how to frame such a possibility is not apparent to me.
In a classical setting block time is the most direct model. The problem of setting up a relational block world in a quantum setting seems to have some connection to issues of quantum gravity and cosmology. It will be interesting to see if the block time can be revised, or whether block world is a classical structure that amounts to excess baggage that is abandoned in quantum gravity.
Cheers LC
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Eckard Blumschein replied on Jun. 23, 2011 @ 07:39 GMT
LC,
I wonder why even physicists apparently dislike the clear distinction between (R) a road in reality and (M) the ideal line that represents it.
I see the block universe an obviously not totally appropriate model, and I also suspect that QM is too much mathematically idealized.
On the other hand, John Lucas considered it worth to illustrate the correct argument by Saint Augustinus that there is no extended time slice between past and future. Not just Einstein wrongly attributed the usual notion of "simultaneity" to simultaneous perception. What nonsense! The only reasonable idea of simultaneity can be explained with a fair duel where the bullets meet exactly in the middle.
While I do not hate anybody, I admire Karl Popper who not just called Einstein Parmenides, i.e. as wrong as Zeno but who also admitted hating Hegel, and I recall Marx speaking of "abstruse Hegelei".
Backed by Popper, I am pretty sure: The block universe is strictly speaking fundamentally wrong but might nonetheless be useful as a model to some extent.
What about noncontextuality, I admit being ignorant of the related and perhaps controversial theories. I merely guess, the real world could not be convincingly described without contextuality.
What about the logical complement, I would like to remind of what I consider flaws in the fundamentals of set theory.
Regards,
Eckard
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Lwrence B. Crowell replied on Jun. 23, 2011 @ 16:02 GMT
Quantum mechanics is to physics almost what logic is to mathematics. It is a system which determines the relationships between qubits in a logico-algorithmic sense. The relationship to classical mechanics or macroscopic physics is what is odd. Of course the macro-world might just be some approximation that we observe in a coarse grained sense. Everything may in effect be quantum mechanical at all levels.
The block world and Einstein concept of time works fine in a classical setting. The thing which muddies the waters is quantum mechanics, and this is compounded by quantum gravity. Quantum mechanics is noncontextual, which means the eigenbasis the state vector is expanded in is not determined quantum mechanically. The context is determined by the observer, such as by the orientation of a Stern-Gerlach apparatus. So the context assigned to quantum outcomes of measurements is determined by the observer in a classical or macroscopic setting. The crystallizing block world in an MWI sense means the present that is materializing involves a set of eigenbranchings, where the “branches” are according to eigenbasis vectors with some contextuality. In the teleportation of states the classical content involves this contextual element, Alice telling Bob how she oriented her SG apparatus. How this happens in a purely quantum mechanical setting is unclear.
The issues of simultaneity and the rest in relativity are pretty clear, and there is no controversy with respect to those results. I have also regarded the Zeno paradox as a funny thing that anyone should ever get wrapped up in. It always struck me as something overcome by calculus, and I think there was some proof to this effect using Robinson numbers derived a couple of decades ago.
As for Hegel, I suppose in keeping with his dialectics I both admire and dislike his work. In some sense what he said is true, and quantum mechanics is an example of Hegelian dialectics. The problem is that Hegel offered no method for using dialectics in some proper fashion. In fact I doubt anything like that could be founded. The founders of QM did not marinate themselves in Hegel before realizing the complementaritiy of QM. Hegel was also more concerned with social issues, which were in flux at his time with the French Revolution and Napoleon. That got taken up by Engels and Marx in a somewhat “loosy-goosy” fashion, but which motivated a lot of unfortunate political stuff in the 20th century.
Cheers LC
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Eckard Blumschein replied on Jun. 23, 2011 @ 21:58 GMT
LC,
Hopefully you will agree with me that perception as well as measurement must be corrected for possibly different delays. I infer from this that Einstein's justification of Popincaré's (de)synchronization is not logical.
Hopefully you will not agree with G. Cantor on that something that is neither smaller nor equal to something must be larger. Logics allows a fourth possibility:...
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LC,
Hopefully you will agree with me that perception as well as measurement must be corrected for possibly different delays. I infer from this that Einstein's justification of Popincaré's (de)synchronization is not logical.
Hopefully you will not agree with G. Cantor on that something that is neither smaller nor equal to something must be larger. Logics allows a fourth possibility: incomparability.
Do we need a quantum logic? Having the textbook "Particles and Paradoxes - The limits of quantum logic" by Peter Gibbins at hand, I tend to deny that.
You are reiterating what is presently common opinion: "QM as well as SR are of eminent importance for modern physics. Therefore they must not be wrong."
-- Really?
You wrote; "Quantum mechanics is noncontextual, which means the eigenbasis the state vector is expanded in, is not determined quantum mechanically."
-- Isn't such expansion arbitrarily assumed?
You continued: "The context is determined by the observer, such as by the orientation of a Stern-Gerlach apparatus. So the context assigned to quantum outcomes of measurements is determined by the observer in a classical or macroscopic setting."
-- This reminds me of Heisenberg's likewise unacceptable interpretation: The path becomes reality if we measure it. Aren't state vectors and the like just abstract models? Could a point or a line become reality? I say no.
-- Maybe I am naive when I consider non-contextuality an simplifying idealization but context about the same as objective while possibly even sub-threshold influences. How do state vectors account for processes and for the embedding of any particle into reality?
You argued: "The crystallizing block world in an MWI sense means the present that is materializing involves a set of eigenbranchings, ... "
-- I desperately hope for understanding: Strictly speaking there is no present.
"... where the “branches” are according to eigenbasis vectors with some contextuality."
-- Isn't this a rather awkward and incomplete substitute for an admission of incalculable influences?
"In the teleportation of states the classical content involves this contextual element, Alice telling Bob how she oriented her SG apparatus. How this happens in a purely quantum mechanical setting is unclear."
-- At least to me the Alice/Bob metaphor is perhaps inappropriate.
Let me summarize: Zeno's flawed arguments indicate that Parmenides/Einstein (the block universe) is strictly speaking wrong. The putative necessity to use i in QM indicates a related and similar flaw in QM. In both cases, an abstract model is arbitrarily equated with reality.
At least laymen might be ready to understand: While time can be shifted, reversed, or otherwise manipulated in a record, a mathematical model, and the like, it cannot be influenced at all in reality. Why? Because pictures are abstractions that will never fully substitute the complete embedding into real life.
Regards,
Eckard
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T H Ray replied on Jun. 24, 2011 @ 10:52 GMT
Eckard,
You wrote to Lawrence: "Hopefully you will not agree with G. Cantor on that something that is neither smaller nor equal to something must be larger."
This is another way of saying that a calculated result must be positive, negative or zero.
"Logics allows a fourth possibility: incomparability."
That's why quantum logic works. Logic in which value is assigned to undecidability allows a superposition of states. "Incomparable" quantities are undecidable -- a measured quantum result is always positive or zero.
Tom
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Eckard Blumschein replied on Jun. 27, 2011 @ 15:08 GMT
Tom,
Galileo Galilei correctly concluded by means of bijection: There are not more natural numbers 1, 2, 3, ... as compared with their squares 1, 4, 9, ... because the comparative relations are not valid for infinite quantities, only for finite ones. G. Cantor claimed having "proved" him wrong by arguing that there must be more irrational numbers than rational ones because something that is neither smaller nor equal to something must be larger." Accordingly Cantor introduced what he first called Maechtigkeit and later renamed cardinality.
Is this "another way of saying that a calculated result must be positive, negative or zero"? Well, explicit finite numerical results are rational numbers and therefore they obey this trichotomy. However, as I tried to explain in my last essay, Cantor's naive transfinite numbers have proven sterile. Already in 1922 Fraenkel admitted: Cantor's definition of sets, including infinite ones, is untenable.
"It is always assumed that a Hilbert space can have no more than a countable infinity of linearly independent state-vectors. This implies that there are no eigenstates of exact position, that the Dirac delta-function is illegitimate." [quoted from Gibbins, p. 90].
Regards,
Eckard
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T H Ray replied on Jun. 27, 2011 @ 16:15 GMT
Eckard,
Physics does not require, nor use, transfinite algebra. Every measured result has to be positive or zero. Negative and imaginary numbers are mathematical artifacts.
If one is disposed (I am) to argue for a continuum of mathematical results with physical phenomena, one has to be careful when speciifying domains. No physical domain that is not measure zero, is infinite. To use a simplistic analogy, though, of the uncountable molecules of water that go into making up a river at its source, we recognize finite phase transitions from vapor to moisture to puddle, etc. Extending that process to the origin of the universe is not a leap -- it is continuous.
You wrote: "Galileo Galilei correctly concluded by means of bijection: There are not more natural numbers 1, 2, 3, ... as compared with their squares 1, 4, 9, ... because the comparative relations are not valid for infinite quantities, only for finite ones. G. Cantor claimed having "proved" him wrong by arguing that there must be more irrational numbers than rational ones because something that is neither smaller nor equal to something must be larger." Accordingly Cantor introduced what he first called Maechtigkeit and later renamed cardinality.
Is this "another way of saying that a calculated result must be positive, negative or zero"?"
No. The idea of the cardinality of sets has nothing to do with numbers per se. It describes comparative relations, so it certainly is appropriate for infinite sets. Infinity is not a number.
"Well, explicit finite numerical results are rational numbers and therefore they obey this trichotomy."
We assume so. Intuitionists and some constructivists would disagree, allowing that without an explicit procedure to decide, one cannot know whether a result is positive, negative or zero. Again, though, this has nothing, at least directly, to do with physics.
You wrote, "However, as I tried to explain in my last essay, Cantor's naive transfinite numbers have proven sterile. Already in 1922 Fraenkel admitted: Cantor's definition of sets, including infinite ones, is untenable.
"It is always assumed that a Hilbert space can have no more than a countable infinity of linearly independent state-vectors. This implies that there are no eigenstates of exact position, that the Dirac delta-function is illegitimate." [quoted from Gibbins, p. 90].
Set theory (arithmetic) is useful to physics. Its usefulnes is limited, however, to the counting function. Physics doesn't address infinite sets.
Tom
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Lawrence B. Crowell replied on Jun. 27, 2011 @ 21:34 GMT
The irrational numbers turn out to be countably infinite. The reason is that they are roots of polynomials and their rings, which have a countably infinite realization. However, this is a dense set in the reals, where transcendental numbers such as π that are not polynomial solutions fill in the gaps. The uncountably infinite number of reals is due to Cantor’s diagonalization procedure, and the number of possible diagonal “slashes” one may perform for n numbers is 10^n. In the limit that n -- > ∞ the cardinality of the set of numbers formed by “slashes” is greater than countable infinity. So this get one into the continuum problem with C = 2^{X_0} > X_0, where X stands for aleph.
As Tom points out this is not terribly relevant for physics. We generally don’t run around worried about levels of infinity. This is connected to Godel’s theorem, and its algorithmic and information theoretic connection is with Turing’s proof. At this point one can bring a computational aspect of this mathematics into physics. Things such as space represents relationships between physical objects, but in spite of all our advances with things such as curved spacetime it is still the case that spacetime is a model system. The assignment of degrees of freedom to spacetime results in problems, with over counting them and entropy measures that are too large. So there is no real worry with respect to the continuum of space. Where physics connects to this is with the algorithmic connections to set theory.
Cheers LC
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Eckard Blumschein replied on Jun. 28, 2011 @ 18:08 GMT
LC and Tom,
David Tong wrote: "discreteness in the world is simply the Fourier transform of compactness". He did not answer my question whether this also holds for cosine transform.
I am voting for realism, i.e., strict distinction on the level of abstract notions.
This includes to not blur the distinction between positive and negative, past and future, countable in the sense of discrete and uncountable in the sense of attributed to a continuum. I am aware of many seeming exceptions. They do altogether belong to missing precision of the used definitions. While a river consists of discrete molecules, it does not have exact borders.
May I reiterate my suggestion to reinstall the Euclidean notion of number as a measure: Instead using f(x) I am suggesting to distinguish for a continuum between the two limits from below f(smaller than x toward x) and above f(greater than x toward x). See my essay.
|sign(0)|=1, not 0.
Regards,
Eckard
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Lawrence B. Crowell wrote on Jun. 14, 2011 @ 17:19 GMT
Block time only makes sense in a classical setting. The idea of the crystallizing block time, or dynamics block time, involves the reduction of quantum states so that the present is something that is materializing. The hitch with this idea is that it means there is some contextual aspect to how quantum states decohere. In a measurement this contextual framework involves the eigenbasis the observer chooses according to how she orients an apparatus. Yet we know that quantum mechanics is non-contextual. This is one problem with the many world interpretation MWI). MWI posits the splitting off of the world according to separate eigenstates, but this can only happen in a contextual framework. Yet if the world is fully quantum mechanical there is no such context by which it splits itself off. So MWI buries the quantum-classical dichotomy more apparent in the Copenhagen interpretation in this subtle contradiction. This is the problem with the whole model here.
My main point is that we impose time as well as space onto the universe. What is physically relevant are the obstructions to flatness which might occur, which we call curvature. These are chosen according to the particular frame we elect to work in and observe the universe. There is no physical prescription which tells us how space is laid out or how time is to organize event in space.
Cheers LC
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John Merryman replied on Jun. 17, 2011 @ 02:56 GMT
Lawrence,
So all curvature is a function of horizon effects, that it is subject to one's perspective?
How do we know this bias doesn't underlay such assumptions as the current cosmology of an expanding universe?
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Lawrence B. Crowell replied on Jun. 17, 2011 @ 19:01 GMT
Event horizons are null congruencies and are invariants. Everything else that is timelike transforms in a covariant or frame dependent way.
Cheers LC
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Douglas William Lipp wrote on Jun. 15, 2011 @ 11:41 GMT
The attached represents my theory.
I have named my own model of the Universe, the Minverse Model (previously Coney Island Green, the name of the theory). See all below & attached.
I would be much greatful if the community consider this new model.
It is named Minverse (miniverse) because each mass entity acts as its own Universe, capable of creating space from mass.
Do not be afraid to believe in the theory.
Any questions, please contact me.
Douglas Lipp
Here are its claims (see also attached)
To Cosmologists and Theoretical Physicists,
The attached theory welcomes intense scrutiny and comment by experts.
Though the paper remains in need of further revision, nonetheless its current content is sufficient to promulgate research directed toward its firm confirmation. It is a "new model" of the Universe/Multiverse. The suggested term is the: "The Minverse Model" (short for miniverse, while at the same time in honor of my grandmother, Minerva).
The theory includes a mass to space quantification. It should be noted that the great physicist Faramarz Ghassemi was pursuing a similar mass to space view of nature. It is time other physicists take a serious look.
The theory offers in a "single view of nature", and "simultaneously", the following:
Varying Cosmological Constant
Possible explanation of Virtual Particles
Combination of the Spacetime Continuum with the Mass-energy equation
Quantification of mass to a spatial quantity
Solution to Dark Matter
Solution to Dark Energy
Solution to Horizon Problem
Solution to Red Shift Anomalies
Solution to Double Slit (Young's) Wave-Particle Duality Quantum Confusion
Physical explanation as to what E=mc² actually represents
New Interpretation of Einstein's Field Equations
True reason for Hubble expansion
Fourth Law of Motion Equating Gravity to Other Forces
Possible meaning of Plancks Constant
Lipps Law of Proportionality
Offers a New Explanation of Pressure
Is Relativitivistic in nature and therefore builds upon current science
Does not rely on extra dimensions
Does not rely on speeds greater than "c" as does current inflationary theory
Combines the Fundamentals (Matter, Time, Space)
Coherently respects conservation of energy (current view of expansion of space does not)
Above all else, the theory is experimentally verifiable.
Comments are welcome and can be delivered here or to lippfamily@earthlink.net
For a hard copy, please email the author.
Once again, the author apologizes for what appears to be a paper not altogether written in scientific/academic protocol.
Enjoy the "Fun" section as well.
Please open the attached to find: "The Coney Island Green Theory".
Thank You,
Douglas W. Lipp
attachments:
3_MTSFINAL15Rollover12.doc
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Lawrence B. Crowell wrote on Jun. 24, 2011 @ 17:44 GMT
Eckard & Tom,
I suppose you are referring to the Banach-Tarski paradox or the addition of transfinite numbers. The axiom of choice (AC) does involve the well ordering of a set. Hilbert space exists because of the AC. The Schmidt orthogonalization procedure employed in quantum mechanics and the theory of Banach-Hilbert spaces is an algorithm which works because the space is well ordered. ...
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Eckard & Tom,
I suppose you are referring to the Banach-Tarski paradox or the addition of transfinite numbers. The axiom of choice (AC) does involve the well ordering of a set. Hilbert space exists because of the AC. The Schmidt orthogonalization procedure employed in quantum mechanics and the theory of Banach-Hilbert spaces is an algorithm which works because the space is well ordered. This is a sort of choice function.
I have been working on the integer partition theorem. Given an integer n, there exists a set of integers (n1,n2,…) which add up to n, and then there are other sets as well, and the number of these sets is the partition. This has physical implications for how microstates of a black hole can be arranged amongst n Planck areas on the event horizon. The partition number grows approximately exponentially for the number of integer sets which sum to n as n --> ∞. Consequently, the set of all possible integer partitions for the integers is a power set, which is an C = 2^{X_0} result. X = aleph
The AC is an undecidable proposition as well. Some research was done on this, which I know about but I don’t have references available, and it was found that the AC is not a consequence of the other axioms in ZF. The axiom of replacement I think has a similar property.
The AC does result in some quirky results though. A sphere can be decomposed in a certain way, group rotations (eg SO(3)) performed, and the pieces further decomposed and rotated, and … infinitely onwards. The pieces may then be reassembled to construct two spheres identical to the first. This is the result of Banach and Tarski.
Some mathematicians consider the Banach-Tarski theorem to be a reducto-absurdum argument against the AC. That's one of the reasons for considering other axioms. The Perfect Set hypothesis "Every uncountable subset of the real line has a non-empty perfect subset." is inconsistent with the AC and seems just as intuitive. This gets into the subject of Polish spaces. However, in what I do it is not my interest to rewrite the foundations of mathematics.
Special relativity and quantum mechanics are “true” in the same way that Newtonian mechanics is “true.” They both work in a broad domain of observation and have been extensively tested. There really are no controversies over the issue of simultaneity and clock synchronization. I worked on problems related to the question of synchronizing clocks for GPS and various other satellites. That gets more complicated with general relativity, but there are no serious controversies with the basic issues. Much the same holds with QM, and recently an experimental version of the Kochen-Specker theorem on quantum nonlocality was performed and the KS result supported.
My take on the issue of space and time is they are configuration variable representations which have a type of complementarity. This being the case there is no physical axiom which can tell us which of these is “real.” Fundamentally there is no such axiom, and the observer imposes the context upon which is real, or how the two are related to each other. Classical spacetime does not share this feature, which is why in the classical domain you can talk about a block time.
The complementarity of space and time and the quantum mechanics of black holes could have had a much earlier start. At the 1930 Solvay conferences Neils Bohr and Albert Einstein debated the nature of quantum mechanics. Einstein was convinced of reality and locality and argued staunchly for an incompleteness of quantum mechanics. Quantum theory could only be made complete if there are some hidden variables that underlay the probabilistic, nonlocal quirky aspects of quantum mechanics. Einstein proposed an interesting thought experiment. Einstein considered a device which consisted of a box with a door in one of its walls controlled by a clock. The box contains radiation, similar to a high-Q cavity in laser optics. The door opens for some brief period of time t, which is known to the experimenter. The loss of one photon with energy E = ħω reduces the mass of the box-clock system by m = E/c^2, which is on a scale. Einstein argued that knowledge of t and the change in weight provides an arbitrarily accurate measurement of both energy and time which may violate the Heisenberg uncertainty principle ΔEΔt~ħ
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Bohr realized that the weight of the device is made by the displacement of a scale in spacetime. The clock’s new position in the gravity field of the Earth, or any other mass, will change the clock rate by gravitational time dilation as measured from some distant point the experimenter is located. The temporal metric term for a spherical gravity field is 1 - 2GM/rc^2, where a displacement by some δr means the change in the metric term is \simeq~(GM/c^2r^2)δr. Hence the clock’s time interval T is measured to change by a factor
T-- >T sqrt{(1 - 2GM/c^2)δr/r^2} ~ T(1 - GMδr/r^2c^2),
so the clock appears to tick slower. This changes the time span the clock keeps the door on the box open to release a photon. Assume that the uncertainty in the momentum is given by the Δ p ~ ħ/Δr \lt TgΔm, where g = GM/r^2. Similarly the uncertainty in time is found as ΔT = (Tg/c^2)δr. From this ΔT > ħ/Δmc^2 is obtained and the Heisenberg uncertainty relation ΔTΔE > ħ. This demands a Fourier transformation between position and momentum, as well as time and energy.
This holds in some part to the quantum level with gravity, even if we do not fully understand quantum gravity. Consider the clock in Einstein’s box as a black hole with mass m. The quantum periodicity of this black hole is given by some multiple of Planck masses. For a black hole of integer number n of Planck masses the time it takes a photon to travel across the event horizon is t ~ Gm/c^3 ~ nT_p, which are considered as the time intervals of the clock. The uncertainty in time the door to the box remains open is
ΔT ~ Tg/c(δr - GM/c^2),
as measured by a distant observer. Similarly the change in the energy is given by E_2/E_1 ~= sqrt{(1 - 2M/r_1)(1 - 2M/r_2)}, which gives an energy uncertainty of
ΔE ~ (ħ/T_1)g/c^2(δr - GM/c^2)^{-1}.
Consequently the Heisenberg uncertainty principle still holds Δ EΔT ~ ħ. Thus general relativity beyond the Newtonian limit preserves the Heisenberg uncertainty principle. It is interesting to note in the Newtonian limit this leads to a spread of frequencies Δω ~ sqrt{c^5/Għ}, which is the Planck frequency.
The uncertainty ΔE ~ ħ/Δt larger than the Planck mass gives an event horizon. The horizon has a radius R ~ 2GΔE/c^4, which is the uncertainty in the radial position ΔR associated with the energy fluctuation. Putting this together with the Planckian uncertainty in the Einstein box we then have
ΔrΔt ~ 2Għ/c^4 = L^2_{Planck}/c.
So this argument can be pushed to understand the nature of noncommutative coordinates in quantum gravity.
This complementarity means that fundamentally with quantum mechanics there is no meaning to space and time outside of the context of a measurement, or the choice of observation. QM has no contextuality of its own, and so any statement made about the spatial and temporal nature of the world is something which is determined by the choice of basis by the observer.
Quantum logic is interesting in some ways, but I don’t think it really buys us that much. It is sort of a formal set theory way of doing what we already understand.
Cheers LC
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Eckard Blumschein replied on Jun. 27, 2011 @ 08:56 GMT
LC,
"Some mathematicians consider the Banach-Tarski theorem to be a reducto-absurdum argument against the AC." You wrote: "...is not my interest to rewrite the foundations of mathematics." You meant the putative ones of mathematics, i.e. the foundations of contemporary mathematics, which are based on Cantor's belief that there are more than infinitely many numbers (ueberabzaehlbar means than countable).
To those who are not familiar with history: The AC was arbitrarily fabricated by Zermelo in 1904 in order to rescue Cantor's well ordering of uncountable sets.
Well, those mathematicians who provided most useful contributions to mathematics used the irrational numbers as if they were rational ones. However, I do not see any compelling reason to ascribe trichotomy to them. If "Hilbert space exists because of the AC" then it might be questionable. I am anyway wondering why Tong meant "no one knows how to write down a discrete version of the Standard Model". Maybe, his essay is not just the usual antithesis to my essay. At least I agree with his last sentence: "We are not living inside a computer simulation".
You repeatedly declared SR correct: "There really are no controversies over the issue of simultaneity and clock synchronization." Don't some hundred
petitors consider the twin paradox an reductio-ad-absurdum argument against SR? What about Van Flandern? What about Popper? Weren't the Pythagoreans, Parmenides, Zeno, G. Cantor, Einstein, and Hilbert most likely wrong altogether in their view of the world?
Regards,
Eckard
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T H Ray replied on Jun. 27, 2011 @ 11:30 GMT
The axiom of choice (equivalent to Zorn's lemma and to the well order theorem) is often convenient for proofs, particularly when one wants to apply calculus and vector algebras to certain Hilbert spaces (limits have to be established); however, no well ordering procedure is required to support the _existence_ of Hilbert space, which is a generalization of the Euclidean space.
It's often said that the Banach-Tarski construction (usually called a paradox) depends on the axiom of choice. However, equidecomposable balls intrinsically allow construction of equal volume spheres (i.e., sets of equal cardinality). So B-T, yes, is supported by set theory, which is generally taken to be ZFC (Zermelo-Fraenkel plus the axiom of choice), but the space is always Euclidean. One could just as eaily prove that AC exists because of the Hilbert space.
None of this formality, though, worries physics. The usefulness of the mathematics to support physical results ends at the real geometry.
In regard to David Tong, one should point out the subtle difference between "simulation" and "emulation." Indeed, one could prove we are not living in a computer simulation. There is no way _in principle_ however, to distinguish an emulation from the original program. No physical principle obviates the universe acting like a computer program -- at least none that we could determine by objective measurement.
Eckard -- to speak of so-and-so "being wrong in their view of the world," is meaningless. _Everyone_ individually is wrong in their view of the world. The scientific view is an aggregate of theories, results and philosophies.
Tom
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Lawrence B. Crowell replied on Jun. 27, 2011 @ 14:56 GMT
Eckard,
There is no controversy over the twin paradox. I am not sure why there is this “petition” or what the point of it is. This matter has been utterly beaten to death, and what are cited as “discrepancies” are probably different approaches to presentation. I have to implore people to avoid faux problems of this sort. Anyone who is caught up in these issues is really in some sort of cul-de-sac. I admonish people to not get into these traps.
The AC was fabricated in a sense, just as it might be argued that all of mathematics is a fabrication or model. Of course the math-realists or Platonists would object to this characterization. I might agree with them on Tuesday, Thursdays and Saturdays, while disagreeing on the other weekdays, Sundays are optional. I am not as I indicated out to rewrite mathematical foundations.
More continued in my response the TH Ray
Cheers LC
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Lawrence B. Crowell replied on Jun. 27, 2011 @ 15:52 GMT
Tom,
The AC permits one to order up the eigenbasis of Hilbert space. In fact it is implicit in diagonalization or Schmidt orthogonalization, where the ordering of eigenvalues and eigenvectors. The connections with physics seem potentially to be with the matter of contextuality. The experimenter has the freedom to orient their apparatus to select a certain eigenbasis, where upon from there the ordering of the Hilbert eigen-vector space is determined. This is the classical piece of information that Alice must communicate to Bob in order to teleport a qubit, so Bob can convert an ancillary state into the teleported state. However, in the absence of such Hadamard transformations which demolish some entanglement the ordering of the Hilbert space is ambiguous. There is no ordering unless there is some selection process that takes place.
The axiom of choice is not a decidable proposition, for all such orderings can be Cantor diagonalized and the register shifted diagonal can form another ordering which is not in the list. Consequently the AC is not proven from other axioms of set theory. This has a Turing machine analogue as well. Each orientation of the apparatus produces an independent ordering of the Hilbert eigenspace. However, the symbol strings corresponding to ordering is different and by the Chaitan Halting probability there is some measure of these which do not correspond to halting procedures. Consequently the ordering of the state space by these means is not decidable, or equivalently the AC is not provable.
This might suggest some foundational issue with the duality between the noncontextuality of quantum mechanics and the contextuality of the measurement procedure. The SLOCC entanglement states determine what sort of classical information may be communicated to teleport states in n-partite entanglements. These have correspondences with the moduli spaces for spacetime configurations, such as black holes. The entropy of these entanglements is computed by determinants, in the case of a 2x2 matrix, or hyperdeterminants for 2^n n > 2 matrices for n-partite entanglements. If quantum mechanics obtains on all levels these results are due to certain coarse graining which we impose on reality which prevent a complete characterization of the system. On the deepest level there is no ordering of the Hilbert space, this is something imposed on it from “outside.” Hence the AC thought of as a “physical axiom” is turned on and off accordingly.
Cheers LC
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T H Ray replied on Jun. 28, 2011 @ 11:14 GMT
Thanks, Lawrence.
I accept the usefulness of AC, I just don't favor it as an axiom. "Contextuality" seems a slippery slope to me -- admittedly, I'm prejudiced by the hope that quantum mechanics derives in a most natural way from a Hilbert space of entire functions without having to invoke AC.
I suppose that just as Eistein wanted to believe "that the moon is there even when no one is looking," I want to believe that information and its mathematical processing is not different from the physics of the moon, even "when no one is looking."
Tom
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Eckard Blumschein replied on Jun. 28, 2011 @ 17:03 GMT
LC,
Perhaps the strongest argument against his SR was uttered by the late Einstein himself. He admitted that the Now worries him seriously, and he suspected something outside science. Well, I agree with Popper, Einstein's view of the world is the same as Zeno's. Has the Ritz matter really been "beaten to death"? I see the last three articles including The Crystallizing Universe tackling it with no convincing to me avail so far. You are not the only one who needs strong words like implore and even admonish instead of strong factual arguments. I guess: Those who signed the petition were aware of swimming against the ruling opinion.
What about me, I found out that it is a detour to include the future when analyzing measured, i.e. past data. In practice cosine transform actually is sufficient. Nonetheless, I was persistently lectured that one has always to use the Fourier transform because spacetime extends from minus infinity to plus infinity, full stop.
In order to find my mistake, I read a lot of original papers. Einstein's SR paper was a bit difficult to immediately understand because it did not give the due references to its sources, in particular Poincaré. However, Poincarè's method of synchronization is not at all convincing.
When Schroedinger succeeded calculating the hydrogen spectrum, he did not calculate relativistic.
Having no clue concerning GPS, I guess, Van Flandern was a good expert in this field, and he argued against SR.
Tom pointed me to a large Wiki collection of putative evidence for SR. Not a single one was obviously compelling to me.
A textbook "Elements of Non-Relativistic Quantum Mechanics" by Luis Sobrino did not even mention relativity except in the title.
Shouldn't I doubt?
Regards,
Eckard
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Lawrence B. Crowell replied on Jun. 29, 2011 @ 11:53 GMT
Non relativistic QM is obvious for atomic physics. The gamma factor for the motion of an electron in an atom is γ = E/mc^2 = (mc^2 + K)/mc^2, where K = kinetic energy of the electron. The mc^2 of an electron is .51Mev = 5.1x10^{5}ev, and the kinetic energy of an electron is on the order of 1-10ev. So for K = 5ev K/mc^2 ~ 10^{-5} and the gamma factor is γ =~ 1. + 10^{-5} = 1.00001. Since γ = 1/sqrt{1 – (v/c)^2} the velocity of the electron is v = 0.00447c. Consequently relativity is not a major factor and amounts to a small perturbation on a nonrelativistic calculation. Research into atomic physics increasingly involves finding ever smaller effects which perturb atomic levels, so atomic physics calculations with the Dirac equation is frequently done to work on such small effects.
Seriously, there is no real debate over special relativity. It has been tested to death and it forms the global symmetries of spacetime. General relativity uses these symmetries as local symmetries on frames that are patched together with connection coefficients. There simply is no scientific controversy over the validity of special relativity in this appropriate domain of applicability.
Cheers LC
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Eckard Blumschein replied on Jun. 29, 2011 @ 13:46 GMT
LC,
"The gamma factor for the motion of an electron in an atom is ..." [near to 1]. Hm, who measured that motion. Being not a physicist, I recall an argument that electrons should have a speed far in excess of c as to overcome the electrostatic attraction of the positively charged nucleus. Do not get me wrong. I merely guess, both models might be premature.
If I recall correctly, the result by Schroedinger differs from relativistically calculated one by a factor two. Remarkably, the relativistic Doppler effect may also differ from ordinary one by a factor of the same order.
I agree, SR "forms the global symmetries of spacetime": symmetries between past and future, world and anti-world, matter and anti-matter, and the like. Exactly these putatively natural but actually artificial symmetries gave rise to me looking for the flaw I am claiming to have found in a view of the world that goes back at least to Parmenides. If there was not yet a debate on this, we should start it now, no matter where we will begin. The topic includes the so called arrow of time, real time physics, the nature of time, emergence, why did von Neumann in 1935 admit he did no longer believe in (his own creation) Hilbert space, all failed efforts to unite for instance the block universe with reality, etc., etc.
Regards,
Eckard
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Lawrence B. Crowell replied on Jun. 29, 2011 @ 16:02 GMT
I am not sure what the departure by a “factor of 2” refers to. However, I must implore there is nowhere the sort of problem you think there is with special relativity. To fret over this is almost as silly as Putnam who thinks that Newton’s F = ma is wrong. I can’t argue these points endlessly, but frankly people who think relativity is all wrong are barking up the wrong tree.
LC
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Eckard Blumschein replied on Jul. 1, 2011 @ 11:41 GMT
LC,
The
petition was mainly signed by those who did not swallow SR. There are, however, also proponents of SR who signed because are desperately seeking for answers. NPA is serious.
What about the factor two, I picked up this strange peculiarity almost 50 years ago in Dresden when Prof. Mierdel told it in his lecture on electro-physics. Look at the appendices of my essay for examples. I already mentioned Schroedinger's non-relativistic result. Mybe, I found it in his original papers, maybe in "Schroedinger - Life and Thought".
I also recall Hendrik van Hees putting a request in sci.physics.research because a result of his calculation was at odds with literature again by a factor two.
As a schoolboy I simply wondered why E=mc^2 is just twice as large as the kinetic energy integral mvdv.
In general it might be a moot point where to start the integration. While an integral over delta (x) dx from minus infty to plus infty = 1 is used for normalization, retardation of potential starts at r=0 and t=0.
As I already tried to explain elsewhere, I do not question the limitation to the velocity of propagation of action. SR might instead be unrealistic because Galilei's principle of relativity is restricted to closed system while electromagnetism is definitely "contextual" in the sense electric and magnetic fields do not have any spatial restriction except for their restriction to a past cause.
Eckard
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Lawrence B. Crowell replied on Jul. 2, 2011 @ 20:41 GMT
The E = mc^2 result is not hard to see. We start with the elementary work-energy theorem
E = ∫F*dx
Where the * means a dot product. The force is by Newton’s second law F = d(mv)/dt. We express everything according to velocity and so dx = vdt. This means the energy is
E = ∫dtv*d(mv)/dt = ∫v*d(mv).
The endpoints are 0 to mv and in what follows limits are assumed. In a nonrelativistic setting the mass is constant and E = m∫v*dv = (1/2)mv^2. In a relativistic setting we have that the mass is m = m_0/sqrt{1 – (v/c)^2}. Now put that into the work-energy formula
E = m_0∫v*d(v/sqrt{1 – (v/c)^2})
= m_0∫v*(v/sqrt(1 – (v/c)^2} – (v^3/c^2){1 – (v/c)^2} ^{-3/2})
= m_0∫v*dv{1 – (v/c)^2}^{-3/2}
and the integration gives
E = m_0c^2(1/sqrt{1 – (v/c)^2} - 1) = E’ - m_0c^2
So the final result is a total energy with a rest mass energy m_0c^2 subtracted out. The kinetic energy term E’ = E + m_0c^2. Now for low velocities the total energy is
E’ =~ m_0c^2[1 + v^2/2c^2} = m_0c^2 + (1/2)mv^2.
LC
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Eckard Blumschein replied on Jul. 3, 2011 @ 00:17 GMT
LC,
In reality, past and future are different because reality is not a closed system. So far, physics ignores this and postulates time a priori extending from minus infinity to plus infinity. From this point of view, SR would be understandable. However, apparent discrepancies, sometimes by a factor two, arise when this somewhat bizarre "relativistic" theory is confronted with the realism of the non-relativistic view.
I reiterate: Galilei's principle of relativity is restricted to closed systems.
A harmonic oscillator would likewise oscillate forever.
However, electromagnetism is definitely "contextual" in the sense electric and magnetic fields do not have any spatial restriction except for their restriction to a past cause.
Doesn't this preclude the equivalence of all imaginable frames of reference?
Mustn't a realistic shift of the origin of elapsed time be restricted to the past? The situation is similar with sound pressure in acoustics. While it is reasonable to choose the atmospheric pressure as frame of reference and consider usually just the AC component, the absolute pressure cannot get negative.
Eckard
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Lawrence B. Crowell replied on Jul. 3, 2011 @ 18:49 GMT
I have to confess I don't quite understand what you are writing about here. I am not sure what is meant by "electric and magnetic fields do not have any spatial restriction except for their restriction to a past cause."
Cheers LC
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Eckard Blumschein replied on Jul. 3, 2011 @ 20:50 GMT
LC,
Stationary electric monopoles and magnetic vortexes in empty space are thought to do not have any spatial restriction but extend from r=0 to infinity. Transversal electromagnetic dipole fields propagate in it from a cause at r=0 to r=ct where t is a measure of past (elapsed) time. This restriction to reality is their spatial restriction. So called future Minkowski cone is merely a theoretical limit to reasonable speculation outside sound physics.
Regards,
Eckard
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Lawrence B. Crowell replied on Jul. 4, 2011 @ 12:08 GMT
Electric and magnetic fields are spatial quantities. Changes in these field propagate on a light cone. A light cone is the projective space in a Lorentzian flat spacetime. To be honest I have a hard time seeing what you are writing about as something which is of any real concern.
LC
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Eckard Blumschein replied on Jul. 4, 2011 @ 21:45 GMT
LC,
It is all about misuse of abstraction and questionable anticipation, i.e. the lost link to reality. Karl Popper implicitly declared SR wrong when he declared the world open and he called Einstein Parmenides.
You wrote: "Electric and magnetic fields are spatial quantities. Changes in these field propagate on a light cone. A light cone is the projective space in a Lorentzian flat spacetime."
Wasn't it Minkowski with reference to Einstein who introduced the two quite different cones, the cone of history and the cone of possibility?
Anyway, they used the common abstract notion of time as something a priori given from infinity to infinity, amen. Considering this scale like something one can move within as along a x-scale, they neglected the fact that the future is open. Actually, negative values of elapsed time rather resemble likewise not measurable negative values of spatial distance r.
Their very useful but nonetheless unrealistic view was already anchored in mathematics at least since Descartes introduced Cartesian coordinates. It resembles the likewise superior abstraction of small-signal AC components.
However, many arguments of the opponents of SR are also correct.
When these opponents were looking for a flaw in SR, they typically questioned the limitation of the velocity of light to c, because they readily accepted the seemingly appealing postulate that the laws of physics must be the same in all frames of reference. While this Galilean principle of relativity holds in cases of closed systems, i.e. without action at distance, the forces of electric and magnetic fields are not enclosed in an overlookable part of the infinite space.
In the real world the future is open and the past unchangeable. This does not at all allow the shift along the scale of elapsed time, which can be performed so elegantly by multiplication with exp(iwt) in our models.
Already Bohm admitted and Van Flandern further explained why so many putative experimental confirmations of SR can be interpreted otherwise. The matter is actually somewhat tricky, and there is a lot on the stake for speculative theories that were build on SR.
Any objection?
Regards,
Eckard
To be honest I have a hard time seeing what you are writing about as something which is of any real concern.
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Lawrence B. Crowell replied on Jul. 5, 2011 @ 12:44 GMT
The Popper idea of an open world, where I have his book on this and read it many years ago, is concerned more with QM than relativity as I recall. I don’t know how to put this, but bluntly there are really no concerns with the physical basis of special relativity. Further, the general relativity is also heavily substantiated as well. There are questions of course with quantum gravity and the foundations/origins of the universe and black hole singularities and the rest. Yet special relativity is less a research issue and more of an application. Every time a person gets a synchrotron radiation treatment to kill tumors and a whole range of other technologies they are getting an application of special relativity. These issues and problems you are raising simply do not exist.
Cheers LC
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Eckard Blumschein replied on Jul. 5, 2011 @ 15:32 GMT
LC,
Why do you believe that there are applications of SR that may prove it correct?
I am ready to check your claim that synchrotron radiation would not work without SR. I just have at hand some textbooks including "SR applications to particle physics and the classical theory of fields" by Saleem and Rafique and where I did not find something that could refute the arguments e.g. by Von Flandern and Popper.
What about the latter, it might well be that he did not seek a detailed personal confrontation with Einstein after he clearly put him into the drawer of those who anticipate the future by calling him Parmenides. Perhaps he did not feel obliged to draw the due consequences in public. Do you have access to belonging documents?
Regards,
Eckard
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Eckard Blumschein replied on Jul. 5, 2011 @ 18:38 GMT
Meanwhile I found written by Jeffrey Ketland in a discussion at FOM:
Apparently, Einstein referred to his own world-view as
`Spinozistic' and made repeated references to God ("The Lord is subtle
but not malicious", "God doesn't play dice"). Popper referred to
Einstein's General Theory as `Parmenidean' (and Einstein didn't
object):
See
[12] Popper, Karl 1982: `A Conversation with Parmenides', in The
Open Universe: An Argument for Indeterminism (Hutchinson),
Chapter IV, Section 26.
Eckard
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Lawrence B. Crowell replied on Jul. 6, 2011 @ 12:55 GMT
Einstein made reference to his idea of Spinoza’s God.
Theories are of course never proven. My point is that special relativity is sufficiently well supported that within the classical domain of applicability. Quantum gravity may be a departure, though it is not likely to recover some Galilean perspective. In fact recent
observations of gamma ray bursts and the coincidence of radiation with widely different wavelengths put tight constraints on Lorentzian violations. Special relativity is well enough supported that it is used in some engineering and applications.
Without special relativity Brehmsstralung radiation emitted by a charge in a circular accelerated orbit (eg a cyclotron) would be emitted in a direction normal to the tangent velocity, or along the direction of the centripetal force on the electron. Special relativity transforms this into a beam-like cone that is more tangent to that velocity. This focused relativistic X-ray production is what is used in various applications of synchrotron radiation, from X-ray deposition on solids to medical treatments.
One problem I see is it is clear you will keep shaving the point of argument to ever smaller scales of minutia. This is something which I have seen by those who argue against Darwinian evolution or the problem of climate change by our production of CO_2. There are even some rather intelligent people who argue this way, from Berlinsky who argues against evolution to Motl who has largely transformed himself from physicist to climate change denialist --- based BTW on rather extreme right winged opinions. I happen to think these are intellectual pits which are best avoided. You apparently have joined a sort of anti-relativity movement (intellectual pit), but as I see things this suggests this sort of argument can persist indefinitely, largely because theories are never proven, they are only supported by data.
Cheers LC
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Eckard Blumschein replied on Jul. 8, 2011 @ 18:37 GMT
LC,
Perhaps it doesn't matter much that I am unable to get access to the link you provided. I do anyway not expect being in position to judge the particular case. Likewise I feel not competent to contribute to the issue of global warming and Darwinism. I agree with you: In these questions there is little room for doubt.
Please do not consider me a denialist. I simply did not yet find convincing counterarguments against my reasoning: In reality the past cannot be changed while the future depends. Physics does not really deal with the original and complete reality but always with models that are abstracted from it. This worried even the late Einstein. For a while I was hoping that Galilean Electrodynamics could overcome some obviously not yet resolved inconsistencies of modern physics. Meanwhile, I found out that the Galilean relativity might not apply to fields with unbounded extension. Moreover, Poincaré synchronization is not convincing to me. I argue that past and future must not be mingled.
Usually, I dislike both extremes: those who speak of an Einstein hoax and those like you and Tom who more or less blindly admire Him. I trust in what already David Bohm admitted and Van Flandern further specified: One cannot easily decide whether putative evidence actually confirms the claims. Maybe, Lorentz arrived at a useful formalism, maybe the approach was nonetheless wrong, maybe just some implications for theory require reconsideration. I need some time for more homework. Thank you for your effort.
Regards,
Eckard
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SUBJECTIVE PHYSICS wrote on Jun. 25, 2011 @ 16:48 GMT
"The fundamental process of nature lies outside space–time but generates events that can be located in space–time."
H.Stapp
Anatomy of quantum superposition
(3- bit Universe)
We are studying the simplest model of a finite deterministic world. Here, we have attempted to answer the following question: what our artificial world would look like from the point of view of an observer (subject), placed in our modeled finite world? To do this, it's necessary to formulate abstract model of the observer. Only in that way is it possible to answer this complicated question. Herein, we have endeavored to show the quantum-similar character of the laws, discovering by the objective observer. As a consequence of this exercise, we can now assume that physical laws of our real world have a similar origin
Digital Physics
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Lawrence B. Crowell replied on Jun. 26, 2011 @ 13:18 GMT
If you employ the 24-cell in four dimensions you can derive a form of the Kochen-Specker theorem in the manner A. Perez did, A. Peres, J. Phys. A 24, L175 (1991). The proof is based on the symmetry of the root system of the exceptional Lie algebra F_4. The proof employs 48 vectors in 4-space which are isomorphic to the vertices of a 24-cell and its dual. These vectors are root vectors of F_4, which under multiplication by any set of scalars defines a set of lines in 4-space. We identify each of these vectors with a quantum state |ψ), I = 1, … ,24, and a projection operator P_i = |ψ)(ψ|. These have three eigenvalues 0 and one of 1. This means one can compute 72 sets of mutually orthogonal lines, where this is four-fold redundancy, and there are only 18 independent lines, which correspond to entangled pairs of 9 lines.
Suppose there were some hidden variable which accounts for this system. This would give an exact value to each of the 18 operators. The 9 must assume the value 1 in each of the 9 sets of pairs, an odd number, However, there is an even number of 1 with the pairs, and an underlying theory which determines the values of the 18 operators would require an even number also be odd. This is an informal proof of the Kochen-Specker theory in four dimensions. Any theory of hidden states or variables will run into this contradiction.
Cheers LC
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Lawrence B. Crowell wrote on Jun. 28, 2011 @ 16:17 GMT
TH Ray,
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Lawrence B. Crowell replied on Jun. 28, 2011 @ 16:18 GMT
I hit send before pasting this in:
Before I continue onwards, I should make clear what I mean by contextual and noncontextual. Contextual means that reality assigned to a quantum system is only found through a measurement, “within the context of the eigenbasis established by the observer.” Hidden variable theories often claim there is some reality which exists independent of this...
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I hit send before pasting this in:
Before I continue onwards, I should make clear what I mean by contextual and noncontextual. Contextual means that reality assigned to a quantum system is only found through a measurement, “within the context of the eigenbasis established by the observer.” Hidden variable theories often claim there is some reality which exists independent of this contextuality, and are often referred to as hidden variable theories with some reality that is noncontexual. What I mean by noncontextuality of QM is that there is no such reality that can be assigned in a noncontextual basis, or at least no reality as understood in a classical setting.
The contextuality of QM is what we observe through experiments, which may involve incommensurate and commensurate sets of detections. In other words the context of the apparatus (whether we measure momentum or position) or the orientation of a Stern-Gerlach apparatus is what determines the outcome, and a succession or ensemble of such measurements will demonstrate nonlocal properties and the incommensurability of measurements between conjugate observables. So the interpretation of quantum mechanics can only be inferred through the types of measurements we perform. These measurements are in the Copenhagen interpretation performed by perfectly classical systems and the outcomes determined by an infinite number of observations. This is an idealization. A perfectly macroscopic or classical system has an infinite mass, and a finite mass has some quantum wave spreading. The CI means context is made within a classical setting, where the world has a duality between quantum and classical physics. In the Many World Interpretation the contextual aspect of QM involves the basis of state vectors the world splits off into. The MWI entangles pointer states to a wave function super-position and the various pointer states that are observed correspond to a particular world-path. Decoherence indicates that wave function reduction is due to such entanglements which become spread into a vast reservoir of states, and the direct observation is a coarse grained result.
In all of these interpretations there is a ways that the context of the measurement produces its outcome: classical-quantum dichotomy, many world eigen-vectors splitting off, entanglement phase or pointer states that grows irreversibly in a coarse graining and so forth. With all of these there is a bit of “fuzz” that is introduced, where this fuzz is something imposed = the “machinery” behind the context. Quantum physics in its pure setting has no such context, and no reality hidden beneath any context = noncontextual quantum waves. The funny issue comes in if we do consider the world as fully quantum mechanical on all scales. The context from which quantum observables are detected must originate then from something which is ultimately noncontextual, and that “something” has no local reality.
The ordering of a Hilbert space is permitted by the AC, and any such ordering in a commutative basis of commensurate observables is what gives the context. However, if reality is quantum mechanical “all the way,” then how do we get contextuality from nonlocal noncontextual waves that have no local or classical reality? This noncontextuality means there is nothing which orders eigen-vectors in the Hilbert space. So we may think of QM in this setting as having not-AC. As such we might have ultimately a duality which involves set theory and undecidable propositions underlying quantum mechanics.
I don’t worry too much about the moon not being there if I am not looking at it. For one thing the separable states (eg thermal states) of photons from the sun interact with the moon and remove what little bit of coherent phase it might have. So this is a sort of Zeno measurement process where the wave function of the moon is constantly jolted away from being in any quantum superposition of position. So I am sure this holds for the entire macroscopic world. So I sure that 120 million years ago the photons reflecting off the moon formed an image in the retina of an Allosaurus, without any conscious awareness of what was being observed --- I doubt dinosaurs had any sense of the moon outside of being a “light.”
Cheers LC
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T H Ray replied on Jun. 28, 2011 @ 18:21 GMT
Lawrence,
My
2006 ICCS paper explains how to get a well ordered sequence from an n-dimension (Hilbert) space, without invoking AC.
As you point out, QM is fuzzy only in the classical context, when operators are aggregated (one tunes the dials of the "machinery"). In its own context, though, quantum mechanics is starkly real and focused one observation at a time.
You ask, " ... if reality is quantum mechanical 'all the way,' then how do we get contextuality from nonlocal noncontextual waves that have no local or classical reality?"
Exactly. I don't think we need contextuality at all -- if the wave function is the only reality. The reason for the "moon" analogy is to suggest that the wave function of the moon entangled with that of the observer (and therefore the observing apparatus) is independent of results that come from tuning dials on the "machinery." To use a weak analogy, as my glasses are independent of my eyes. My glasses do not create reality, though what I choose to see, may.
The moon has no such choice. I am reminded of a nursery rhyme my grandmother used to recite to me when a full moon shone through the window of my upstairs bedroom::
I see the moon
and the moon sees me;
The moon sees the one I'd like to see.
God bless the moon and God bless me,
God bless the one I'd like to see.
Hence no contextuality required. The moon doesn't have any classical dials to tune that make it fuzzy, and the Hilbert space is equally indifferent to the choice function.
Tom
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T H Ray replied on Jun. 28, 2011 @ 18:23 GMT
Lawrence B. Crowell wrote on Jun. 29, 2011 @ 12:33 GMT
The wave function is not random and discrete. It is perfectly continuous and is a C^∞ solution to a partial differential equation. The randomness and discrete aspect of QM emerges with the measurement or decoherence of wave functions as observed with coarse grained coherent sets. Further, the wave function is not “real” in a standard sense, or equivalently it has no ontology, but is rather a set of existential potentialities or an epistemology. This means that any ordering occurs with the measurement of a wave function and is imposed on an ensemble of quantum systems, not on a quantum system by itself. The ordering of the Hilbert space is then derived by this imposition.
The GHZ state does demonstrate that the nonlocal aspects of quantum mechanics can be inferred without an ensemble of measurements, but rather with one measurement. However, even with one measurement the teleportation of this 4-partite state requires the SLOCC state ~ C^4/[sl(2,C)]^4, with a root system that imposes an ordering.
Cheers LC
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T H Ray replied on Jun. 29, 2011 @ 13:45 GMT
No, the wave function is not real in the standard sense (of observer-dependent and measurement-verified) reality.
Applying Einstein's definition* of "physically real," however: " ... independent in its physical properties, having a physical effect but not itself influenced by physical conditions ..." we can successfully argue for _either_ the ontology of the wave function or the ontology of spacetime (which is where Einstein applied his definition).
Suppose that spacetime and the wave function are identical, in the sense of a Hilbert space plus time, rather than a complete Euclidean 3-space plus time as in general relativity. One would then have an n-dimension extension of general relativity, as well as access to the hyperbolic space where string theory and holography originate -- that's what my
"time barrier" preprint is all about.
While Einstein maintained,** in the spirit of classical mechanics, particularly the mechanics of Mach, that "From the standpoint of epistemology it is more satisfying to have the mechanical properties of space completely determined by matter . . ." I doubt that Einstein would object to a spacetime ontology and a matter epistemology. The advantage would be to lay a foundation toward explaining the origin of mechanics, and hence the origin of inertia.
I continue to maintain that science has no use for the assumptioon of any particular "reality." We can as easily live with the general relativity result of a reality finite in time and unbounded in space, as with the reality I propose: one that is finite in space and unbounded in time.
Tom
*Einstein, _The Meaning of Relativity_ Princeton 1956
**ibid
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T H Ray replied on Jun. 29, 2011 @ 14:24 GMT
Lawrence B. Crowell replied on Jun. 29, 2011 @ 16:08 GMT
In the arguments between Bohr and Einstein I think it is clear that Bohr got the upper hand. Einstein was frankly wrong about all his concerns over quantum mechanics. He insisted there must be some noncontextual reality, but from Bohr, to Bell and then to Kochen-Specker it is clear that to impose such leads to logical contradictions.
Quantum mechanics is just plain weird.
Cheers LC
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T H Ray replied on Jun. 29, 2011 @ 23:28 GMT
He lost the argument with Bohr, but he won the argument for mathematical completeness, or there would be no more theorists today.
Tom
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Eckard Blumschein replied on Jul. 1, 2011 @ 11:04 GMT
Tom,
The reason for me to question some fundamentals of set theory were obviously and admittedly not satisfactory resolved problems concerning zero and infinity.
I came to the result that mathematics lost to some extent its anchoring in realism. We may safely benefit from idealizations as long as we are aware in what they are different from reality.
What about completeness and compactness, e.g. the expansion of an impulse into a converging series is a good example while the usual interpretation of delta(0) reveals to me the mentioned imperfections of current arbitrariness. Did you deal with the appendices of my essay?
Eckard
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T H Ray replied on Jul. 2, 2011 @ 15:34 GMT
"We may safely benefit from idealizations as long as we are aware in what they are different from reality."
We here this same objection over and over in this forum.
It is based on a false premise, however, and is therefore invalid. Science discovers reality; science does not presume reality.
Tom
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T H Ray replied on Jul. 2, 2011 @ 15:36 GMT
Eckard Blumschein replied on Jul. 2, 2011 @ 23:23 GMT
Tom,
"We may safely benefit from idealizations as long as we are aware in what they are different from reality."
Example: A railroad is something real. It is idealized as a one-dimensional line by neglect of two less important dimensions.
You did disagree:
"We hear this same objection over and over in this forum. It is based on a false premise, however, and is therefore invalid. Science discovers reality; science does not presume reality."
What false premise do you refer to?
A line is not something real that can be discovered. I cannot measure future data, I cannot predict the future from the laws of nature alone. I got increasingly aware that just the laws of nature are independent from frame of reference. Reality depends on influences from the past unless one takes the (criticized by Popper) point of view of reality as a closed system.
Eckard
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T H Ray replied on Jul. 3, 2011 @ 13:22 GMT
"What false premise do you refer to?"
That science presumes any particular form of reality.
"Reality depends on influences from the past unless one takes the (criticized by Popper) point of view of reality as a closed system."
Same false premise. Physical science assumes only that reality is objective, i.e., independent of the observer. Objective reality is determined solely by correspondence of theory to measured result. Causality is not necessarily time dependent -- in a positive feedback loop, cause and effect are not distinguishable.
Tom
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Eckard Blumschein replied on Jul. 3, 2011 @ 21:19 GMT
Tom,
"Physical science assumes only that reality is objective, i.e., independent of the observer."
A god is also objective in the sense of not observable. Sound physics must not be based on something like future that can not be measured in any case. Future is objective but not yet a reality.
"Objective reality is determined solely by correspondence of theory to measured result."
Objective reality as a whole cannot be determined at all. We merely can construct and possibly falsify some models of it. According to Popper, any agreement between theoretically predicted results of a preparation and measured data may just help us to find out theories that are perhaps appropriate.
"Causality is not necessarily time dependent -- in a positive feedback loop, cause and effect are not distinguishable."
The arrow of causality is already to be seen in the word feedback. Chicken_n and its egg that becomes chicken_n+1 are distinguishable.
Eckard
Causality is not necessarily time dependent -- in a positive feedback loop, cause and effect are not distinguishable.
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Lawrence B. Crowell wrote on Jul. 9, 2011 @ 12:24 GMT
I decided to start another column, for this is getting too nested. The link is:
http//www.sciencedaily.com/releases/2011/06/110630111540.
htm
where sometimes if links are embedded there is a http://%20 automatically put in front of the address which screws it up. These results are serious game changers, and a lot of theory may be headed for the paper shredder as a result.
Special relativity is so central to physics these days that there are really no question with respect to its basic form and applicability in its appropriate domain of observation. General relativity is still a subject of research. In the Parameterized Post-Newtonian (PPN) formalism general relativity has been supported by data out to second order. The third order involves weak gravity waves. The Hulst-Taylor observation of pulsar orbital period change supports indirectly the existence of gravity waves, but gravity waves have yet to be directly detected.
The arrow of time problem, assuming it really is a problem, may involve some CP violating mechanism. The discrete symmetry CPT = 1 C = charge conjugation, P = parity change, T = time change, with ψ = ψ_q(r, t) (q = charge, r = position and t = time) acts as:
Cψ_q(r, t) = ψ_{-q}(r, t)
Pψ_q(r, t) = ψ_q(-r, t)
Tψ_q(r, t) = ψ_q(r, -t).
Then CPTT = CP = T, and if CP is violated then T is violated. That TT = T^2 = 1 is easily seen by how it acts on a wave-field above. A CP violation would then mean there is some underlying breaking of chiral symmetry which underlies gravitation. A chiral breaking on CP is then equivalent to the breaking of time symmetry with T.
Cheers LC
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T H Ray replied on Jul. 9, 2011 @ 14:21 GMT
"Then CPTT = CP = T, and if CP is violated then T is violated. That TT = T^2 = 1 is easily seen by how it acts on a wave-field above. A CP violation would then mean there is some underlying breaking of chiral symmetry which underlies gravitation. A chiral breaking on CP is then equivalent to the breaking of time symmetry with T."
An expert summary, Lawrence, as usual.
I find CP violation equivalent to scale invariant information loss, as described mathematically in my 2008 FQXi essay, and my "time barrier" preprint, applying complex analysis to Kepler's classical second law of orbital motion.
This works, by giving the time metric a specifically physical definition requiring n-dimension infinite orientability (and therefore, a Hilbert space domain of infinite range).
Tom
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Eckard Blumschein replied on Jul. 9, 2011 @ 17:41 GMT
LC,
http://www.sciencedaily.com/releases/2011/06/110630111540
.htm reminds me of a predicted impossibility to discover more galaxies. Admittedly, I did not wonder if there was no limit of resolution at all. Is there any compelling reason to consider space and time grained?
Eckard
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Lawrence B. Crowell replied on Jul. 10, 2011 @ 13:01 GMT
The graininess of spacetime is because of quantum fluctuations. If I invoke the Heisenberg uncertainty principle ΔEΔt = ħ and use E = mc^2 there is then a fluctuation of mass given by Δm = ħ/Δtc^2. The uncertainty in time is and uncertainty in position Δt = Δr/c so that Δm = ħ/Δrc, and a metric δg_{00} = 1 – 2Għ/(rΔr c^3), where the metric radius r >> Δr.
Now let the length uncertainty be Δr ~ L_p = sqrt{Għ/c^3}, and we substitute this into the metric uncertainty
δg_{00} = 1 – 2Għ/(rL_p c^3) ~ 1 – 2L_p/r.
This is a nice compact result. Now let the radius term be the probe length, which is given by the wavelength of the different radiation r = λ, and we assume λ >> L_p. The approximate metric for radiation of a certain wavelength is then
ds^2 = c^2δg_{00}dt^2 – dx^2 – dy^2 – dz^2
= c^2(1 – 2L_p/λ)dt^2 – dx^2 – dy^2 – dz^2.
For EM radiation ds = 0 and for radiation propagating along one of the directions we have
dx/dt = c sqrt{1 – 2L_p/λ}.
This predicts then a wavelength dependency on the speed of light
c’ = c sqrt{1 – 2L_p/λ}
So if radiation travels a distance D = c’T the time of travel is T = D/(c sqrt{1 – 2L_p/λ}) and I use the binomial theorem for λ >> L_p
T ~ (D/c)(1 + L_p/λ).
So this is the effect of quantum fluctuations, really a naïve theory of such fluctuations, should have on radiation. Clearly very short wavelength radiation is slowed down.
The FERMI spacecraft detected gamma rays of 33GeV and much radiation at the bottom of the bandwidth at about 10^3eV from a Gamma Ray Burst event GRB 090510 out 7.3 billion light years. We can use these to estimate the time of arrival for the two forms of radiation. L_p/λ = E_γ/E_p =~ 33GeV/1.2x10^{18}GeV = 2.7x10^{-17}. For the softer gamma ray this is E_γ/E_p ~= 10^{-24}. Input this into our formula for the change in speed of light and we get
T – T’ = (D/c)( 2.7x10^{-17} – 10^{-24})
=~ (7x10^{25}m/3x10^8m/sec) 2.7x10^{-17} = 6.7sec.
The GRB event observed had a time spread of 2 seconds and the two photons which a 10^6 spread in energy arrived at the detector within .8 seconds. Given the error margins and so forth this puts some pretty tight constraints on the role of such fluctuations on physics.
This type of spacetime fluctuation is basically ruled out, which are fluctuations that on a small scale violate Lorentz invariance. With heterotic string theory E_8 -- > SU(3)xE_6, which gives a twistor type of theory. Twistor theory does not invoke this sort of energy dependency on light cone structure. Rather the uncertainty is in a null congruency, but where all null rays in the bundle, such as a null plane, all have the same spacetime direction.
Cheers LC
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Eckard Blumschein replied on Jul. 10, 2011 @ 15:59 GMT
LC,
"Now let the length uncertainty be Δr ~ L_p". Doing so, don't we assume a graininess that can possibly be falsified by intelligent measurements?
Even our ears outperform Heisenberg's uncertainty relation, see Fig. 1 in my essay. Didn't Aephraim Steinberg also overcome uncertainty when he pinpointed mean trajectories of single photons?
Regards,
Eckard
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Lawrence B. Crowell replied on Jul. 11, 2011 @ 02:48 GMT
This is basically how a lot of science is done, "crank 'er up and see why she don't run." The assumptions of metric fluctuations of this nature lead to this sort of dispersion, which as it turns out we do not observe.
Cheers LC
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Eckard Blumschein replied on Jul. 11, 2011 @ 18:03 GMT
"Now it's over to the theoreticians, who must re-examine their theories in the light of this new result."
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J.C.N. Smith wrote on Jul. 9, 2011 @ 12:36 GMT
What we perceive as the flow of time is, in reality, nothing more and nothing less than the evolution of the physical universe, an evolution which is governed by rules which we strive to understand and which we refer to as the laws of physics. This view is fully consistent with Ellis' concepts of a crystallizing block universe and free will. As sentient beings, we are able not only to perceive the ongoing evolution of the universe around us, but also, by our own actions, to influence that evolution, albeit in limited fashion.
When viewed from this perspective a causal arrow of time is inevitable, as is discussed further
here and
here.
Best,
jcns
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Eckard Blumschein replied on Jul. 9, 2011 @ 17:46 GMT
jcns,
Doesn't the idea of a block universe contradict to causal evolution? Doesn't Poincaré (de)synchronization mingle past and future?
Regards,
Eckard
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J.C.N. Smith replied on Jul. 9, 2011 @ 19:28 GMT
Eckard,
You raise a good point. I have always been personally uncomfortable with the "block time" and/or "block universe" concept and terminology. As discussed in this FQXi article, however, I can coexist with it. I take Ellis' "crystallization" to represent the evolution of the physical universe from previous configurations into the current configuration (i.e., "the present,") which, in turn, will evolve into yet other configurations which we refer to as "the future." These hypothesized future configurations, unlike the configurations which we refer to as "the past," have never been objectively real.
I can accept that someone might consider the set of all previously objectively real configurations as constituting an unchangeable "block" of past reality, despite the fact that those past configurations are not now objectively real. Future configurations, on the other hand, are not determined, nor can they be, due to the impossibility of precisely knowing their initial conditions. This leaves the future open to to the possibility of being influence by any number of factors, including by sentient beings such as ourselves. Unfortunately, the long-term consequences of such influences also cannot be predicted.
This comes down to the long-ongoing Heraclitean vs. Parmeidean debate; i.e., between "presentism" and "eternalism." I side strongly, of course, with Heraclitus in this debate.
Best,
jcns
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Eckard Blumschein replied on Jul. 9, 2011 @ 22:13 GMT
jcns,
Einstein followed Spinoza who equated nature and God, which are both imagined to be inexhaustible. With respect to such original meaning of infinity, I consider Spinoza correct but Cantor and Zermelo wrong. On the other hand, I do not see any justification in science for religious eternalism, rebirth and fatalism. Zeno's defense of Parmenides looks ridiculous to me. Einstein put himself outside science when he did not object to Popper who called him a Parmenidean and even more when he uttered that for him as a believing physicist the distinction between past, present, and future is just an obstinate illusion.
Unfortunately, SR and spacetime have been based on this denial of necessary in reality distinctions between past and future as well as reality and theory. I do not yet see my position represented in old debates, neither in presentism nor in eternalism. I am arguing that the concrete future can never be completely modeled for sure. Closed systems are idealizations.
Regards,
Eckaed
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Det Ector wrote on Sep. 7, 2011 @ 21:30 GMT
Misleading presentation of the experiment.
In this article there is a suggestion that the detectors "placed behind the screen" somehow detect trough which slit the photons went, -detect some time after! the photons have passed the slits. But that is misleading! There are no such detectors. In the actual experiment the detection happen at the time the photons pass through the slits (before they hit the screen). Big difference.
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amrit wrote on Mar. 28, 2015 @ 09:46 GMT
the solution for time is: time is a mathematical parameter of motion in space where is only NOW.
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Amrit Srecko Sorli wrote on Mar. 28, 2015 @ 09:50 GMT
here is the paper http://cosmology.com/CaligiuriConsciousTime.pdf
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