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Florin Moldoveanu: on 12/16/09 at 14:28pm UTC, wrote Errata: Page 5, second paragraph, line 4: Change “background...

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FQXi FORUM
November 25, 2017

CATEGORY: What's Ultimately Possible in Physics? Essay Contest (2009) [back]
TOPIC: Heuristic rule for constructing physics axiomatization by Florin Moldoveanu [refresh]
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Author Florin Moldoveanu wrote on Jul. 17, 2009 @ 08:16 GMT
Essay Abstract

Constructing the Theory of Everything (TOE) is an elusive goal of today's physics. Godel's incompleteness theorem seems to forbid physics axiomatization, a necessary part of the TOE. The purpose of this contribution is to show how physics axiomatization can be achieved guided by a new heuristic rule. This will open up new roads into constructing the ultimate theory of everything. Three physical principles will be identified from the heuristic rule and they in turn will generate uniqueness results of various technical strengths regarding space, time, non-relativistic and relativistic quantum mechanics, electroweak symmetry and the dimensionality of space-time. The hope is that the strong force and the Standard Model axiomatizations are not too far out. Quantum gravity and cosmology are harder problems and maybe new approaches are needed. However, complete physics axiomatization seems to be an achievable goal, no longer part of philosophical discussions, but subject to rigorous mathematical proofs.

Author Bio

Florin Moldoveanu received his PhD in theoretical physics from University of Maryland at College Park working in the area of soliton theory, nonlinear dynamics, and fiber optics. His research interests are algebraic and relativistic quantum mechanics and the foundational issues of physics. Other research interests include general relativity, non-commuting geometry, category theory, geometric quantization, Clifford and geometric algebra, and algebraic quantum field theory.

Download Essay PDF File




Doug Huffman wrote on Jul. 24, 2009 @ 11:23 GMT
Dr. Moldoveanu, how can your assertion be falsified? If it cannot be falsified then can it be 'scientific' and, if not, physics? Thank you.

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Author Florin Moldoveanu wrote on Jul. 25, 2009 @ 03:49 GMT
Dear Doug Huffman,

What assertion are you referring to?

Thank you.




Jason Wolfe/wulphstein@gmail.com wrote on Aug. 2, 2009 @ 21:10 GMT
Florin,

I appreciate that you touched upon the role of the heuristic approach to physics; I interpret that to mean 'creative' or 'out of the box' thinking. However, I believe that an axiomatic and mathematical approach to heuristic thinking will prove those to be mutually exclusive. There comes a time when we must ask: what is causing the universe to behave mathematically?

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Author Florin Moldoveanu wrote on Aug. 3, 2009 @ 01:14 GMT
Jason,

Your comments touch on multiple topics. Let me try to address them all. In general, heuristic methods guide us in obtaining results when we lack the complete understanding on a subject. I did not claim I have obtained the complete physics axiomatization, only that I am proposing a way to lead us there. In this sense my essay is a research proposal backed by existing results under a new paradigm of looking at the problem. If new results will be obtained in this paradigm then the new research program will be successful, otherwise it will be a sterile approach. I have additional unpublished results I did not mention in the essay, therefore I know this new approach is fruitful, the question is to what degree?

The major problem standing in the way of physics axiomatization is the complexity of nature. Tegmark proposed he Mathematical Universe Hypothesis, and I believe this to be false. We already know we cannot axiomatize math, and the universe contains mathematicians which discover inconsistent math. If the Mathematical Universe Hypothesis is true, then the mathematical structure which explains reality should also explain the inconsistent math. However, I think he and others like Gordon McCabe are right in their understanding of reality as having a mathematical origin. So if a direct approach does not work, maybe there is a different way. And indeed there is. We use this approach in our real life. When we buy a car for example, we have requirements: price, color, etc. Requirements act as filters of desirable features.

So how do we apply this to physics axiomatization? The platonic world of math contains an infinite numbers of mathematical structures. Only a handful of them are used by reality: the Hilbert space, the Minkowski space, SU(3), SU(2), U(1) in standard model, etc. All we need is a way to filter the “good” and useful mathematical structures from the ones that play only a limited role. In other words, we need the requirements of nature. If the ultimate nature of reality is mathematics, then comparing math and reality is a good place to start. As I show in the essay this generates physics principles which I think are self explanatory. Additionally we need old fashion axioms. My current understanding is that the principles of physics acting as filters and the additional axioms helping to derive consequences from them, are complementary, not mutually exclusive as you state. Pure axioms are not enough because reality is too complex, while pure principles for now cannot have mathematical consequences without a minimum of technical axioms.

So now back to your last question: “causing the universe to behave mathematically?” my answer will be because at core, reality is only the platonic world of math arranged in a specific way.




Jason Wolfe/wulphstein@gmail.com wrote on Aug. 3, 2009 @ 04:43 GMT
Florin,

I consider myself a layperson, not a professional physicist. I freely admit that I have motives in terms of what the physics community should look into. I do understand that professional physicists have careers and political considerations. If I talk about hyperdrives and other crazy ideas, who cares. That's not how I earn my living. But a professional physicist has to approach physics from a completely mathematical and axiomatic point of view. It is important that real physicists approach the physical universe with cautious mathematical and axiomatic techniques. You may or may not agree, but I believe that it is my job, as the 'crack pot' to attempt to insert radical ideas that have a grain of truth in them. The advancement of physics is best served by the interplay of both approaches.

I believe it will be necessary for someone to hold the conviction that mathematics can explain everything that is observable. This is a dynamic interactive process. You must embrace your 'mathematical physics' conviction and carry it through to its conclusion. Because ultimately, the physics community will discover that the universe is not made of mathematics; the universe is made of 'something' that has mathematical properties.

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Author Florin Moldoveanu wrote on Aug. 3, 2009 @ 15:09 GMT
Jason,

Again you raise excellent points. There is a tension between mathematics and reality. In mathematics, we are concerned about pure abstract relationships, regardless on how they appear or not in the physical world. There is an old saying: “stones and sticks can break my bone but words will never hurt me”. Paraphrasing that, we do not seem to get hurt by Pythagoras’ theorem, or … are we?

So let’s put this tension on hold for a minute and discuss other points. All physics theories have axiomatizations, some with more alternative axiomatizations than others. But what is the glue that holds everything together? Nature seems unified in exhibiting all those features like relativity and quantum effects. It is therefore very natural to seek a unified axiomatization approach. So far we have none that works completely, and I am only proposing an alternative way at looking at this problem. If it works, great, if not, we learned how not to do it. However, there are rigorous mathematical results showing that this approach is at least worth of consideration.

In general it is extremely difficult to solve open ended questions like: what is existence, or what is the nature of time, etc because of the myriad of points of view one need to consider. Typically those issues are left for philosophers to discuss. As David Gross puts it, it is very easy to recognize well posed mathematical problems: those are the problems that one can give a graduate student to work on for his degree and expect an answer in a reasonable amount of time. Changing the angle on how we look at physics axiomatization has precisely this effect of making the problem mathematically tractable. Currently I have four very well defined mathematical problems (and I mention one of them in the essay: obtaining the SU(2,2) and the Klein Gordon equation in a particular case) which satisfy David’s criteria. Four is not a lot, but is a start. All we have to do now is follow the math and see if it will lead us to better understanding, or to a dead end. Time will tell.

So now let’s come back to the tension between reality and math. Math is relational, and the idea of reality as relational is not crazy, nor new. Loop quantum gravity takes this principle at heart. How hard is to understand reality has to have an independent existence, has to be able to change and has to be infinite in complexity? This should be self-explanatory. The hard part is deriving mathematical consequences from them. But if reality is relational and can be understood as the platonic world of math rearranged, then by looking at the differences between reality and math we should recover all the mathematical structures which describe reality. Suppose we can prove the necessity of time, space, quantum mechanics, Standard Model, and explain the origin of the universe. Then at that point we can conclude with certainty that the universe is made out of nothing but mathematical relationships.




Stefan Weckbach wrote on Aug. 3, 2009 @ 17:12 GMT
Dear Florin,

though our both approaches to discover ultimate reality could not be much more different as they are yet, i want to mention one thing i realize as common in our both lines of reasoning. But let me say some more general things before i come to the point.

I made up myself with some (more or less) deep thoughts about the nature of maths and why it can be that our world can...

view entire post


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Lawrence B. Crowell wrote on Aug. 3, 2009 @ 17:48 GMT
I finally read your paper last night and some this morning. This is an interesting proposal, I am not sure whether it will work, or even if so whether it has much applicability.

Axiomatizing physics strikes me as a case where physical states are information bits, quantum bits, which are processed by logical gates or some process. The logic gates here are quantum processes, such as unitary operations. The unitary process is similar to a Hadamard matrix, for instance This perspective is similar in a way to how I look at what might be the next level in depth with natural principles. In some ways the Turing approach to axiomatization and logical completeness has connections to physics. A Turing machine is after all a model of a physical machine. A physical process involving a change from one state to another has a computational or algorithmic element to it. So an axiomitization of physics might be thought of as some theory of processes or processors which are algorithmic. So in that setting we can certainly pose the question to what extent incompleteness results impact a program like this.

The Godel theorem indicates that no axiomatic system is able to determine the truth value of its own predicates. This is demonstrated with the predicate which acts on its own Godel number as a variable. So no axiomatic system is able to list all its Godel numbers in some complete list of provable theorems which are true. With physics there is of course the added problem that one can’t identify causal sets as having a truth value. Clearly a causal set which leads to contradictions is false, but this does not mean a causal system which is consistent is necessarily true. This touches on Hume’s thesis of course, but one can’t establish a causal system as being true, and even if it is mathematically described empirical demonstrations don’t establish its truth value (even if massively supported by such evidence), and the mathematical system used to describe it ultimately has these incompleteness with respect to foundations.

Axiomatizing physics is more of a meta-math-physics sort of idea than straight physics. It is not clear how successful or useful such a program would be. I have thought that maybe at the Planck scale quantum gravity dissolves into some self-referential system of vacuum states. I am not sure if the total chaos which may be present at L_p is really of this nature or not, but it might be. If so then this sort of program might be of some worth.

LC

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Author Florin Moldoveanu wrote on Aug. 3, 2009 @ 20:15 GMT
Dear Stefan,

Thank you for your comments. There are many topics I would like to reply to, so I will be brief in my first reply and I will touch on additional topics later.

First about infinity. This is a huge topic and different people use it differently to derive results. For example Cantor showed that real numbers are not countable and that there are different types of infinities,...

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Author Florin Moldoveanu wrote on Aug. 3, 2009 @ 21:39 GMT
Lawrence,

Thank you for taking the time of reading my essay. I know this program works because of all the results obtained so far. The real question is can it generate anything else? I am very hopeful it will work because for me it helped framed the physics intuition behind Connes’ results and also pointed the way towards obtaining the Standard Model parameters. I do need to properly obtain the local gauge symmetry principle from the three axioms, but gauge theory is basically dimensional analysis. Being algebraic, the composability principle is stronger than that. Also the composability principle is best understood in category theory framework, and quantions can be cast trivially as a Hopf algebra.

About Godel’s result, I showed how its roadblock is avoided, but I am not sure about nature as a Turing machine. In math research right now there is a new area called inconsistent math. One can arrive there for example by considering the Peano arithmetic in conjunction with an axiom of a maximum number (like the maximum representable natural number in a physical computer). Then we can ask questions of how we can obtain anything valuable while avoiding the inconsistencies? I am thinking in this case one can always convert this into a Turing machine because we necessarily need to introduce the idea of a state that will protect us from contradictions and we can also do recursive manipulations. But then if this is true and the universe is just a giant Turing machine, we cannot tell this apart from a brain in the vat case. And I think simulating reality is not the same thing as reality itself. A computer program can have logical errors and crash, but reality seems to be able to avoid all logical inconsistencies.




Author Florin Moldoveanu wrote on Aug. 3, 2009 @ 22:31 GMT
Dear Stefan,

You ask: “Is your view of maths, is ultimate reality just another variation of "anthropic" reasoning with respect to human observation of repeatability and lawfullness that can - for whatever reasons - be desribed mathematically?”

I am not sure what anthropic reasoning is, but I can explain my understanding of the anthropic principle. This will also tie up with your earlier mentioning of complexity. So let’s start at complexity. In this area you have emergent phenomena that cannot be explained by the individual parts only. For example one of the millennium problems asks for a rigorous proof of the so called mass gap, while the Yang Mills lagrangian has no mass term to begin with. The anthropic principle is borrowed from biology and is suppose to explain the fine tuning of the physics parameters that makes our universe livable. I view this not as clarification, but as a way to hide our lack of understanding in a catch all explanation, not unlike the idea of God. Life takes advantage of the emerging complexity which appears during the evolution of our universe. In a different universe, maybe the complexity there will have a completely different scales and nature. Why is life suppose to exists only at scales of 10^-3 – 10^1 meters? Why not at the Plank space-time foam level, or at the astrophysical scales in other universes for example? The anthropic principle seems to bind us into imagining life similarly to what we see around us, not unlike how B-rated movies imagine aliens: with 2 feet, two hands, 2 eyes, etc. Wherever there is enough complexity, life will emerge in one way or another. But is our universe unique, and do we really need the anthropic principle? I believe our universe is the way it is because there is no other mathematical way it can be. Not if you want to satisfy the three principles. There is only one conceptual problem remaining. If the universe is unique, why does it happen only once as Guth asks? I can only offer a wild speculation at this point: there must be some “universe nursery” where all the universes get born, live, and die. This “nursery” should not have the universal truth property, and from composability, apart from standard QM and classical mechanics there is a QM-type theory based on split complex numbers which satisfy this. I suspect hyperbolic QM may be responsible for generating universes very much like ours.




Jason Wolfe/wulphstein@gmail.com wrote on Aug. 4, 2009 @ 00:20 GMT
Florin,

If I understand you correctly, identifying all of the mathematical properties that are valid in the physical universe might have benefits. Physical properties and observations can, without our even noticing, deceive us because of some influence that we didn't account for. At least with a set of physically confirmed mathematical axioms, we can break everything down into axiomatic building blocks. That will make it a little easier for physicists to give engineers more powerful mathematical tools to work with. For crazy laypersons like me, I known which axiom I need to counteract to get somthing fun like a hyperdrive. Another advantage to creating axiomatic building blocks is that, if they really are absolute, then we truly know what we can ever expect to observe. In contrast, if the physics community ever confirms an observation that should never be observed (e.g. transmitting information FTL; consistent thermodynamic violations; etc...) then we can find the fault line in the mathematics, and either remove that axiom, or figure out why we observed something that should be observable.

I say make a list of axioms. It makes it easier to track anomalies, anyway.

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Georgina Parry wrote on Aug. 4, 2009 @ 00:41 GMT
Florin,

I have only just begun reading your essay.

You have said "In the physical world truth is usually defined as something corresponding to reality and has a ubiquitous and non trivial universal property."

This is a statement about how the term truth is used in general parlance rather than a statement about the nature of truth itself. Truth is tied up with perception. Truth that is perceived may in fact be untrue, due to lack of evidence to draw contrary conclusions or misinterpretation or deception etc.

There is also the whole conundrum of what is meant by the term reality and is this in any way a universal objective truth or just subjective interpretation of sensory input by each individual.

You also say "In physics events are true for all observers and across all contexts." I would also have to disagree here, as due to relativity, different observers may disagree about the order in which events occurred and when they occurred. So there is no single truth that will apply universally.It once again comes down to perception. If one observer closed his eyes, at the very moment the event could have been observed by him, he might not observe it at all.For him it is true that no event was observed and therefore he may conclude that the event did not occur.

Why do you assume that there is a "universal truth property" of the "real world" as you put it?

I intend to continue reading your essay and will try to give further thought to it and feedback on it but have limited time available to me at the moment.

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Author Florin Moldoveanu wrote on Aug. 4, 2009 @ 01:08 GMT
Jason,

I hate to disappoint science fiction fans, but there is no time travel, faster than light communication, warp drives, etc. (I continued to be amazed at how serious physicists like Kip Thorne, and Karl Svozil take those things seriously.) Finding the final axioms is work in progress, but we already know what is possible in principle. One very interesting frontier is quantum computers, quantum cryptography and quantum information. This is an area in physics were we are genuinely surprised by what is realistically possible to achieve in practice.




Author Florin Moldoveanu wrote on Aug. 4, 2009 @ 02:24 GMT
Georgina,

I follow your posts on the blogs, but in general I do not have the qualifications to discuss your posts which are more on the philosophical side. I will try however to reply to your questions here to the best of my (modest philosophical) abilities. Let me start with an easy answer. In relativity, different observers disagree about the order of events if they are spatially separated. But I was not talking about 2 events which can be compared, but about a single event in general which by itself is the same for every observer. If a star goes supernova, observers from different galaxies see the same thing, not one see the explosion while others do not (taking into consideration the time it takes for the light to reach different observers).

I cannot provide an answer regarding my universal truth property idea in the Vienna circle framework, or Hillary Putnam’s approach, but I can tell you this is simply an elementary observation. In the real world, (historical) events are the same for everyone: monarchy was abolished in France and everyone agrees with that: the universe did not split itself in two copies and for some observers France remained a monarchy while for others it did not. (maybe it did split in two copies according to Everett, but within each copy everyone observed the same thing). Another way of looking at this is universal non-contextuality: it does not matter how we observe something, it is the same for everyone (not the same in math).

Perhaps a “counter example” can clarify this. In special relativity suppose you have a car of a given length, and shorter garage with two front and back automatic doors. Now suppose the car is entering the garage at a relativistic speed. For any stationary observer, the car undergoes a Lorentz contraction and they will observe the car inside the garage with both doors closed. From the car driver’s perspective, it is the garage that becomes shorter and he will never see the car completely inside the garage. In this case the “car fits completely inside the garage with both doors closed” statement has different truth values for the two kinds of observers (stationary with regards to the garage or the car) and both are right (they can even take pictures to show as evidence).

Now compare this with the event’s universal truth property. The situation above will never happen when one considers only one event. This is the meaning of the universal truth property. (So can we reconcile the universal truth property with this seemingly counter example? Yes, because the “paradox” in easily explained away by noting that the sentence about the car inside the garage actually contains two events: front door closes, and the back door opens and it all boils down at the relativity of simultaneity)




Lawrence B. Crowell wrote on Aug. 4, 2009 @ 02:59 GMT
The axiomatization of physics is useful within a physical theory which has the universe as a universal quantum computer which computes its own states. A unitary operator can be thought of as rotating a state vector from one basis to another, and a coupling between two fields as being a CONTROL-NOT operation. So the universe itself is a great universal Turing machine.

This of course leads to all sorts of questions, for it demands that the physical states be recursive or first order logical. This must hold at least to within some cut-off in a renormalization group flow. The cut-off might be the Planck scale, where beyond that Godelian chaos might take over.

The world of structured spaces has only four types R, C, H, and O, according to the Cayley number sequence. We are pretty familiar with R and C, and H is a bit odd. However, quaterionic systems

i^2 = j^2 = k^2 = ijk = -1

do exist in physics with Dirac matrices and Clifford algebras. The failure of closed loops to close up vectors under parallel transport according to an algebraic structure or roots is some Clifford basis. Octonions are of course the really odd man in the crowd. It is not hard though to think up some nonassociative logical operations. It we make Q some logical process, such as a Hadamard gate, it is not hard to wee that inputs ABC into two O's, where A--Q--B means "A and B feed into Q" which gives the immediate symbol on the other side of the equal sign: A--Q--B = D. The nonassociativity is then

A--Q--B = D--Q--C =/= A--Q--E' = B--O--C,

so that nonassiative structures

So the universe can be consdered to be a system which operates according to the algebra A, some self dual error correction code which defines a Hilbert space. The E_8 has the [8,4,4] which computes the Hamming distance 4, which is a quantized system. The Leech lattice has [24, 12, 12] and [24. 8, 8]. So the universe is a quantum universal Turing machine.

For this machine to operate without Godelian influence it must be first order in logic and recursive. That is the requirement for any axiomatization program. The 3 principles you outline must then satisfy this requirement with in the Church thesis or Lambda calculus.

Lawrence B. Crowell

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Georgina Parry wrote on Aug. 4, 2009 @ 03:31 GMT
Florin thank you for your prompt reply.

History is also a question of perspective, reflecting the bias or interest of the historian, who subjectively "paints a picture of the past"for the reader.He does not just amassing an impartial collection of equally objective, verifiable facts without supplying any subjective selection or interpretation of those facts.Some events are recorded, some are given significance, others are forgotten.I can not personally verify all historical facts that I am told or read, but may accept some of them as truth without any verification.

Perception varies between individuals, who perhaps vary in the amount of attention they give to an event, or who pay attention to different features of the event. So the qualitative experience and description of the same event also varies.The police are well aware that eye witness accounts of events may vary significantly. Too much similarity or too little discrepancy between accounts may in fact be suspicious, indicative of fabrication of the truth.

Although there may be an objective reality external to experience, no one has access to that objective reality.It is not therefore the "real world" that we experience, but our own subjective "fabrication".

However I accept that there may be a general consensus as to those singular events that have happened. The consensus of a significant number of independent witnesses or agreement of a significant number of independent replications of an experiment may be accepted as likely evidence in favour of an approximation of an underlying objective truth.

Florin, I would like to read the rest of your essay. I intend to write again when I have done that. I am interested to see how you have developed your ideas. The beginning part of your essay just caught my attention because of the way in which I perceive certain concepts such as truth and reality, which you already understand having read some of my previous posts.

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Author Florin Moldoveanu wrote on Aug. 4, 2009 @ 03:51 GMT
Lawrence,

The universe may be a giant universal Turing machine, I do not know, but what consequences can you derive from that? On the other hand, in an UTM, you can make copies of the state you are in, but in QM you have the no clone theorem so I cannot see how the two can agree. First order logic is also very constrictive and why this should be the case in general is not clear. You seem to agree with Tegmark’s approach though, but I have deep reservations about his assertions.

There were some attempts to obtain QM from information theoretical approaches by Bub and others, but as of today I am not aware that this approach succeeded completely.




Author Florin Moldoveanu wrote on Aug. 4, 2009 @ 03:55 GMT
Georgina,

I am looking forward to your questions.




Stefan Weckbach wrote on Aug. 4, 2009 @ 07:36 GMT
Dear Florin,

thank you very much for your prompt replies on the communities questions including my own. It's a pleasure for me to see that the discussions in the essay contest start up, for it is a main goal of the contest to stimulate discussion and fair exchange of thoughts. Thank you therefore again for this contribution to the contest.

So at first i want to say that your approach...

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Lawrence B. Crowell wrote on Aug. 4, 2009 @ 12:57 GMT
I failed to state that what obeys first order logic are the combinatorics of the state space or state of the universe. Godel's theorem is in a way a combinatorial result. To skirt the Godelian problem with a cosmological structure that is quantum computational this restriction or something similar seems necessary. It is not that hard to arrive at from a mathematical perspective. Most mathematical developments of late, proofs of Fermat's conjecture and Poincare's homology conjecture, don't run into Godelian problems.

The conservation of quantum information with black holes and other quantum gravitational systems requires there be some great quantum error correciton code that underlies quantum gravity. This leads in some sense to the idea of the universe as a grand quauntum computer. While issues of consistency and completeness in the Godel-Turing sense are not my primary focus I can well imagine these problems coming to the stage. This then does seem to require the domain of computation, the state space, must be some primative recrusive or first order. Quantum cosmology might well have to be of this nature to within some cut-off in energy E < E_{planck}, which is curiously only about 1/2 Planck units of energy below E_{planck}.

Lawrence B. Crowell

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Author Florin Moldoveanu wrote on Aug. 4, 2009 @ 16:05 GMT
Dear Stefan,

Thank you for your time to read my essay and comment on it. I am too very glad that finally the discussions started happening and I found them very stimulating. The universal truth property (for lack of a better description) expresses the concept of independent reality of the world. The world is still out there regardless of what I may think about it or how I perceive it. But if reality emerges from pure math, then this property is absolutely remarkable because this does not exist in general in the Platonic world. Because of the existence of time, reality can have this property, otherwise all sorts of paradoxes and contradictions can ensue. Those contradictions are OK in the Platonic world, precisely because this world exists outside space time.

Now you raise a very interesting point by asking if our discussion for example will simply vanish with the disappearance of our universe. A related problem is why our universe is happening only once. From composability, there are only 3 solutions possible: quantum mechanics, classical mechanics, and hyperbolic quantum mechanics. The hyperbolic quantum mechanics does not satisfy the universal truth property because different pseudo-unitary representations are not isomorphic (unlike in the regular QM). Consequently we do not see any hyperbolic quantum mechanical effects in our universe. However, this is a very good property for a hypothetical “universe nursing ground” where new universes just like ours can be born, evolve, and die. This is a wild speculation at this point, but maybe our universe started by quantum tunneling form a chaotic hyperbolic QM domain into a regular QM domain. So now for the answer, our current discussion can have reality only in a domain where the universal truth property holds (meaning in our universe – frog eye view), but it does not have reality from a hyperbolic QM perspective – bird eye view. (There is no such thing as reality from the bird eye view: reality is a concept made possible only when the universal truth property holds). Also the mathematical relationships that are making our discussion possible will still live forever in the frozen Platonic world of math. In other words, our discussion was potentially possible from before our universe was born, but it could became actuality only within a coherent universal truth property domain, if this makes sense.




Author Florin Moldoveanu wrote on Aug. 4, 2009 @ 16:20 GMT
Lawrence,

Thank you for your clarifications. I still think the Turing idea is an unnecessary complication. Quantum mechanics is based on unitary groups which preserve information. There are isomorphisms between orthogonal and unitary groups and I think the most important one is SO(2,4)~SU(2,2). I think those isomorphisms play the central role in your quantum error correction code idea for quantum gravity.

A critical question is then how should we understand the relationship between classical and quantum mechanics? Is ‘t Hooft right in his idea of emergent quantum mechanics, or is Zurek right in his decoherence approach? By the way, browsing the fqxi site I have read the Azores’ talks, and in particular Joy Christian’s amazing claim. Were you aware of his claim and if yes, what do you think of it? If no, I would highly recommend his papers and replies to criticisms on the archive.




Stefan Weckbach wrote on Aug. 4, 2009 @ 20:05 GMT
Dear Florin,

thanks again for answering. I think i expressed myself a little bit ambiguous in my last post concerned with the "reality" of our current discussion.

I ment this not in respect to reality, but in respect to the property of "truth", hence to logics and its truth/false-values. My question is, is it further true that we corresponded at Aug. 4. 2009 16:05 GMZ when our...

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Author Florin Moldoveanu wrote on Aug. 4, 2009 @ 22:28 GMT
Dear Stefan,

You raised many valid points, which would take a long time to answer, so let me start answering a few critical questions first. Based on your satisfaction with my answers here I can provide further clarifications if needed.

You asked: “My question is, is it further true that we corresponded at Aug. 4. 2009 16:05 GMZ when our universe doesn't exist anymore in a far away...

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Lawrence B. Crowell wrote on Aug. 5, 2009 @ 02:53 GMT
Between 't Hooft, Zurek and Christian I choose Zurek for sure. I tend not to give much interest in ideas about hidden variables and other ideas which purport to have quantum mechanics wrong. If quantum mechanics goes oft aglee it will likely do so in the quantization of gravity.

A bit of interesting calculation I did. A shild's ladder construction is describable by a Galois field GF(4). Curiously the spin 1/2 system in QM is described by the same Galois field. GF(4) is the Dynkin diagram for SO(8), which is a central root with three others at 120 degree angles. This has triality for SO(8). So QM and GR are on a Galois level equivalent, and further they are both SO(8), or spacetime is SO(7,1), which are contained in SO(16), or Cl_{16}(C) = Cl_{15,1}(R)xC.

In effect I think general relativity and quantum mechanics are functorially equivalent. This little bit above indicates something of that sort of going on.

LC

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Author Florin Moldoveanu wrote on Aug. 5, 2009 @ 03:23 GMT
Lawrence,

I know clearly now what mistake is Christian making in his attempt to disprove Bell’s theorem. Unfortunately for me, two of his critics discovered the same thing from different perspectives and therefore my explanation is spurious and has only a pedagogical value.

I have never learned Galois theory, but I highly doubt relativity and QM are functorial equivalent. QM is a combination of a Lie algebra with a Jordan algebra and the Jordan side does have shared characteristics with relativity. The Lie side however is where the main differences arise. Hence I cannot see how QM and relativity are functorial equivalent. And if they were, then I would expect quantum gravity to be a trivial problem.




Stefan Weckbach wrote on Aug. 5, 2009 @ 07:52 GMT
Dear Florin,

thank you very much for your comments.

"the universe itself is true" - i ment it in the sense of being necessary, means, all the properties you mentioned are necessary (time, space, quantum mechanics, Standard Model). Necessary to fit with our observations and mesurements made to this point in time.

Surley they are necessary too in the meaning of being valid and...

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Lawrence B. Crowell wrote on Aug. 5, 2009 @ 16:27 GMT
Quantum mechanics and relativity as similar within a partial functor. A spin 1/2 quantum system and the Schild's ladder construction in general relativity are both Galois constructions of GF(4). So there is what I might call a functorial overlap. Their commonality with Jordan algebra of octonions works because there is a triality centered around SO(8). The Dynkin diagram of SO(8) is FG(4).

I have not read Christian's argument, but I tend to think that quantum mechanics is pretty secure. I don't think that there is some underlying flaw in it, at least on the level of photons, atoms and so forth. The measurement problem is still outstanding in some ways. I think that Zurek's decoherence and einselection model is most likely correct. I am not much on quantum interpretations, such as Bohm or Many Worlds, and Zurek's approach seems to offer the least in the way of metaphysical ideas these interpretations bring.

Lawrence B. Crowell

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Author Florin Moldoveanu wrote on Aug. 5, 2009 @ 18:29 GMT
Dear Stefan,

It is I who need to thank you for your insightful comments. Let me present in this post the framework of my thinking, and I will come back in a second one to reply to your specific questions.

Suppose for the sake of argument that my heuristic rule is indeed fruitful and it will lead to complete mathematical understanding of our universe. (A tall order for, unlikely to...

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Stefan Weckbach wrote on Aug. 5, 2009 @ 20:20 GMT
Dear Florin,

thank you very much for exposing your ideas. It's a pleasure for me to read your lines of thinking and to grasp more and more the framework you are working with.

I agree with your answer to the question "why is there something rather than nothing?". As you surely noticed, your answer to that question is a plain fact. Though i still cannot see wherefrom the dynamics of...

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Septickii wrote on Aug. 5, 2009 @ 21:15 GMT
Newton discovered the universal gravitation law without using any heuristic rules. Einstein also discovered relativity without using Florin’s heuristic rules. Why are you sure that the future constructor of TOE is in need of your heuristic rules? If you wish to contribute in physics, you may propose a model of TOE or quantum gravity, but not rules and advises how to build it.

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Author Florin Moldoveanu wrote on Aug. 6, 2009 @ 01:16 GMT
Lawrence,

A partial functor is probably right.

Christian’s argument is very interesting, but as one of its critics pointed out from Bell’s result hidden variables in QM cannot be real and local. Bohm’s theory is real but nonlocal; Christian’s theory is local but not real. Christian proposes using a Clifford algebra element to describe his hidden variable and obtains all the violations of Bell’s inequalities precisely like QM. From this he concludes (incorrectly) that Bell’s inequalities can be violated by a real local hidden variable theory. If you are interested I can tell you what his mistake is; it is subtle. Finding the mistake was fun, I only wish I were aware of his results two years ago.




Author Florin Moldoveanu wrote on Aug. 6, 2009 @ 02:41 GMT
Dear Stefan,

Let’s see if I can convince you of point 3 for math and 1 and 4 for the universe.

Point 3 is as follows: in math, all theorems are already there just waiting for mathematicians to reveal them. It is only an accident of history that Pythagoras theorem is named like that. This mathematical fact was there the moment you specify the axioms. Frozen means that in one...

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Lawrence B. Crowell wrote on Aug. 6, 2009 @ 03:49 GMT
Sure enough let me know. I only heard about J Christian a few weeks ago.

LC

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Author Florin Moldoveanu wrote on Aug. 6, 2009 @ 03:58 GMT
Dear Septickii,

I love pointed questions. I think there are three things to consider here.

1. More important than answers is asking the right questions. Before Galileo and Newton people considered rest as the natural state of objects, not uniform motion. The mathematics in Einstein’s general relativity was discovered in the prior century, but Einstein overcame the conceptual barrier that even empty space can bend. By asking the right question, a new paradigm can form. My heuristic rule is just this, a new paradigm at this point. Is it going to be fruitful? I surely hope so and this leads me to the second point.

2. No Nobel Prize was ever given in physics for new paradigms, but for solving concrete problems. Even Einstein did not get the prize for relativity. But if the question is right, result will surely follow. Can we imagine discovering relativity and not solving real physical problems? No, because relativity is a real physical phenomenon and its discovery were bound to lead there. So how can we approach the quantum gravity problem? This leads me to the last point.

3. String theory is a very consistent, beautiful, and coherent theory, but with not much to show for all the effort that was put in. A common misconception is that ALL good ideas in physics are in there. I believe the right approach for quantum gravity is non-commuting geometry and I do intend to contribute in this area. Viewed through my heuristic rule paradigm, non-commuting geometry becomes suddenly very intuitive. But there are easier problems to solve first: obtain the strong force and the electroweak force beyond the semi-classical approximation and solve the Standard Model parameter values problem. Based on AdS/CFT correspondence, if we completely understand gauge theory, quantum gravity should follow.

I am currently working on four problems suggested by the new paradigm. It is not much, but it is a start. Suppose I will be successful and I will publish the results. Will anybody pay any attention? How many people paid attention to Grgin’s structural unification of quantum mechanics and relativity? How many people noticed Jochen Rau’s results based on dimensional analysis of Lie groups? How many people are aware of David Hestenes’ zitter phenomenon which was experimentally confirmed?

How can I compete with 30 years of effort by many bright physicists working in string theory and come up with the solution for quantum gravity overnight? The time for quick theories like electromagnetism has passed. Rome was not built in a day, neither was quantum mechanics, general relativity, or string theory. A coherent new paradigm will attract the critical mass of researchers to make significant progress if there is indeed progress to be made.




Stefan Weckbach wrote on Aug. 6, 2009 @ 07:09 GMT
Dear Florin,

Thank you very much for your effort to write back at length and elaborated.

To your point 1:

Imagine that at some day in the future all observers have died but two of them.

Imagine further that these two observers have a conversation and after that suddenly both die (not trouth a car accident, but perhaps trouth a natural desaster).

After that...

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Lawrence B. Crowell wrote on Aug. 6, 2009 @ 12:59 GMT
The notion of paradigm shift has been over used IMO, but there are occassions where this happens according to some definition. The concept was advanced by T. Kuhn in this "Structure of Scientific Revolutions," and while it has some validity to it, I also think the idea is overblown.

However, running with this football, there does seem to be a paradism shift waiting in the wings. Maybe several changes are required. Such paradigm shifts usually involve the removal of excess baggage that keep two categories distinct. As indicated above I think that QM and GR have similar structure, or are equivalent under a partial functor. I will also say I think that in GR the distinction between inertial and accelerated frames is a stumbling block.

I wrote a paper last spring concering the zitterbewegung, and communicated with Hestenes about this. I have not submitted it for publication yet. If you are interested in it I can transmit it. Zitterbewegung may be telling us something about the end of renormalization group flows and the onset of mass at low energy. The leptons and quarks all have masses ~ .5 to 100 MeV, and sitterbewgung suggests this mass is associated with a confining potential at the Compton wave length of a particle.

Lawrence B. Crowell

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Author Florin Moldoveanu wrote on Aug. 6, 2009 @ 17:47 GMT
Lawrence,

Christian’s argument is as follows. The hidden variable in spin measurements in his theory is the pseudo-scalar from the Clifford algebra Cl 3,0 (a trivector). From this he very nicely obtains the GHZ state and the Bell’s inequality violations precisely like QM does. This is the valid part. The interpretation is completely wrong however. He completely misunderstands what QM, classical mechanics, and real hidden variables are about. His main points are 3:

1. The trivector contributes only counterfactually towards his final answer.

2. All possible orientations should be considered when averaging over hidden variables in a realistic theory. (This is his main point in the recent Azore conference.)

3. The non-commutativity of the trivectors only reflects the fact that two rotations do not commute.

So what are his mistakes?

1. If the trivector contributes counterfactually only, this is not a realistic hidden variable theory in the sense of Einstein and Bell. In experiments we read real numbers from dials or other devices. When you generalize the statistic to go beyond real numbers you are no longer in the Kolmogorof’s realm or the realm of realistic hidden variable theory. You can either be in the realm of QM, or in an inconsistent statistical theory.

2. Considering all possible orientations will generate a continuous state space, the Bloch sphere in his case and this is precisely the distinguishing factor between classical and QM and it is no wonder he recovers all QM predictions.

3. Non-commutativity of hidden variables is also a distinguishing characteristics between classical and QM. In fact he is only casting the EPR experiment in the language of quaternions, hardly a novel thing after Adler’s results. So why can he use geometric algebra and why does his model look realistic? Because Cartan’s classification of classical Lie groups can be done in the language of geometric algebra and he is only benefitting from a particular isomorphism between orthogonal and unitary groups: SO(3)~SU(2). In general his method will not work for SU(3) for example.

The other thing he does is that he uses a very obnoxious and aggressive tone in his rebuttals.




Author Florin Moldoveanu wrote on Aug. 6, 2009 @ 20:58 GMT
Dear Stefan,

Let me clarify a last point. Let’s use “e” and not
, because it is easier to explain.

We all know that its value is given by this series:

[equation]$

e = 1 + \frac{1}{1!}+\frac{1}{2!}+\frac{1}{3!}+...

$[/equation]

This value is the same whenever anyone computes it, and “e” existed during the dinosaur era, or during big bang. Its existence means only that if someone adds those numbers it obtains 2.7182… REGARDLESS of the existence of a person, computer, etc to perform the calculation. A mathematician on another planet, in another time, or in another universe, will obtain the same value as we have done it here on Earth. Similarly, all math just exists in its abstract Platonic world. Math is one thing, mathematicians is another. Mathematicians need space time, math does not.

So now to your statement/question:

“As long as observers can prove pi by drawing a circle in the Egyptian sand and calculate the ratio, this is true in your framework. But what happens when there isn't nomore an observer to do so? Doesn't this mean that the cited lines of reasoning above, made by you, are in this case also ill-defined?”

No observer means no actual computation of e (no mathematicians), but as abstract mathematical concept, “e” still exist. Reasoning and math are not ill defined in the absence of mathematicians.




Author Florin Moldoveanu wrote on Aug. 6, 2009 @ 21:03 GMT
Lawrence,

Yes, I would be very interested in your zitterbewegung paper. (why did Hestenes had to give it this impossible name?)




Stefan Weckbach wrote on Aug. 6, 2009 @ 23:03 GMT
Dear Florin,

thanks again for replying.

I have an analogy to contribute concerning the platonic realm, infinity and my own asumptions about "empty space".

Imagine there exists nothing. Nothing but an (in)finite (white) plain. This is my "empty space".

Now, imagine drawing a circle onto the plain. The plain has now a circle on it. Was the circle there at the plain before "someone" has drawn its borders onto the plain? Surely, and i agree with you.

Now imagine not drawing a circle onto the plain, but a rubber duck. Was the rubber duck there at the plain before "someone" has drawn its borders onto the plain? Surely, i would say, because i know what Rubber duck looks like and what it means and can imagine it to be on the plain.

The meaning of a circle in our universe is fascinating. It is symmetric, a strong symbol and a very practical thing too. But it is anthropic (in the sense of being used to use maths as everyday-language) in my opinion to think that the whole plain contains nothing more but mathematical relationships. I will try to expose this.

There may exist relations that are immovable. Pi could be one of them because the too properties of a circle (diameter and Perimeter) that relate to pi cannot be considered as independent from each other. Because a circle is a "oneness". If we would divide the circle into two halfs, we couldn't obtain anymore pi. So pi is a property of a categorial oneness, named "circle". The same is true for the rubber duck and for the number "e". Whenever i imagine this rubber duck in the same way i did it in the example above, i get the same result. And the same is also true for the imagination of the whole landscape of maths. Whenever someone speaks of the whole landscape of maths, he/she presupposes a certain picture of it.

Although we can describe my rubber duck very precisly by mathematics (for example by a computer animation), two things we can't describe by maths: Firstly my inner impressions about the colors red, green etc. and many more things that are subjective. And secondly also we can't describe by maths the whole landscape of maths itself. At least i do not believe that we can do that. My conclusion out of that is that (out of space-time) there must exist some more than only maths. Because math may not need space-time to exist, but it needs a oneness that it can divide into parts and relate them to each other. So maths is not an independent concept that can exist on its own right somewhere, but depends on something more.

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Lawrence B. Crowell wrote on Aug. 7, 2009 @ 02:27 GMT
The term zitterbewgung is German for frantic motion, which goes back to the very early days of quantum mechanics. Tehre are those who interpret this as a hidden variable, which I don't do. Zitterbewegung does suggest some sort of confining of a particle by a potential field however.

LC

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Author Florin Moldoveanu wrote on Aug. 7, 2009 @ 02:58 GMT
Dear Stefan,

You say:

“My conclusion out of that is that (out of space-time) there must exist some more than only maths. Because math may not need space-time to exist, but it needs a oneness that it can divide into parts and relate them to each other. So maths is not an independent concept that can exist on its own right somewhere, but depends on something more. ”

I do not understand the oneness idea, but again I am not a philosopher. What I am proposing in my essay is only physics: extract mathematical facts about the universe which are all validated by experiments and then draw mathematical conclusions from that. What I was trying to explain in my replies was (mostly) the philosophical interpretation of it, but at the end of the day, our perception of the results does not matter.




Stefan Weckbach wrote on Aug. 7, 2009 @ 05:37 GMT
Dear Florin,

thank you for your feedback and your effort to make me understand your point of view. I am thinking about your comments and contemplating the possibility of your arguments being right, absolutely right or partially right. Please let me therefore make a few final remarks.

Concerning our main theme here, the question of what could/couldn't be possible in physics, although...

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Author Florin Moldoveanu wrote on Aug. 8, 2009 @ 04:38 GMT
Dear Stefan,

Thank you for the opportunity to better explain my ideas. I still strongly believe in the sentence below:

"Reasoning and math are not ill defined in the absence of mathematicians"

and this has nothing to do with Gödel’s theorem. Consider the Peano arithmetic and the Presburger arithmetic. They exist completely independent of each other. If I can have an analogy, one arithmetic is like a PC, and the other like a Mac, and the software that runs on them corresponds to their particular theorems. Of course there are similarities between Peano and Presburger arithmetics, just like there are similarities between a PC and a Mac, but just as the PC software does not run on a Mac and the other way around, the contradictions between those 2 axiomatic systems are irrelevant to their internal self-consistency. In the example above, just because a PC software program crashes when running on a Mac, it does not mean it will not run perfectly on a PC. In other words, just because axiomatic systems are at odds with each other, this does not make them ill defined.




Stefan Weckbach wrote on Aug. 8, 2009 @ 06:05 GMT
Dear Florin,

thanks also for your feedback!

you wrote:

"In other words, just because axiomatic systems are at odds with each other, this does not make them ill defined."

That's not what i am saying.

I said:

"There can be many axiomatic systems that are at odds with each other and lead to mutually exclusive perspectives about the validity of the arguments. All that is surely nonetheless based on reasoning and therefore resoning isn't an ill-defined concept in that case. But the conclusions drawn out of these maths could be simply arbitrary and therefore not even ill-defined."

Firstly, i do not consider Peano or Pressburger arithmetic to be ill-defined. They are just defined (on the grounds of reasoning). In the case of the Pressburger arithmetic, Gödel's restrictions may not hold anymore. So we have to systems, Peano arithmetic and Pressburger arithmetic. The first may run on a PC, the latter may run on a Mac. But to conclude out of that with necessity that there must exist a(n) (infinite) platonic realm of all abstract maths with all possible and thinkable axioms already fixed and independent of perception, that's what i doubt and what i tried to say.

You wrote:

"Reasoning and math are not ill defined in the absence of mathematicians...and this has nothing to do with Gödel’s theorem."

Yes to the first part of your statement concerning reasoning. No to the statement concerning "ill defined", because in the absence of mathematicians, i don't think that there exist fixed mathematical axioms independent of human reasoning. And no to the second part of your statement, because Gödel's theorem is a result of math and (human) reasoning and for Gödel's result i don't believe that it could be an everlasting, eternal truth in a platonic realm of abstract maths. Not because i think that "independent" axiomatic systems are deeply contradictory, but because i think that there isn't such a fixed platonic landscape of all possible ("thinkable") mathematical axioms, theorems and finally distinctions.

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Lawrence B. Crowell wrote on Aug. 8, 2009 @ 12:52 GMT
Godel's thoerem says that no axiomatic system is able to enumerate all of its own Godel numbers. The Turing machine approach I find more understandable. A Turing machine either halts or it does not. A Turing machine can get caught in a loop, such as MicroSoft's software often does. So it would be nice to have a universal Turing machine which can determine whether any Turing machine will halt or not. So the UTN emulates all other TMs, including itslef. This leads to a problem since the UTM must emulate itself emulating other TMs, and so forth. This leads to something isomorphic to the Cantor diagonalization argument with Godel numbers: No axiomatic structure can enumerate or encode all its Godel numbers. This means consistency is not provable in any formal axiomatic system.

This inconvenient fact has strangely had minimal impact on mathematics so far. Most proofs, including the outsanding proofs of conjectures by Fermat and Poincare, are not impacted much by this. Though there are some curious aspects with this involving "proof theory."

LC

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Author Florin Moldoveanu wrote on Aug. 9, 2009 @ 01:43 GMT
Dear Stefan,

Thank you for your clarifications. I think I understand where you are coming from. If I understand your argument correctly, you are a believer in solipsism. Is this true? (I will stop here and wait for your answer so that I will not take the discussion in a wrong direction).




Author Florin Moldoveanu wrote on Aug. 9, 2009 @ 01:58 GMT
Lawrence,

There is a very nice paper by Chaitin about his rewrite of Gödel’s results in computers using a UTM. I think you would like that very much. For me it was this paper that spurred my interest in algorithmic information theory and Gödel’s results. In his paper, Chaitin worked with Barry’s paradox: N = the smallest natural number that cannot be expressed in less than 100 words. The paper appeared in No 1, Volume 1 of Complexity (I am not sure if the journal still exists.)

I think the reason Gödel’s theorem did not have a bigger impact is that once you go from natural numbers to continuous real numbers, you can prove quantifier elimination results which make his theorem inapplicable.




Stefan Weckbach wrote on Aug. 9, 2009 @ 07:15 GMT
Dear Florin,

thanks for your feedback too.

If i would believe in solipsism, i wouldn't correspond with you, because there wouldn't be someone to correspond to - who has feelings and is much more trained in logics than i am.

But nonethelesss, i don't understand your conclusion of solipsism out of my writings (maybe you could expose this more in detail). All i said about my belief is, that i don't believe that there is such a thing as a fixed infinite landscape of mathematical axioms, theorems and mathematical inductions. So being sceptic about this, i would say i am merely a skeptic (and maybe a displeasing one, - i would admit :-).

And maybe i am wrong in my belief that there isn't such a thing as the fixed mathematical landscape. Maybe it does really exist!! (for whatever reasons). For that case i would not automatically assume that that's all that can exist. Although the imagination of a fixed infinite landscape gives the impression to me that there isn't much "room" anymore for other things to exist because this landscape would be somewhat "infinite in all directions", i am not convinced of the conclusion that in the case of the existing fixed infinite landscape of maths there couldn't exist additional features of ultimate reality.

Provability, i think, doesn't lead us any further here, and also the term of truth. It seems to me that an intuitive description of ultimate reality must at first place have an overall consistence that, for all practical purposes in the universe we live in, at least seems to be the ultimate truth. Maybe that's the case with your fixed landscape and your universal truth property in cooperation. Therefore i insist on my comment from Aug. 4, 2009 @ 07:36 GMT, second chapter. My comments on your essay and your concept were thought as comments on possible loopholes that one could consider as relevant regarding the results you may obtain with your approach. But sorry for my somewhat smart-alecky type of criticism. It is my type to consider radical, new and far reaching assumptions about the world we live in, because such assumptions could have - and in my opinion indeed have - impacts on our view of the world (at the latest then when they are presented in popular scientific magazines especially also for people which can't evaluate every line of reasoning in every such assumption). I am convinced that this is a legitimate behaviour in a forum like ours.

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Author Florin Moldoveanu wrote on Aug. 10, 2009 @ 01:36 GMT
Dear Stefan,

I have to admit; now I am completely confused. You do not believe that the mathematical landscape does exist by itself and yet you are not a solipsist. So did Pythagoras’ theorem exist before Pythagoras? And was Gödel’s incompleteness theorem valid 2000 years ago? How about 5 billion years ago before Earth was formed? If yes, how would reconcile that with your belief that the mathematical landscape does exist?




Author Florin Moldoveanu wrote on Aug. 10, 2009 @ 01:38 GMT
Stefan, sorry about the typo. The last statement should read:

"If yes, how would reconcile that with your belief that the mathematical landscape does not exist?"




Stefan Weckbach wrote on Aug. 10, 2009 @ 04:37 GMT
Dear Florin,

i am not confused. Because "solipsism" is too crazy for me to waste more than the one or two following thoughts on it for the aim of considering it as deeply irrational. Everything else would be deeply irrational, wouldn't it?

See for example the possibilities of a "solipsist" to explain the only fact (in the meaning of a fact that does *resist* until this solipsist...

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Lawrence B. Crowell wrote on Aug. 10, 2009 @ 13:44 GMT
I read Chaitan's paper some years ago. He appears to argue that mathematical systems emerge from self-referential propositions as accidents of sorts. As for the continuum there is of course the matter of the continuum hypothesis. Bernays and Cohen demonstrated by Godel's thoerem it is consitent with ZF, but not provable.

LC

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Author Florin Moldoveanu wrote on Aug. 10, 2009 @ 13:56 GMT
Dear Stefan,

I did not mean solipsism as a negative term. In fact, from standard QM, not only solipsism makes perfect sense, but it is hard to contradict: the spin direction for an electron does not exist until measurement and the direction is set by the free will of the experimenter. So in this way reality sets in because of the observer’s collapse of the wavefunction. There are many observers and the collapse of the wavefunctions happens everywhere. When there are no living observers, you can still have the background environment according to Zurek, or gravity according to Penrose to do the trick. The real problem sets in when you apply the wavefunction idea to the whole universe, resulting in a Wheeler-DeWitt equation. So basically it was this framework I was envisioning when I was talking about solipsism.

So let me try again to restate my understanding of your position: once the universe starts to exists, math comes into existence as well. Is this true?




Stefan Weckbach wrote on Aug. 10, 2009 @ 19:02 GMT
Dear Florin,

I am not quite sure if i understand the meaning of your term "solipsism". I think you mean the problem that the decoherence-concept could break down if the universe is considered as causally, physically closed. Is that right? (solipsism as i heard of it is the position of an individuum to assume itself as the only individuum to exist).

I do not believe in superpositions in a mainstream-manner as real mutually exclusive states somewhat and somewhere overlapped with each other until divided by a measurement.

Superpositions for me are another term for an "undefined" state. That they look pretty like overlapping real states is due to the environment and its imposing limits, in which the undefined area gets a special contextual meaning for experimenters and their calculation-schemes.

"So let me try again to restate my understanding of your position: once the universe starts to exists, math comes into existence as well. Is this true?"

No. Once the universe starts to exist, something other than maths is transformed into dynamical structures and substructures that can partly be grasped and translated into the language of maths.

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Author Florin Moldoveanu wrote on Aug. 11, 2009 @ 00:07 GMT
Dear Stefan,

Since I am not a philosopher, my understanding of solipsism is irrelevant. To keep things clear, let’s ignore it for the moment. You say: “Once the universe starts to exist, something other than maths is transformed into dynamical structures and substructures that can partly be grasped and translated into the language of maths.”

So now my question becomes: does the language of maths have universal independent existence? My position is that it does because mathematics is abstract.




Author Florin Moldoveanu wrote on Aug. 11, 2009 @ 00:35 GMT
Lawrence,

Cohen’s forcing argument is interesting (but I do not quite understand it yet).

I am still reading your paper; it is very interesting. I think that the central issue is accepting the claim that particle’s confinement is due to space-time non-commutativity. Regardless of the math arguments, from an order of magnitude analysis point of view this is implausible because gravity is very weak. If your math argument is indeed correct, you may want to include some actual computations about the magnitude of the effects.




Stefan Weckbach wrote on Aug. 11, 2009 @ 05:28 GMT
Dear Florin,

you wrote:

"I did not mean solipsism as a negative term. In fact, from standard QM, not only solipsism makes perfect sense, but it is hard to contradict".

All philosophical considerations could be considered as abstract, too. So also solipsism. Some of these considerations are consistent and could be hard to contradict just like in maths, some could be...

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Author Florin Moldoveanu wrote on Aug. 12, 2009 @ 02:02 GMT
Dear Stefan,

Thank you for the opportunity to present my ideas and I think we are in agreement now. The journey was not easy, but this made the ending that much more valuable. The problem is that outside math and physics, the potential for miscommunication is large. However, mathematical and physics ideas are never born in a vacuum and they are always surrounded by fuzzy philosophical considerations. Pure results without the surrounding philosophical cloud are dry, abstract, and boring.




Lawrence B. Crowell wrote on Aug. 12, 2009 @ 02:57 GMT
The noncommutative coordinate terms do not involve the gravitational constant G. They are as such not due to the classical gravity field.

LC

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Author Florin Moldoveanu wrote on Aug. 12, 2009 @ 03:05 GMT
Lawrence,

Is it not true that non-commutativity of the space-time coordinates occurs at the Plank length scale? And the Plank length is proportional with sqrt(G), and therefore G does enter the picture.




Stefan Weckbach wrote on Aug. 12, 2009 @ 08:00 GMT
Dear Florin,

thank you also for the possibility to exchange our standpoints and lines of reasoning. Maybe our arguments could lead others to one or another considerable conclusion, too, independent in which direction. I enjoyed the exchange and wish you all the best at FQXi contest.

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Lawrence B. Crowell wrote on Aug. 12, 2009 @ 18:04 GMT
The gravitational constant does lurk in the wings of course, but it is not a scale factor which determines the strength of an induced field by noncommutative coordinates. Noncommutative geometry is of course stronger the smaller the region one looks at. If you look up to equation 12 the commutation of q and q' is

[q, q'] = ħ^2∂_{[p}A_{p’]}.

For |q| = |q’| = L_p = sqrt{Għ/c^3} we have the magnitude of the B_q field is G/c^3 which is pretty small. For the commutation in the momenta

[p, p'] = ħ^2∂_{[q}A_{q’]},

where for |p| = |p’| = P_p = sqrt{ħc^3/G} there is the field B_p which is appreciable. This is the gauge-like field on the Dirac matrix element. The magnitude of the momentum coordinate commutator is going to scale as (L_p/L). For the Compton wavelength 10^{-11}cm this factor is about 10^{-22}. Converting the commutator of momenta into energy units then on this scale the energy associated with this field is about 10^5ev, which is about the mass of an electron. So the mass of an electron might be due to the effect of noncommutative coordinates (induced by Planck scale physics) which bottles up a massless particle.

Lawrence B. Crowell

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Lawrence B. Crowell wrote on Aug. 12, 2009 @ 18:15 GMT
As a point of clarification, at the opening I said the gravitational constant is not a determinant of the strength of the induced field. I probably should have better said it does not scale things as a G&M/M (& = delta) for &M a fluctuation in a mass that is ~ L_p.

LC

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Author Florin Moldoveanu wrote on Aug. 13, 2009 @ 13:26 GMT
Lawrence,

Thanks for your answers. I re-read your paper and now I have another question. You state that the length does not matter at the critical point in RG. But this is kind of backwards: if the physics is the same at different scale, then of course the length is irrelevant. So my question is: why is the relevant physics the same at different scales? In this case we have the Compton length and this seems to fix the scale. In other words, establishing rigorously the RG is necessary.




Lawrence B. Crowell wrote on Aug. 13, 2009 @ 14:14 GMT
Your question is a pretty good one. To be honest I will have to read exactly what I wrote. The upshot is this. Renormalization group flow, in particular conformal flow, works when mass is zero or sufficiently small. The HIggs mechanism then comes in and things get muddied up and RG flow becomes broken up so to speak. So there is an apparent end to RG flows. However, if the zitterbewgung, the mass of basic elementary particles (quarks, leptons etc), the Higgs field and so forth are involved with noncommutative geometry then there might be some way in which RG flow can be continued to zero energy. I think it should be possible in principle to continue to ever lower energy where the zitter motion of particles enter into a type of condensate.

The Higgs field enters into the vacuum at 10^{-16}E_{planck} and the physical vacuum appears to have no RG flow. Yet at much smaller energy it appears that if zitter is due to non-commutative geometry and a gauge-like field that RG flows can be continued from the MeV scale down. There appears to be a grey zone here from the TeV to MeV range that I don't understand, and I am not clear on whether RG flow holds there. So there are some open questions here.

LC

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Author Florin Moldoveanu wrote on Aug. 14, 2009 @ 02:20 GMT
Lawrence,

If non-commutativity of the space-time is ultimately responsible for electron's mass, it should also be responsible from muon's mass as well, and the two whould not be different. The three generations of particles show that the story is more complicated.




Author Florin Moldoveanu wrote on Aug. 14, 2009 @ 04:58 GMT
Errata:

After submitting the paper, the author discovered the typos below. Because FQXi does not allow correction after submission, these errata will list the corrections.

Page 5, second paragraph, line 4:

Change “background invariance” to “background independent”

Page 5, second paragraph, line 10:

Change “approached” to “approach”




Lawrence B. Crowell wrote on Aug. 15, 2009 @ 12:10 GMT
Of course the situation is more complex. The three doublets of leptons and similar doubles of quarks have different masses. In the SM approach this mass is determined by a Yukawa lagrangian of the form q-bar Hq or l-bar Hl (q, l = quark or lepton), which are different. If the Higgs field is dynamical it might be due to some gauge-like force or in a technicolor sense due to top quark condensates. So clearly if there is anything to this idea of mine there are additional complexities of coupling strengths for different quark and lepton generations and their components.

LC

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Author Florin Moldoveanu wrote on Aug. 21, 2009 @ 01:27 GMT
In the attached document below I have fixed the reported typos and I have added another section.

attachments: Articol.pdf




Lawrence B. Crowell wrote on Aug. 25, 2009 @ 23:47 GMT
I intend to do much the same. I have written the mathy-technical paper for this and am now converting a copy of it for a more general audience.

Cheers, LC

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Author Florin Moldoveanu wrote on Aug. 26, 2009 @ 03:08 GMT
Lawrence,

I started with a bigger paper and half way through I discovered the FQXi limit and I had to greatly compress it. I added the last sections in hope to post it on the achive, but I did it only for logical cohesion purposes.

If any qualified endorser for hep-th is reading this, likes my entry, and is willing to endorse my essay, please contact me at fmoldove@gmail.com

It is very unfortunate FQXi does not allow corrections, and one particular typo I was mortified when I discovered it: instead of writing background independent” I said “background invariance”. I was thinking diffeomorphism invariance and after I discovered the typo I was only thinking how bad this would look to all those LQG experts that will judge the papers. I guess typos are unavoidable because you become blind at them as you re-read the paper and know what you mean already.

Anyway, good luck writing a paper for this contest, as of right now there are very few entries compared with last time and the rate of new entries is very slow as well.




Lawrence B. Crowell wrote on Aug. 26, 2009 @ 23:12 GMT
How many loop variable (LQG) people are there vs string people? I have an idea that string theory and LQG should work together or unify. But I might want to tailor some things with that in mind if necessary.

I am composing a general perspective on what I am presenting. I will attach a more detailed version for those who want to look.

Cheers, LC

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Author Florin Moldoveanu wrote on Aug. 27, 2009 @ 03:58 GMT
I think in general the ratio of LQG to string research is 1:9, but on FQXI, the ratio is reversed, something like 7:3. I do not quite see how string and LQG research can merge. From the pure general relativity point of view, LQG is better than string theory, but it is very unfortunate that the ¼ factor for the entropy of the black hole cannot be directly obtained in LQG.

It does not seem possible to unify LQG with strings because of the background independence issue, and string theory is rather rigid in this aspect: either you tie down the curled dimensions and prevent them from changing, or you can allow the dimensions to change at the expense of instability.




Lawrence B. Crowell wrote on Aug. 28, 2009 @ 04:01 GMT
The connection between LQG and string theory is with the electric-like field component in LQG constraints and the quantum critical point which ties AdS in string theory according to AdS_4xV^7 for V^7 a world volume for a 6-brane in 11-dimensions. The 4-field form indcident on D7 is set by a quantum critical point, the same which set the constraint on the LQG charge

Q_a = nabla_iE^i_a

I am not sure about the 1/4 or the Barbero-Immirzi ambiguity. But this appears to be some sort of connection between the two.

The natural background here is a de Sitter cosmology, or the anti-de Sitter cosmology. On the dS the gravitational perturbation (gravitons on the background) might have some sort of connection to LQG by the above argument.

Cheers LC

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Lawrence B Crowell wrote on Aug. 28, 2009 @ 20:30 GMT
I submitted my article this morning. I can't imagine why it would be rejected, so we can compare notes on LQG and strings

Chhers LC

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Author Florin Moldoveanu wrote on Aug. 29, 2009 @ 02:32 GMT
Good luck with the paper. If it is under the character limit, it will get posted.

Yes, the Barbero-Immirzi parameter is liked with the ¼ and there were quite a few papers about it. I am not a string expert, and I cannot comment on your proposed link, but it still looks improbable.

By the way, I just discovered some very interesting works of Irving Segal. He did fundamental work in algebraic quantum mechanics, and he unified classical and quantum mechanics in the same mathematical structure. But I did not know that he was interested in axiomatizing relativity and that he invented a different kind of cosmology called the chronometric cosmology. Very interesting, but not quite believable. Anyway, he also studied SO(2,4), SO(3,3), and SO(1,5) in the context of relativistic quantum mechanics.

(By the way, he was also the advisor of John Baez.)




Lawrence B. Crowell wrote on Aug. 29, 2009 @ 12:39 GMT
Before indicating how the string LQG link might happen, here is the problem I have. I can put on the string theory "hat" and work there or read papers related to that. The structures are vast and rich. Witten's find that the S-matrix theory is a flat space limit of a holographic principle, or the Maldecana AdS/CFT correspondence and so forth contain rich structure which are too physically apparent. On the other hand I can put on a loop variable hat and see how the close correspondence with basic general relativity is such that this structure also must have some bearing on nature. There is also twistor theory as well.

The Sen connection in LQG and the "charge" due to the electric-like field is a constraint in LQG which is sentisive to the same quantum phase transition as the is field flux on AdS_4xD7 which sets the cosmological constant. The Barbero-Immirzi ambiguity stems from a gauge fixing problem. It is possible that this stting of the net charge Q = nalba E, on the manifold removes this ambiguity. This produces an additional constraint in LQG that might be used to cure the B-I ambiguity.

Cheers LC

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Frank Martin DiMeglio wrote on Sep. 1, 2009 @ 03:21 GMT
Hi Florin. This is a very important/relevant question.

How do you see the following as applicable to, and substantiated by, your essay:

The ability of thought to describe or reconfigure sensory experience is ultimately dependent upon the extent to which thought is similar to sensory experience.

That statement is clear enough. If you think that the above statement is not true, then please clearly explain why you believe that this is so.

Thanks.

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Author Florin Moldoveanu wrote on Sep. 1, 2009 @ 13:59 GMT
Hi Frank,

There are two kinds of learning: supervised and unsupervised. Suppose I take a young child and show him a chair. I say: this is a chair. Then the child learns in a supervised manner. Suppose also I show him the color red. I say: this is the color red. On one hand this is also supervised learning, but since I cannot really know how the child is actually seeing the color, learning the color perception is unsupervised learning.

Then this begs the question: is my color red the same as your color red? For most people we know it is, but for color blind people is not. The reason it is not is because they are missing one or two color receptors in their eyes. The color perception depends on the dimensionality of the receptor and this is very reminiscent of quantum mechanics.

Now to answer your question. The brain naturally evolves towards identical perceptions and this given by the general topology of the neuron connection. With similar connection patterns, self-feedback unsupervised learning leads to the same eigenvalues modes of representing information for all people. That is why we all see red as red, and my red is the same as yours. The way the neurons are connected, and the tools of analyzing information (like the number and type of color receptors) determine critically the outcome of measurement. Same in quantum mechanics: what I observe in a double slit experiment depends if I put polarizers to determine the “which path” or not. But regardless of the tools we use to interpret the world, there are precise mathematical predictions we can make about the world like quantum mechanics and relativity.

I hope this answer your question, if not, please feel free to ask additional questions.




Steve Dufourny wrote on Sep. 1, 2009 @ 17:29 GMT
Dear Florin ,

Interesting work of math .

Sincerely

Steve

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Author Florin Moldoveanu wrote on Sep. 1, 2009 @ 21:37 GMT
Dear Steve,

Thank you for your kind words. I hope I was not too technical and the essay is not too hard to understand.

Regards,

Florin




Frank Martin DiMeglio wrote on Sep. 1, 2009 @ 22:46 GMT
Florin, you didn't answer the question. The question was: Do you agree that the following is a fact:

"The ability of thought to describe or reconfigure sensory experience is ultimately dependent upon the extent to which thought is similar to sensory experience."



Stefan says: "It seems to me that an intuitive description of ultimate reality must at first place have an overall...

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this post has been edited by the forum administrator

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Author Florin Moldoveanu wrote on Sep. 2, 2009 @ 03:35 GMT
Frank,

Sorry if I was not clear. Let me try again. You state:

"The ability of thought to describe or reconfigure sensory experience is ultimately dependent upon the extent to which thought is similar to sensory experience."

I am not sure about the reconfigure part, but I do agree with the rest of the statement with the exception of “ultimately”. Yes, sensory experience is very important, but we cannot deny the ability of mathematics to describe not only the experiences we do not directly encounter but even the ones we do. In other words, although I agree it is very important, I do not grant to the sensory experience.

However, I had a second question, relating to what happen before the first dream. Were gravity and electromagnetism unified then? In my opinion this is a show stopper issue and if this point is not addressed, the rest of the discussion degenerates into parallel monologues.

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Author Florin Moldoveanu wrote on Sep. 2, 2009 @ 03:37 GMT
Sorry, but some formatting commands erased a key word. Here is my post again.

Frank,

Sorry if I was not clear. Let me try again. You state:

"The ability of thought to describe or reconfigure sensory experience is ultimately dependent upon the extent to which thought is similar to sensory experience."

I am not sure about the reconfigure part, but I do agree with the rest of the statement with the exception of “ultimately”. Yes, sensory experience is very important, but we cannot deny the ability of mathematics to describe not only the experiences we do not directly encounter but even the ones we do. In other words, although I agree it is very important, I do not grant “exclusivity” to the sensory experience.

However, I had a second question, relating to what happen before the first dream. Were gravity and electromagnetism unified then? In my opinion this is a show stopper issue and if this point is not addressed, the rest of the discussion degenerates into parallel monologues.

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Steve Dufourny wrote on Sep. 2, 2009 @ 18:20 GMT
Hi ,

No Very easy in fact ,I understand speedly,maths ,physics ,sciences are for me like plant a flower ,I think all is there ,when you like sciences ,too speedly for some people ,but it's like that .

I beleivewhat you need to be more pragmatic in physics I think ,I invite you to insert limits .In all case congratulations,I think what Lawrence can help you in math and Ray in physics .The complemenatrity Florin ,always .

Best regards

Steve

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Steve Dufourny wrote on Sep. 2, 2009 @ 18:22 GMT
On the other side ,I need improve my understanding in computing ,there I am very very bad .

If you can help me ,don't hesitate I am here to learn too .

Regards

Steve

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Lev Goldfarb wrote on Sep. 7, 2009 @ 19:35 GMT
Dear Florin,

You see, historically, axiomatization *always* came *after* at least a crude version of the corresponding (formal) model was in place. This is simply because you have to have *something* that you want to axiomatize *before* you can actually axiomatize it.

To axiomatize a system of knowledge is to show that its claims can be derived from a small, well-understood set of sentences (the axioms). There are typically multiple ways to axiomatize a given mathematical domain.

Physics is not a ‘mathematical domain’, so you must be attaching an entirely new meaning to the term ‘axiomatization’. If, indeed, this is so, what kind of meaning do you attach to that term?

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Lev Goldfarb wrote on Sep. 7, 2009 @ 19:40 GMT
Sorry, the middle part is actually a quote:

To axiomatize a system of knowledge is to show that its claims can be derived from a small, well-understood set of sentences (the axioms). There are typically multiple ways to axiomatize a given mathematical domain.

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Author Florin Moldoveanu wrote on Sep. 7, 2009 @ 20:52 GMT
Lev,

Indeed one can axiomatize a given domain in many ways. Special relativity can be axiomatized in at least 3 ways, quantum mechanics in at least 10. What I am doing is to try to solve Hilbert’s sixth problem. And we do have this “something”: it is our physical reality.

You are right about the fact the physics is not a ‘mathematical domain’, and this is precisely the reason why physics axiomatization resisted many attempts at solving it, starting with Hilbert himself. As I am showing in my essay you do not do the axiomatization directly, but indirectly via finding the "requirements" of nature. It is absolutely remarkable that we have already solid mathematical proofs about the uniqueness of various parts of reality. What I am doing is taking a leap of faith and speculating that all of physics can be obtained in this way. This is not the old fashion mathematical axiomatization, but a generalization of the concept and you do get rigorous uniqueness results out of it. There are additional preliminary results showing that at least in the case of the Standard Model we should be very optimistic.

If in the end we manage to mathematically prove that our universe cannot be except the way it is: with 3 spatial dimensions, with time, with quantum mechanics, with the Standard model, etc, then we should be able to claim that whatever mechanism we use for this proof deserves to be called axiomatization of physics, although technically it is not the standard mathematical definition.

I highly suspect (but with no mathematical proof yet) that Gordon McCabe is right in his duality hypothesis between math and reality. If true, my heuristic rule should cut both ways and describes mathematics as well: math is the collection of domains that are locally consistent, isolated, and with finite algorithmic information theory content. If nature is relational at core, the platonic world of math and reality are nothing but the two aggregation states of those relational structures.




Leshan wrote on Sep. 8, 2009 @ 16:03 GMT
Dear readers,

I do not see the critique of essay. It is not a forum for cosmetics and women, it is a forum for physics! If you rate an essay, it means that you read and understand the essay. Therefore, please publish your opinion and critique of the essay. We do not write holy papers, all essays have errors.

Why all physicists are afraid of criticism? I'm sure it is the main cause of the crisis in science. Every year a lot of papers are published but a little critique appears only. The false theories will grab all the world without critique!

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Irvon E. Clear wrote on Sep. 8, 2009 @ 16:36 GMT
Florin,

It is difficult for me to understand how a chosen model of an evolving physical universe becomes both the truth recorder and the truth predictor of that physical universe. Is a theory of everything also an explanation of everything? Where is the axiom of creation? How did the things observed become the things observed?

I do applaud your approach. It certainly would bring us closer to a categorical understanding of our environment that could then be mathematically manipulated to predict statistical magnitudes of possibility for the occurance of an observed event that is actually not observed. Would all of humanity therefore find themselves more confident of surviving their own futures? Sorry, it's that missing link between recorder and predictor that keeps me confused.

Perhaps humanity will eventually satisfy itself with mathematical proofs for experiencing reality instead of actually sensing it. Certainly it would remove the risks of making decisions and then having to survive the consequences within a sensory reality that could include the serious injury or death of the decision maker. It think you could be leading us to a new dimension for human experience and responsibility so I also applaud your courage in taking us there.

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Author Florin Moldoveanu wrote on Sep. 8, 2009 @ 19:03 GMT
Irvone,

Please see the attachment on my post on Aug. 21, 2009 @ 01:27 GMT. This contains an extended version of the essay with additional sections which did not make it in the official entry because of the very strict character limit of the contest. Please read the second additional section on a possible mathematical approach to the problem of creation.

To me the core critical question is to what degree were God’s hands tied at the moment of creation? Did he have any freedom in making our universe any different the way it is today? Could we live in a universe without quantum mechanics, or time, or the Standard Model, or can we mathematically prove there was no other way possible?

A theory of everything is not likely will explain all. Physics will be more like medicine: we know the bones, the circulatory system, the muscles, etc, but we are still battling cancer. Once we know the general framework of nature and we can mathematically prove their necessity, there will always be secondary and tertiary phenomena to be explained. Let me give you an example. Light propagation in optical fibers obeys Maxwell’s equations which are known for a very long time. Still, from them in a certain approximation one deduce the nonlinear Schrodinger equation which exhibits solitonic solutions and the full understanding of this equation involves very complicated and different math than the original Maxwell’s equations.




Author Florin Moldoveanu wrote on Sep. 8, 2009 @ 19:17 GMT
Leshan,

I did not see a criticism of my essay in your post either. Do you have any comments or questions about it?

Let me poke holes in your entry as well. You cannot remove space time from a region because any tools you can use they can exist only in space time themselves. The only possibility is that your space-time vacuum appears by itself, but you cannot control or detect it. You may disagree on the detection part, but how can you tell apart a change in clock rate from the effects of a gravitational wave or simply from a local curvature of space time generated by mass? You can only tell it apart from normal curvature by violations of the equivalence principle.

Who knows, maybe near your perfect vacuum, left and right shoes do fall differently. (That was a joke, I could not help it.)




Leshan wrote on Sep. 8, 2009 @ 20:00 GMT
Florin,

'You cannot remove space time from a region because any tools you can use they can exist only in space time themselves'.

To create an absolute vacuum, we must remove all the matter very quickly (instantly) from the region. For this purpose I can use some nuclear processes where particles disappear instantly. For example at annihilation (decay) both particles disappear instantly due to a hole must appear. A hole is the absence of extension and duration, therefore external observer must detect time dilation and length contraction.

Thus, if the clocks near atomic station will tick slower than control clocks, it will be the experimental proof for my hole theory.

Another proof: near massive bodies also appear time dilation and length contraction. Thus, gravitation have the hole nature; massive bodies emit holes!

About 'left and right shoes do fall differently'. The purpose of forum is analysis and critique of essays, but I don’t found ever a critique. Women praise and rate a '10' its essay without reading and understanding it.Therefore I published my review.

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Author Florin Moldoveanu wrote on Sep. 8, 2009 @ 21:02 GMT
Leshan,

Nice try, but still will not work. When particles decay or collide with anti-particles, they simply get replaced by other particles and no “space-time hole” is generated.

Now do you have questions regarding my essay?




Lawrence B. Crowell wrote on Sep. 9, 2009 @ 02:10 GMT
Florin,

It could just as well be argued that physics and cosmology requires some insight into a new physical principle. This will remove an obstruction in our current understanding of thing --- think of throwing out excess baggage.

Cheers LC

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Author Florin Moldoveanu wrote on Sep. 9, 2009 @ 02:17 GMT
Lawrence,

I agree, but is your post a reply to my 2 questions on your essay blog I just wrote a minute ago, or is this a new thread?




Leshan wrote on Sep. 9, 2009 @ 07:16 GMT
'Nice try, but still will not work. When particles decay or collide with anti-particles, they simply get replaced by other particles and no 'space-time hole' is generated'

If the free neutron decay, it disappears instantly. Then you see the products of its decay - proton, electron and antineutrino, but you know nothing about these processes. Since we remove the matter (neutron) instantly from the volume, a hole in space time can appear for a very short time 10^-24 s. We can test this idea experimentally; if the clocls placed near the neutron storage tick slower, it will be the experimental proof for the hole theory.

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Author Florin Moldoveanu wrote on Sep. 9, 2009 @ 14:01 GMT
Leshan,

When a free neutron decays it decays into an electron and a “W-“ who later decays into an electron and an anti-neutrino. The proton is basically replacing the neutron.

An easy way to see that no hole is made is in the context of string theory. A string propagates in such a way that it minimizes the area it sweeps in space time. A Feynman decay diagram is replaced by a string “pants” diagram and spacetime (and the string world sheet) is everywhere continuous including at the cusp.

Another counter example is the electron expulsion from an ionized atom. No space time hole there either. The only net effect is the atom becoming positively charged.




Leshan wrote on Sep. 9, 2009 @ 16:47 GMT
Florin

When a free neutron decays it decays into an electron and a 'W-' who later decays into an electron and an antineutrino. The proton is basically replacing the neutron.

It does not contradict the existence of holes. First appears the hole for the short time, then 'W who later decays into an electron and an anti-neutrino. We must introduce the holes in the Feynman's diagrams. Do you can see how neutron decays? You have the speculative theoretical models only.

Another counter example is the electron expulsion from an ionized atom.

It is not a good example for creation of holes. I need nuclear physics and massive particles.

The string theory prove nothing, it is a very speculative theory. In the same way you can affirm that holes cannot exist because a holy bible forbids holes.

Now I look for 2 atomic clocks and soon I'll have the experimental proofs that holes exist. How can you explain the appearance of time dilation and length contraction effects at decays of neutrons? I'll show also another signs of holes - the destruction of chamber. Thus I can show all experimental signs for holes. The theory predicts and experiment confirms. It is the exact proof for vacuum holes. You cannot go against experimental proofs! Please remember that Experiment governs physics, not dogmas.

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Author Florin Moldoveanu wrote on Sep. 9, 2009 @ 17:55 GMT
Leshan,

It is obvious you do not understand quantum field theory. The neutron decay model is not at all speculative. In electroweak perturbation theory, you can compute very precisely anything you want and experiments agree with calculations to the limit of experimental precision.

However, you are making a more serious (conceptual) mistake. Space-time is not like matter which can be removed. In the current accepted body of knowledge in physics, space and time cannot be removed. Usually the readers of your essay stop reading after seeing this statement.




Leshan wrote on Sep. 9, 2009 @ 19:42 GMT
Florin

If you can compute very precisely anything you want it is not the proof that the theory is true. All the Standard Model is a mathematical model mainly, that can compute all but cannot explain a lot of things like mass, inertia ets. And all Standard Model can fall in the next years because the Higgs cannot be found. There are also other flaws in the Standard model.

The appearance of holes do not contradict the neutron decay model. Please understand that the physical effect with holes is disguised under known model of decay. I do not have intention to change the oficially known model of neutron decay, I must find there signs for holes only.

'In the current accepted body of knowledge in physics, space and time cannot be removed.'

I used words 'remove space-time' in order to explain how to shield gravity only. At quantum level there is another picture. Pay atention to my words: if neutron disappears, it means that we remove this neutron only, but not spacetime. You see, really I remove the matter only to create a hole. But since this operation create holes, I spoke that I can remove spacetime. Now you understand? The both explanations are true. But really I remove matter, not spacetime.

That is it, my theory is a NEW theory that is outside of current accepted body of knowledje. In general, you are now at the FQXi essay contest that looks for a new knowledje at the limits of physics, therefore I don't understand your example with current knowledje. The destination of this forum is just to change the current knowledje.

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Author Florin Moldoveanu wrote on Sep. 9, 2009 @ 23:13 GMT
Leshan,

You say: “If you can compute very precisely anything you want it is not the proof that the theory is true.”

Wrong. QCD agrees 100% with observations. This is precisely the power of physics and this is what distinguishes it from philosophy or astrology. It is falsifiable and has tremendous predictive power. When all is explained, a new theory can only be wrong.

“And all Standard Model can fall in the next years because the Higgs cannot be found.”

Wrong again. There are extensions of SM without Higgs. They are fully compatible with the current experimental results.

“I used words 'remove space-time' in order to explain how to shield gravity only.”

Gravity cannot be shielded due to the equivalence principle. The neutron has energy in its rest mass. When it decays, energy is conserved and the space-time curvature remains locally the same. A “space-time hole” can only be possible if the energy is not conserved and this is not what we observe.

“But really I remove matter, not spacetime.”

That is not what I understood from your essay. But suppose you are right. Vacuum is not the naïve pre-Dirac era notion of a complete void. The vacuum is filled with energy and virtual particles. This is responsible for the spontaneous symmetry breaking for example.

“That is it, my theory is a NEW theory that is outside of current accepted body of knowledje. In general, you are now at the FQXi essay contest that looks for a new knowledje at the limits of physics, therefore I don't understand your example with current knowledje. The destination of this forum is just to change the current knowledje.”

I agree, we should enhance the existing knowledge, but this means we should be compatible with what we already know to be true so far, otherwise, it is only a self-delusional fantasy.




Leshan wrote on Sep. 10, 2009 @ 04:42 GMT
'I agree, we should enhance the existing knowledge, but this means we should be compatible with what we already know to be true so far, otherwise, it is only a self-delusional fantasy.'

How the new theory of strong interaction can be compatible with old theory of strong interaction? They cannot be compatible in general because they remove one another. You cannot have two theories of strong interaction to be compatible at the same time, it is a logical error. In the same way, my new theory of spacetime cannot be compatible with old concept of spacetime. Einstein's theory for example also removed the old concept of spacetime. It is the main your error in this discution that you try to reconcile the existing knowledje with new knowledje.

My new theory must be compatible with EXPERIMENTAL DATA only but not with QCD or old vision of spacetime! The Experimental data, but not your theory is the main knowledje.

QCD agrees 100% with observations - because theorists hides all errors. We never observed quarcks and gluons. To hide this error, they invented konfinement. QCD is not a logical theory in general because confinement do not follow logically from theory. It is a mathematical model only. I'm sure that this theory can fall during next 10 - 20 years. In general QCD is a darned and full of logical holes theory.

QCD has a major problem - it is not possible to unify QCD with gravitation and other interactions. It is the main cause why QCD must fall.

My holes can unify 3 interactions. If holes appear between nucleons, they 'glue' nucleons as a Descartes vessel. Holes can explain also gravitation and weak interaction.

Another example for you that spacetime can be really removed. Imagine that spacetime consists of virtual atoms of spacetime that appears and disappears (Smolin and other scientists are agree that space is also made of discrete pieces). If the atom of spacetime disappear, then appear a vacant place - a hole that do not have the properties of space-time. You see, quantum spacetime allow for space to be removed. My theory use just the quantum spacetime.

'Gravity cannot be shielded due to the equivalence principle' Gravity can be shielded FOR A CLOSED region of spacetime. For an isolated volume we can shield gravity and it cannot violate EP.

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Author Florin Moldoveanu wrote on Sep. 10, 2009 @ 05:24 GMT
Leshan,

First a typo correction: I meant QED, not QCD. In general in QCD we cannot use perturbation theory for low energy, and we use numerical simulations which are only accurate to about 90%.

Second, a disclaimer: I hope you are not offended by my criticism. Please feel free to poke holes in my essay as well.

“We never observed quarcks and gluons.” Not true. Quarks were...

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Leshan wrote on Sep. 10, 2009 @ 12:40 GMT
Florin,

Let us discus holes on my page and your essay on this page. Please feel free to enter on my page to discus this item.

http://www.fqxi.org/community/forum/topic/481

It is the last post about holes in this page because your page is overloaded by text (127 posts).

'I meant QED, not QCD' I have nothing against QED, it is a good theory. But QCD is my opponent and enemy.

'I hope you are not offended by my criticism' I don't see any criticizm, you don't found any holes in my theory.

'Please feel free to poke holes in my essay as well' Thank you, if I find some holes, I'll place they here.

'For an isolated volume we can shield gravity and it cannot violate EP' Shielding gravity is equivalent with a violation of EP: the inertial mass stays the same, but the gravitational mass is decreased because of the shielding. Hence the two masses are no longer the same for the duration of the shielding and therefore the EP is violated'

There your opinion is VERY erroneous. Imagine a closed volume with a body inside. Then we envelope a body with absolute isolation. How you compare now the inertial and gravitational mass? You do not have access to this volume because it is an AVSOLUTE isolation, that shield all the fields including gravitation. It is equivalent to sending a body in another universe.

Since you cannot compare the inertial and gravitational mass, you cannot speak about violation of EP.

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Jayakar Johnson Joseph wrote on Sep. 10, 2009 @ 15:49 GMT
Dear Florin Moldoveanu,

You have provided essential guidelines to work on new physics and renormalization. Though the axiomatization in quantum mechanics, U(1), SU(2) and SU(3) are the background for supersymmetric quantum mechanics; the axiomatization in cosmology, the cosmological constant is inconsistent and thereby the axiomatization in quantum gravity may be divergent for the construction of physical axiomatization in entirety.

As the relativity of the critical mass with its environmental parameters are in natural realities, we may proceed with multiple axiomatization of physical realities that are universally valid and the outcome may be an abstract universe mathematically.

Thereby my perception on your article is that the axiomatization of multiple axiomatization in natural realities is your conclusion to proceed with TOE, as the physics and mathematics are inseparable.

With Best wishes,

Jayakar

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Author Florin Moldoveanu wrote on Sep. 10, 2009 @ 20:08 GMT
Dear Jayakar,

Thank you for your good words. Indeed, the “axiomatization of multiple axiomatization in natural realities” is one way to express the idea, and math an reality are truly inseparables.

I have some ideas about the cosmological issues, but for quantum gravity I really do not have any good intuition at this point. Based on what I do know, I think Connes’ approach is better than both string and loop quantum gravity, but I need to read more before I will pass judgment and this is why I put a disclaimer in the paper saying that this is only my biased opinion.

Best wishes to you too.




Florin wrote on Sep. 13, 2009 @ 14:54 GMT
If you have time, feel free to enter on my page to continue discussion. I had a short conflict with Corda. He doesn't found any error in my theory, only notes like 'no mathematical proofs'. What is your opinion about violation of EP?

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Leshan wrote on Sep. 13, 2009 @ 14:57 GMT
Sorry, I make errors in hurry. The previous post is my post.

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Author Florin Moldoveanu wrote on Sep. 13, 2009 @ 16:12 GMT
Leshan,

You are "curing" the EP violation with something even worse, a violation of the speed of light. The teleportation argument looks like a rabbit out of a hat trick, and 1. it is not convincing (I did not see any concrete mechanism for how it would happen in your essay) and 2. it will violate a basic rule of relativity of not being able to transmit information faster than the speed of light. If your teleportation would happen slower than the speed of light, then you cannot outrun the gravitational waves resulting in n EP violation yet again.

PS: the Soros foundation has nothing to do with scientific credentials. I should know since it was them who funded my plane ticket to US to come and study physics here.




Anonymous wrote on Sep. 18, 2009 @ 23:49 GMT
Dear Lwrence B. Crowell-

You wrote: "I wrote a paper last spring concering the zitterbewegung, and communicated with Hestenes about this. I have not submitted it for publication yet. If you are interested in it I can transmit it. Zitterbewegung may be telling us something about the end of renormalization group flows and the onset of mass at low energy. The leptons and quarks all have masses ~ .5 to 100 MeV, and sitterbewgung suggests this mass is associated with a confining potential at the Compton wave length of a particle."

In my essay, "Ultimate Possibilities of Physics", which covers Quantum Field Mechanics (QFM), the origin of the origin of the zitterbewegung is explained a bit. According to QFM, a confining potential is indeed the reason for the zitterbewegung. Kirilyuk, the originator of QFM demonstrates in his papers [2] (see also the tutorials on my website [3]) that a pulsating potential well causes this trapping, which results in a pulsating random wandering state function (the references can be found in the back of my essay).

Regards,

Ben Baten

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Author Florin Moldoveanu wrote on Sep. 19, 2009 @ 02:24 GMT
Dear Bean Batten,

I have read Lawrence’s paper and it is extremely interesting how he puts everything together. However, the renormalization group arguments have to be made more rigorous because of the huge orders of magnitude he has to explain in generating the mass. I also mentioned indirectly the zitter effect in my essay when I cite Hestenes’ results in the context of U(1)XSU(2). The most important thing about zitter it is that it was recently confirmed experimentally and Hestenes won a prize about this in the first FQXi essay contest. I doubt that Lawrence will read your post here, and I would advise you to write him a message in his essay entry: “Can we see inside a black hole.”.

PS: Good luck with your essay in this contest.




Anonymous wrote on Sep. 19, 2009 @ 16:52 GMT
Dear Florin,

I would like to start with saying that my background is in engineering and not in physics or mathematics. I am only more or less familiar with many of the modern theories in math or physics.

I enjoyed reading your essay. I think you captured the essence when you say: "physics is an experimental science" and "mathematics deals with abstract relationships."

In my opinion, there is a long journey for science in front of us. To create a TOE we still need to discover new laws of physics, and for sure those may come with new mathematics. When comes to existing theories which we hope to lead to a TOE, I am a believer that the Standard Model is more of a mathematical success than a physical one. There are many basic questions it fails to answer even if in my opinion it should. Same with string theory. Instead of finding out a mathematics which "fits" our world, we need to discover first if the model of the world we have it is complete to begin with. Have we discover all the simple truths? Only after that task is done we can start thinking towards an axiomatizing of physics.

Best regards and good luck with your essay.

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Author Florin Moldoveanu wrote on Sep. 20, 2009 @ 01:16 GMT
I have mixed feelings about the TOE. It is poorly defined, and it is more like a marketing ploy, a nice buzzword, but it will surely be very nice if it is possible. If it is indeed possible, the road there will take us outside the classical Galilean era of doing physics and here I agree with Smolin that we should not put all eggs in a single basket (be it string theory, loop quantum gravity, etc)




Lawrence B. Crowell wrote on Sep. 21, 2009 @ 02:54 GMT
To anonymous: Zitterbewegung reflects something about how renormalization group flow ends. It cuts off the scale at which nature is largely invariant with respect to scale. This is of course absolute necessary for there to really exist a physica world. A completely scale invariant world would be one where quantum fluctuations on all scale can obtain completely. In other words the degree of order in the system is determined by quantum fluctuations, which is what happens with quantum critical points. At that point exactly the quasi-particle mass diverges to infinity, which is unphysical. The small breaking of this scaling is wrapped up in the existence of Higgs fields and the zitter.

Cheers LC

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Lawrence B Crowell wrote on Sep. 22, 2009 @ 03:26 GMT
With respect to the zitterbewegung I worked a numerical analysis of it. The attached file is a one dimensional representation of zitter motion.

Cheers LC

attachments: 1_zitterzag.gif

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Author Florin Moldoveanu wrote on Sep. 22, 2009 @ 14:31 GMT
Lawerence,

So I assume that one of the colors is the real part and the other is the imaginary of the function, right? From the gif, it looks like you used too few grid points because of the sharp angle changes. I also see some “chirp” artifacts in you simulation: the function has more oscillations on the left side in the beginning and they gradually move to the right side. To alleviate the simulation spurious effects you may use split step fast Fourier transforms, or the Crank-Nicolson method to solve the second derivative problems at the boundary of your domain.




Lawrence B Crowell wrote on Sep. 23, 2009 @ 01:01 GMT
Yes the two colors reflect the real and imaginary parts. The chirping I think is a real part of the dynamics. The wave is caught in a bottle and bounced off the "walls" of the bottle. The wave function is squashed in a sense as it impinges on one of the sides. Again this is a two dimensional realization of the problem. A three dimensional realization will not have quite this feature. There are some computer simulations of waves interacting with square barriers which were done in the 1960s. They are of remarkable quality in fact. But when the wave, initially a gaussian enveloped wave, reaches the boundary it tends to do this chirping.

Cheers LC

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Lawrence B Crowell wrote on Sep. 23, 2009 @ 01:02 GMT
PS, on my site I mentioned today in a rather long post zitterbewgung in refrence to scaling principles. LC

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Author Florin Moldoveanu wrote on Sep. 23, 2009 @ 02:23 GMT
I'll read your post. Bouncing left-right is understandable, but the frequency squeezing left-right looks like a boundary issue (I did a lot of numerical simulations for my thesis). You may cure this with a periodic boundary condition where the pulse exiting right re-enters from left. It is not realistic, but it can clarify if the chirping is a genuine effect, or a boundary artifact.




Helmut Hansen wrote on Sep. 23, 2009 @ 05:18 GMT
Dear Mr. Moldoveanu,

I am dealing with the development of a modern, that is, scientific metaphysics. This dealing is based on the conviction that a modern metaphysics provides significant insights into a TOE because it is based on a foundation that is by its nature absolutely fundamental. In ancient times this foundation was called the ONE.

But this foundation could never be found....

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Lawrence B. Crowell wrote on Sep. 23, 2009 @ 17:23 GMT
I attack a numerical computation of a Gaussian wave function tunnelling through a barrier. On the left hand side near the barrier there is the occurrence of interference waves between ingoing and outgoing Fourier modes of the wave. This is not the image I was thinking of. There was a numerical study of a wave on a barrier done back in the 1960s, which is quite exquisite given the technology of the time. It exhibited the same peaking up or chirping due to interferences between incident and reflected waves.

A periodic boundary condition would seem to be to be a completely different problem. I might use some digital filtering techniques to try to eliminate some numerical overshoots or spurious results. I agree that some of what I compute could be artificial.

Cheers LC

attachments: EffetTunnel.gif

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Author Florin Moldoveanu wrote on Sep. 24, 2009 @ 04:15 GMT
Dear Mr. Hansen,

I have read your essay, but I have to admit I still have problems understanding it. What is transcendence exactly? Here I am more in agreement with the Vienna circle (although care must be exercised not to adopt a naïve local realism and materialistic point of view which can be at odds with quantum mechanics).




Author Florin Moldoveanu wrote on Sep. 24, 2009 @ 04:32 GMT
Lawrence,

This simulation looks beautiful. I am not sure the meaning of chirp is universal. In optical fibers it has a well defined meaning, but outside this domain, it may be replaced with skewness. The boundary problem is stemming from the discretization of the second derivative. Crank–Nicolson works reasonably well in this case. Another method which works faster than this is the split-step FFT: divide the evolution operator into the linear and nonlinear parts. Solve the linear part analitically using Fourier transforms. One step in time is done by ¼ FFT on the linear part, ½ on the nonlinear evolution by itsef, and the last ¼ by the linear part again. Using Baker-Hausdorff one can prove that the error is of third order compared with the standard methods which achieve only a second order. Because of this one can use a much smaller grid resulting in dramatic gains in computational speed.




Narendra Nath wrote on Sep. 24, 2009 @ 14:27 GMT
Huge number of postings do make me worried about the relevance aspect I note that there is mention that Nature is complex. To me it seems that the Nature is simple but our minds run in a complex way, different for each individual. If the problem at hand does not get simplified by an approach, to me it seems that our approach needs improvement. i hardly know anything about the topic under discussion and hence i leave my comments here for experts to consider.

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Author Florin Moldoveanu wrote on Sep. 24, 2009 @ 22:22 GMT
Dear Narendra,

I am not sure what are you referring to when you comment on the number of posts. My essay was posted in the very first batch of essays and because of the time exposure, a lot of people got to comment on it.




Don Limuti wrote on Sep. 25, 2009 @ 01:28 GMT
Florin,

Thank you for your essay. It is a bold proposal at the foundation of physics.

I always thought mathematics contained all of physics (reality) as a subset.

Now I am thinking that is not "true".



Don L

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Author Florin Moldoveanu wrote on Sep. 25, 2009 @ 02:25 GMT
Don,

Thank you for your kind words. I admit: the idea is bold, but my contribution besides finding a piece of the puzzle is only to show how to put together the results of so many profound thinkers of our time: Emile Grgin, David Hestenes, Gordon McCabe, Jochen Rau, Alain Connes, Max Tegmark.

Now the hard and exciting work is ahead of us in proving additional results.




Lawrence B. Crowell wrote on Sep. 27, 2009 @ 00:31 GMT
Florin,

I will take your suggestion under advisement on the numerics. The purpose was not to get the most ideal solution, but to giev a rough idea of things. To be honest what I want to do is to work out a 3-dimensional version, but I just have not gotten to that as yet.

Cheers LC

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Georgina Parry wrote on Sep. 27, 2009 @ 03:06 GMT
Florin,

I said I would comment again when I had had time to complete reading your article. I have read it several times to try to grasp it and be sure that I have not misunderstood.I have also read your diligent answers to many previous posters which has been very helpful.

I think it is well written and I admire what you have set out to do. I would very much like it if we could...

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Author Florin Moldoveanu wrote on Sep. 27, 2009 @ 07:23 GMT
Georgina,

I am glad you read my essay and thank you for your kind words. You ask very relevant questions and I am glad to answer them.

> Is there a danger that the very things filtered out by this approach may be the important elements that might lead somewhere significant?

Yes, and yes. But it does not appear the exclude anything that is conceptually fundamental. Let me...

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Steve Dufourny wrote on Sep. 27, 2009 @ 17:03 GMT
Hi Florin ,all ,

Incredible thread ,many interesting discussions ,a pleasure for me to read them.

Good Luck Florin....well begun all that for the first prize perhaps

Sincerely

Steve

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Author Florin Moldoveanu wrote on Sep. 27, 2009 @ 17:27 GMT
Hi Steve

Thank you for your good words. Solving Hilbert sixth problem is really very, very, very hard, and if others will appreciate my way of attacking the problem and will join me in this quest, than maybe it will be solved in our lifetime. What I wanted to do was to put together the new paradigm and challenge the perception that all good ideas only exist in string theory.




Georgina Parry wrote on Sep. 27, 2009 @ 21:41 GMT
Florin,

thank you very much for explaining.

Only the UTP still puzzles me. You have explained that it is the Mathematic idealisation of perfect observers.I tried to express that even when many observers agree their observation is not necessarily truth. It is merely an interpretation of reality, which may be incorrect. As there is no perfect observer that can see all viewpoints simultaneously, excluding a hypothetical omnipresent being, should this be considered as something like the mean average of all possible observers?. What is it mathematically? Or is it just a term assigned to any event because it is assumed that it possesses it, despite conflicting observations?

I can accept that fundamentally there is a Universal truth property but only such an omnipresent being could state what that absolute truth is. So it would seem to me that truth, in the subject interpretation of reality that we inhabit, is also contextual. Therefore how can UTP be practically applied? Am I thinking about this in entirely the wrong way?

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Lawrence B Crowell wrote on Sep. 27, 2009 @ 23:10 GMT
I read Grgin's paper with considerable interest. I am always looking for connections between what I am thinking with others, or between what others are thinking. I posted this on his site. I have been reading your paper

arXiv:0901.0332v2 [quant-ph] 16 Jan 2009

and a couple of bits from it I used at the end of this, with liberties taken as this is not really plagerism since this is a...

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Author Florin Moldoveanu wrote on Sep. 28, 2009 @ 01:27 GMT
Lawrence,

I have tried to make the quantionic case as clear as I could in my paper, and if there is something unclear I can gladly explain it. The basic idea was of the 2 products and how the structure is self-preserving when 2 systems interact. The original insight was however the 1 to 1 mapping between observables and generators (energy vs. Hamiltonian for example), but by tinkering with this Grgin and Petersen arrived at the 2 product and composability idea. This has nothing to do directly with quantions, and quantions were discovered much later as arriving from a different kind of complexification procedure to construct the state space from the algebra of observables. In this complexification procedure, one of the elements of the algebra plays the role of sqrt(-1). This so called internal complexification was only possible in non-unitary representations of the quantal algebra, and simple closure arguments in the 2 products restricted the dimensionality to either 3 or 6. The 3 case led back to standard QM and it was actually used by Joy Christian in his papers. The 6 case can be only SO(2,4). Once the sqrt(-1) element is chosen in the SO(2,4) space, the centrelizer leads to quantions. The norm of the quantions can be understood as a probability current density and if its divergence is zero, it leads directly to Dirac and Schrodinger equation. (I think there is another solution leading to Klein Gordon, but I need to complete the computation). The divergent case is properly understood only in the non-commutative geometry framework and it is much more complicated.

In passing, quaternions do not have the composability property and in quanternionic QM there is no 1-to-1 correspondence between observables and generators because the derivative operator is not uniquely definable.




Lawrence B. Crowell wrote on Sep. 28, 2009 @ 13:11 GMT
The initial set up by Grgin and Peterson is an interesting map between the octonions and thse objects which structurally lie in between complex numbers and quaternions. What you display of quantion algebra in eqns 14-17 what I referred to seems to more or less apply with product rules.

I have frankly only read half way through your paper at this point. My main question here is whether this structure provides a way of illustrating how octonionic fields are some underlying topological aspect of quantum field theory. It is interesting to me that this leads to SO(2,4) as the centralizer, which is the AdS_5 group, with connections to conformal field theory. I also question whether this complexification can be illustrated as a way of finding a renormalization group flow similar to the Zamalodchikov c*-theorem.

If I am asking the wrong question or have some misconception of things you might disabuse me of such. Quantions are one of the number of structures I have in the last couple of months had on my stack of things to address, which Grgin’s paper posted last week piqued my interest.

Cheers LC

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Author Florin Moldoveanu wrote on Sep. 28, 2009 @ 19:22 GMT
Quantions have very little to do with octonions. Only real, complex numbers and quantions have the composability property. This may be related to the Cayley-Dickson construction for complex numbers, and of a similar construction for quantions.

SO(2.4) in quantions does not seem to be (yet) related with the renormalization group, but they are related with the conformal compactification

of the Minkowski space.




Robert L. Oldershaw wrote on Sep. 28, 2009 @ 22:41 GMT
Hi Florian,

I have finally discovered your paper and downloaded a hard copy.

The issues you discuss look very interesting at first reading and I look forward to studying your approach more carefully in the next two days.

Hopefully I will have some substantive comments to offer in the near future.

RLO

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Lawrence B. Crowell wrote on Sep. 29, 2009 @ 01:50 GMT
I read your article: arXiv:0901.0332v2 [quant-ph] 16 Jan 2009 on quantions again. This is very much related to twistor theory in a way. The distinction between the A(z) and M(z) appears to be similar to a type of geometric quantization. The set of PT^{+/-} and PN is capture in the definition of the inverse, where the lack of division algebra for determinant = M(q) = 0 along null directions...

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Author Florin Moldoveanu wrote on Sep. 29, 2009 @ 02:52 GMT
Hi Robert,

Looking forward to your comments.

PS: Thank you for 't Hooft's paper.




Author Florin Moldoveanu wrote on Sep. 29, 2009 @ 02:56 GMT
Lawrence,

I am currently trying to understand the link between quations and geometric quantization and I even have a conjecture I hope to prove in this area.

Because A(z) and M(z) are different, quantions can also be cast as a Hopf algebra and this promises again additional insights.




Lawrence B Crowell wrote on Sep. 29, 2009 @ 12:36 GMT
Connections with Hopf algebras would be interesting. This would bring things in contact with K-theory.

Cheers LC

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Narendra nath wrote on Sep. 30, 2009 @ 13:01 GMT
My comments were not precise enough to elicit your response. Briefly, i seek your priorities among the three tools broadly needed to work out a problem in Physics: 1. Conceptual aspect leading to some precepts;2. Mathematical formulation: 3. Experimental data and its critical analysis. How you prefer to proceed helps you to come with a final product. Speciality approach is self-confining and may mislead you to ignore factors that may be significant for your overall consideration.

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Author Florin Moldoveanu wrote on Sep. 30, 2009 @ 14:33 GMT
Dear Narendra,

I did answer you on Sep. 24, 2009 @ 22:22 GM, but maybe I misunderstood your question.

Let me try to explain how my approach scores against your 3 tools.

1. Conceptual aspect: The working conceptual assumption in my approach is that nature is relational at core and nature is just mathematics reorganized in a different way. All mathematical structures are...

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Steve Dufourny wrote on Oct. 1, 2009 @ 13:30 GMT
Hi Florin ,

You are welcome ,it's sincerely.

I didin't know these Hilbert Problems ,the Riemann Hypothesis is interesting ,I always though what the zero don't exist .

It's a human invention I think .

About the fith H.Problem ,it's very interesting this axiomatization ,the physicality is essential I think dear Florin.The real numbers and sequences must be inserted for a real mathematical extrapolations .

Like the Riemann hypothesis ,with infinity and imaginaies more zeros ,it's not possible ,we need limits ,the sphere and its laws will help without any doubt .

Just to help you a little .

A triviality and an axiom are evidents when the physicality is encircle with its specifics numbers ,the naturals and prime numbers thus appears differently in a closed system and its oscillations ,periodocities ,rationalities .....

Best Regards

Steve

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Robert L. Oldershaw wrote on Oct. 1, 2009 @ 16:06 GMT
Greetings Florian,

When you are able to use your abstract axiomatization method to say something definite about the actual objects and processes of nature, please let me know of the results.

RLO

www.amherst.edu/~rloldershaw

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Author Florin Moldoveanu wrote on Oct. 2, 2009 @ 04:16 GMT
Hello Steve,

Thank you for your good wishes,

Best Regards,

Florin




Author Florin Moldoveanu wrote on Oct. 2, 2009 @ 04:27 GMT
Robert,

I do have many things in progress. I am about done with my paper on axiomatizing QM, and with another one regarding global hyperbolicity. Then I am working on 3 other topics stemming from my approach. I hope to derive the Klein-Gordon equation from quantions, to investigate maximum entangle systems and their link with geometric quantization and composability, and to explore the link between relativistic QM with Hopf algebras.

If you are interested, you can check on my progress by searching for my papers on the archive from time to time.




Emile Grgin wrote on Oct. 3, 2009 @ 03:47 GMT
Dear Florin,

In re-reading the posts above, I noticed the following statement of yours in your discussions with Lawrence (Sept 28, 01:27 GMT):

"I think there is another solution leading to Klein Gordon, but I need to complete the computation"

Let me bring you up to date: You are right!

This is not evident in my book of 2007, where Dirac's equation is derived only in the second pass (the first pass being the 2005 book). If you remember, I point out on page 5 of my essay that the last stage in the development of a theory is "finalization", which is not merely a matter of cosmetics. This is part of what I've been doing recently to quantions. In the new formalism, which seems final (third pass), the quantionic derivation of both Klein-Gordon's and Dirac's equation takes only two lines of algebra. Structural unification is also much clearer (even trivial). Seneral other things become essentially trivial as well.

Regards, Emile.

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Author Florin Moldoveanu wrote on Oct. 3, 2009 @ 04:01 GMT
Dear Dr. Grgin,

Congratulations!!! Can you share your proof with me? This is bitter sweet; you beat me to the punch line. Let me ask you a question. Is this related to SU(2,2) (and the second linking vector) as I suspect it is?

Regards,

Florin




Narendra Nath wrote on Oct. 3, 2009 @ 04:47 GMT
Dear florin,

i thank you for the exhaustive response you have given to my three queries. I am partially convinced that you do have an approach to Physics through the tool of mathematics and do reject Maths that is not relevant to the physical conditions. It is fine that you choose your variable and boundary conditions properly. But ca one ever bs sure that nothing has been lefy out.You are right when you that time will tell if your approach is right when the predictions get verified. That is true for all the scientists worth the name. I certainly wish you all success.

My primary hesitency howver remains, Maths can not be the starting point in Physics. One must first work out a conceptual network based on existing proven knowledge, including data and theories. Ony then one should examine the relevance of appropriate maths to the problem at hand. We explain in Physics what Nature has already provided us to view, feel and experience. The human mind is at the centre of our knowledge. With any change in the way the mind is set up, we may arrive at a innovative aspect, not considered in the past. i hold such an approach the best for Physics. Lately, Physics has had hardly any breakthroughs, as partlyb reflected by the award of Nobel prizes for past works, life time studies, etc. AS serious questions/mysteries still remain to be tackled, specially in Cosmology, nanotechnology and other sub-disciplines, the freshness of approach to me is mor eimportant and it should not start with pure mathematics.

i have not checked my post and may be some errors/mistakes are left untackled.

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Emile Grgin wrote on Oct. 3, 2009 @ 09:17 GMT
Dear Florin,

Absolutely not! I mean it's not related to SU(2,2). And I don't see how it could be. Therefore, if you discover a connection I will be both amazed and pleased. Pleased because it would open up unexpected relationships between objects I think are unrelated.

SU(2,2) is the twistor branch on the SO(2,4) trunk. I informally call it the geometric branch. Since the Lie algebras so(2,4) and su(2,2) are isomorphic, twistors are related to the conformal group, which does not preserve the Minkowski metric.

Quantions are the algebraic branch. They are derived from so(2,4) by way of internal complexification. Their metric norm is Minkowskian.

You see now why I don't believe quantions and twistors will ever meet again, even though they are siblings -- their mother being so(2,4). Have a peek at Figure 26.1 on page 550 of my 2005 book.

As for the proof, it is not based on some "clever" new idea that could be easily conveyed. The idea of the proof is exactly the same as in the book. The difference is that I longer work with matrices. The formalism is different. Many things just 'fall into place' once that formalism is developed -- which I am doing these days, making sure that there is no mistake. As an analogy, consider 19th century differential geometry, where we (humans) had to do all the work, and compare it with tensor analysis, where the formalism does 99% of the work for us.

The secret to being good at mathematics is not smarts (there is plenty of that around) but laziness. The lazier you are, the harder you'll work at developing the tools that will do the work for you. The funny thing is that those tools end up BEING the next mathematics.

Incidentally, as part of the finalization effort, I think I also found a much simpler way of re-doing Part I of the four-part paper in Fizika, where composability is put to work. After I've gone through the details, making sure that I am not deluding myself, I'll be happy to send you the first draft.

Regards, Emile

PS: Why not drop the stuffy "Dr. Grgin"? On this forum we are all on first name basis, which is much nicer.

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Steve Dufourny wrote on Oct. 3, 2009 @ 12:59 GMT
Dear Florin ,

Do you think it exists a maximum prime number ?

Personally yes .Possible it's the number of spheres perhaps.

This oscillation ,periodic is fascinating ,let's imagine a distribution in a spherical logic in a physicality with thermodynamics laws .

The periodicity of twins primes numbers is relevant about the oscillation .

Inside a sphere ,if we begin...

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Emile rgin wrote on Oct. 3, 2009 @ 14:12 GMT
Correction to my post of 09:17 GMT.

As written in the fifth Paragraph:

" The difference is that I longer work with matrices."

As you probably figured out it should be:

"The difference is that I no longer work with matrices."

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Cristinel Stoica wrote on Oct. 3, 2009 @ 14:55 GMT
Dear Dr. Moldoveanu,

I read your essay with attention and pleasure. I have some comments and questions.

Your universal truth property principle, which you say "is clearly distinguishing between the real world, and the Platonic world of mathematics", if I understand well, states that the physical truth is independent of context, unlike the mathematical truth, which depends on the set of axioms. If the Universe can be described by a mathematical structure (which you are trying to axiomatize), then, within that structure, the truths are universal. But this also holds for all mathematical structures: within their model, their axioms are universally true. In an Euclidean space, to take your example, the parallels postulate is true, without regard that it is not true in noneuclidean geometry. I don't understand how this principle may differentiate between the physical reality and the Platonic world. All mathematical structures seem to respect it, although, you are right, putting all together will break this principle. But nobody is putting them together. I also don't see why this principle by itself restricts the allowable structures to the global hyperbolic ones, giving thus rise to time. I look forward to see your article in preparation in which you detail this idea. Please understand that I am trying to understand your essay. Certainly these heuristic rules have much more meaning for you, than for me, who I am just reading something you had to concentrate in a short paper, so I have to ask.

Congratulations for your essay, and success with this contest,

Cristi Stoica

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Author Florin Moldoveanu wrote on Oct. 3, 2009 @ 15:49 GMT
Dear Steve,

There is no maximum prime number. Here is the proof.

Order all prim numbers from smallest to largest: P1, P2,…,Pn and let Pn be the largest prime number. Construct the number A = P1*P2*…*Pn + 1. A is bigger than Pn by construction and it should not be a prime number because we assume Pn is the largest prime. Therefore there is a prime number Pr such that A is divisible by Pr. But A - P1*P2*…Pn is also divisible by Pr because A is divisible by Pr and Pr is is one of the numbers in the product P1*P2*…*Pn But A - P1*P2*…Pn = 1 and this means that 1 is divisible by Pr which is false. Therefore out original assumption of a maximum Pn is false and there is no maximum prime number.




Author Florin Moldoveanu wrote on Oct. 3, 2009 @ 18:04 GMT
Dear Cristi,

I also read your entry with interest and pleasure and good luck to you too.

I need to clarify on one misunderstanding about my approach. You say: “If the Universe can be described by a mathematical structure (which you are trying to axiomatize)”. This is not what I am trying to do. This is Tegmark’s approach and I do not think it has a good change of success for...

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Robert L. Oldershaw wrote on Oct. 4, 2009 @ 03:02 GMT
Hi Florian,

What I am looking for is someone who can offer real understanding of:

1. Benford's Law (why is nature dominated by power law distributions)

2. Why are there two basic types of galaxies (disk/spheriodal [Ferm./Bos.?])

3. Why are galaxy radii so limited in range

4. What is the Dark Matter

5. What are the lessons of the dynamics and kinematics of Rydberg atoms

6. Why is nonlinear dynamical systems theory so AWOL in atomic and subatomic physics.

7. Etc., etc., etc., etc.,...

What I am not looking for is ever more name- and technical term-dropping and pushing around abstract [and childlishly oversimplified] theoretical constructs on paper, with no apparent connection to the real world of atoms, stars and galaxies.

A great deal of modern theoretical physics virtually ignores nature and speaks in content-less Babel-talk. But our purpose is to understand nature. Or at least that is what it was in great awakening of 1900-1925. When will the next great awakening finally arrive?

Consider the typical cosmology text. It probably does not even have "hierarchical" or "fractal" or "self-similar" in the index. Pathetic ignorance of nature.

Yours in science,

RLO

www.amherst.edu/~rloldershaw

http://arxiv.org/a/oldershaw_r_1

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Cristinel Stoica wrote on Oct. 4, 2009 @ 07:27 GMT
Dear Florin,

I think that such a proof of global hyperbolicity is great, so I look forward to read it.

If I understand well, you think that Physics is axiomatizable, but the axiomatic system doesn't have a model (as in model theory)?

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Author Florin Moldoveanu wrote on Oct. 4, 2009 @ 13:27 GMT
Dear Cristi,

As I was saying in the essay, global hyperbolicity only demands the existence of time, it does not provide a mechanism of how. In other words, we do not yet have a complete mechanism of why time travel is impossible and this should come from a complete quantum gravity theory. Non-relativistic quantum mechanics also does not have an inherent notion of time, but relativistic QM does in Grgin’s algebra of quantions.

For physics axiomatization, a model is simply not needed to proceed with the research program, but there is a loophole. Suppose any of the 3 principles (events, interaction, complexity) are emergent (in string theory particles are no longer points, changing the usual understanding of events as vertices in Feynman diagrams, or in LQG, space-time is emergent). Then models are possible, but a lot of clever guessing has to be made just right to be able to make and sustain progress. Without help from experiments, it is easy to guess the model wrong and end up in a dead end. Also there may not be universal models because of Gödel, but only particular ones. So in a sense I am doing the “thermodynamics” approach to axiomatization, not the “statistical mechanics” approach, but it seems to be a better approach because we can derive results which are out of reach for now in the usual approaches of strings and LQG.




Robert L. Oldershaw wrote on Oct. 5, 2009 @ 03:26 GMT
Florin,

My previous post was a rant, but hopefully not a totally unjustified rant.

I do believe that every scientist should follow his own intuition and inner voice, without undue coercion from external authorities of any type.

But here is my essential point.

If one does not have the right paradigm within which to work, then all the mathematics and analytical techniques in the world will not help one to a better understanding of nature. In fact they will be more likely to mislead one into thinking one has achieved a "deep" model of nature, when in fact one merely has the intoxicating and intimidating illusion of real understanding. Witness "string theory".

In my opinion, we are desperately seeking a new paradigm and the only way to create one is by studying the objective empirical properties of nature, searching for one coherent comprehensive pattern that fits the entire hierarchy of nature.

I am studiously aware of t'Hooft's work, and have watched him evolve from saying that my discrete cosmological self-similarity was worthless to his saying things that sound very much like they come from the foundations of my paradigm: e.g., (1) G is NOT scale invariant, and (2) 'same physics on different scales, and (3) causality, 4d S-T and General Relativity dominating in the subatomic realm, as well as in the macrocosm.

I believe that the resolution of the dark matter enigma will demonstrate that Discrete Scale Relativity is the correct paradigm for the 21st century. Or prove that DSR is fatally flawed.

Yours in science,

RLO

www.amherst.edu/~rloldershaw

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Emile Gergin wrote on Oct. 5, 2009 @ 07:43 GMT
Dear Florian,

In one of your posts on Robert Oldershaw's blog space you wrote

"I was hoping to derive the Klein-Gordon equation (see note [1] on page 4 on my essay) in the near future but Emile Grgin just beat me to it."

Maybe not. It all depends how you do it. If your proof contains a new idea that could be applied elsewhere, it's the idea, not the end result, that would make your derivation interesting.

Regards,

Emile

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Author Florin Moldoveanu wrote on Oct. 5, 2009 @ 19:25 GMT
Dear Emile,

You may be right; I was approaching the problem from the linking vector point of view, speculating that one is leading to Dirac, the other to Klein-Gordon. (I still think the second linking vector will lead to SU(2,2). The interpretation is not Zovko in terms of conserved probability density, but in terms of conserved positive and negative charges and I will see if the math agrees with this intuition.)

Because any solution of Dirac is also a solution of Klein-Gordon, I suspect this fact may play indirectly a role in your derivation but I do not know since I did not see your proof yet.

Regards,

Florin




Author Florin Moldoveanu wrote on Oct. 5, 2009 @ 19:36 GMT
Robert,

Your points are well taken. However, my only argument with your approach is that we cannot just brush aside the existing results confirmed by nature and start fresh with a radical new paradigm without first attempting to explain the predictions within the existing framework. You can certainly do it, but there will be very few followers and in the increasingly complex business of today’s physics one person cannot do it all by himself.

Florin




amrit wrote on Oct. 5, 2009 @ 21:18 GMT
Dear Florin Moldoveanu

Physics can not be based on mathematical axioms, physics is based on experiment.

Mathematic should be only a tool of physics and not ruler.

For example with creation of Minkowski space-time idea has arisen in physics that space-time is physical reality. Before mathematical space-time was constructed no one was thinking space-time is fundamental arena of the universe. Today 99,9 % of physicists is convinced it it so. However there is no experimental data space-time being physical reality. Math has overruled physics and i see this mistake should be improved.

Physics should be based on elementary perception and experimental data.

Sincerely yours amrit

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Author Florin Moldoveanu wrote on Oct. 5, 2009 @ 22:35 GMT
Dear Amrit,

You say: “Physics can not be based on mathematical axioms, physics is based on experiment.”

You are right and I fully agree with you, but perhaps my essay was a bit misleading. In my essay I asked for all the mathematical properties of the real world that are universally true in nature and not universally true in math. Because of this, the 3 ultimate broad physics principles (derived from events, interaction, and infinite complexity) should pass al past, present, and future experiments. Make no mistake, my approach is still old fashion physics.

You also say: “Mathematic should be only a tool of physics and not ruler.”

To this I only agree partially. If you are talking about all math, you are right again. However, only some mathematical structures play a distinguished role in nature. Why is that? Why do we encounter a Hilbert space in nature, why do we have the U(1)XSU(2) electroweak symmetry, and not SU(29,5) for example? Why is the event manifold not described by Finslerian geometry? To answer those questions we cannot look only at math because in math all structures are unique: there are no 2 Pythagoras theorems for example. We cannot look only at nature either. But by looking at the difference between nature and math, those distinguished mathematical structures present themselves naturally.

But yet again, why we would expect such a heuristic rule to be successful and in the end to provide the correct axiomatization of physics? Because if reality is not relational at core (just like math is) then we would definitely need to look at transcendental and God arguments to completely describe nature. Looking at transcendental arguments to complete the explanation of nature is against an experimental based science like physics. Therefore if reality and nature is indeed relational then we would expect mathematics to be the building block of nature and there will be no mystery about its “unreasonable effectiveness”. In this view, reality is made out of mathematical objects and some mathematical objects will play global distinguished roles, while others will play secondary roles. Reality and the Platonic world of math are two possible ways of organizing mathematical structures.

The next question is why do we need the 3 principles? Without events, there will be no ontology. Without interaction we will live in a frozen world, just like the Platonic world of math. Without infinite complexity we could be only cartoon characters on TV, or software programs on someone’s computer. The amazing thing is that by demanding only those 3 requirements, distinguished (unique) mathematical structures can be obtained, and moreover, those are the mathematical structures confirmed by experiments.




Emile Grgin wrote on Oct. 6, 2009 @ 02:26 GMT
Florin,

You can find the derivations of Klein-Gordon's equation in my books, but they are easily missed as accidental to what was more important to me: figuring out the allowed mass matrices. The proofs are quite messy, but the new one is elegant to the point of being trivial. The same is true for the mass matrices. Anyway, here are the references:

In the 2005 book: Theorem 134 on page 432. While you are there, please get rid of the mass parameter m in equation (19.29). It's a typo.

In the 2007 book: Corollary 65 on page 215.

Emile.

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Robert L. Oldershaw wrote on Oct. 6, 2009 @ 02:46 GMT
Florin,

Imagine Barberini saying virtualy the same words to Galileo!

Galileo's response would be that we never throw out the experimental and empirical results that have been won by hard effort. But we must be willing to seriously consider junking any and all theoretical constructs if we want to understand nature [or call ourselves scientists].

Following your approach we could be bogged down in the swamp of string theory for millenia.

Get real!

RLO

www.amherst.edu/~rloldershaw

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Author Florin Moldoveanu wrote on Oct. 6, 2009 @ 04:12 GMT
Emile,

Thank you for your page references. I re-read your chapters and I am really relieved. Your Klein-Gordon derivation is not what I am after; I thought you obtained something different that what is in your books. In my interpretation the true K-G equation is the end point which cannot be further simplified to Dirac. Your K-G equation is only an intermediate step towards Dirac and this is expected since any Dirac solution is a K-G solution but not the other way.

What I am talking about is not under the original Zovko continuity equation from the first linking vector, but under a different kind of continuity equation from the second linking vector. The interpretation should also change because the current probability density will not always be positive (because of the positive and negative charges) and I suspect that this would lead to SU(2,2).

Florin




Emile Grgin wrote on Oct. 6, 2009 @ 06:27 GMT
Florin,

Good! I am looking forward to seing it.

Emile,

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Owen Cunningham wrote on Oct. 6, 2009 @ 17:32 GMT
A copy of this message is being left in each thread of the essay contest forum.

Submitters: Tired of constantly checking the FQXI site to see how your paper's doing in the rankings? I've written a simple program that periodically checks the FQXI site and sends you an email if the status of your paper has changed in any way. Here is a sample email:

The following changes were detected in the status of your paper:

* Number of posts in discussion forum went from 0 to 20.

* Community rating went from 0 to 3.4.

* Community vote count went from 0 to 10.

* Public rating went from 0 to 4.3.

* Public vote count went from 0 to 6.

* Community ranking went from being in 0th place to being tied for 16th out of 112.

* Public ranking went from being in 0th place to being tied for 19th out of 112.

You just run the program once, in a command prompt window, and then minimize that window and let it do its thing in the background.

If you're interested in a copy (with source for those who care) drop me a note at ramblinplan@yahoo.com.

Thanks,

Owen Cunningham

P.S. This program requires Windows and the .NET Framework. It has been tested only on Windows XP Service Pack 3 running .NET Framework 3.5, but has a good chance of working with earlier versions.

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Author Florin Moldoveanu wrote on Oct. 6, 2009 @ 21:50 GMT
Robert,

Your argument is seriously flawed. Of course you do not throw out experimental results. You try to understand them first in the existing paradigm, and ONLY IF that does not work, you try to construct a new model. Constructing your fractal explanation to fit your experimental data at the expense of ignoring all we already know about gravity and electromagnetism is doing it backwards and is hardly scientific.

To make my point clear let’s take it to the absurd extreme: there are 7 days in a weak, 7 continents, 7 wonders of the ancient world, etc. Can I conclude that 7 is a special number in nature then? Of course not; there are other explanations in each of those cases. This is the problem you can get into postulating a (flamboyant) fractal structure of the universe while the explanation can be more mundane in what we already know about electromagnetism and gravity. However, if you can actually derive your best fit parameters from existing knowledge, then your predictions about dark matter will suddenly become very credible. If the derivation is not possible, then you have to show at least the effort of trying to do it first and why it did not work.

About the string theory comment, this is misguided. First, I am not a string theory supporter and I am not sure where did you get the impression that my approach will result in an approach similar with string theory.

Second, while I am not a fan of string theory, I do respect its results and I am only choosing not to spend my time into this pursuit at this time. My only argument with string theory is not about its math, but about starving other promising approaches out of resources while not offering experimental predictions. Only if you offer genuine testable predictions you should be in the front of the line for resources.

I think you cannot just badmouth string theory without arguments. Very good results were obtained there expanding our knowledge, and if you think you have an argument for the non-existence of the landscape besides personal distaste, I and everyone else will like to hear them.




Robert L. Oldershaw wrote on Oct. 7, 2009 @ 02:05 GMT
Florin,

Saying that I ignore "all that we already know about gravity and eletromagnetism" is absurd.

This only proves that you have no idea what Discrete Scale Relativity is.

For example I uniquely use the Kerr-Newman solution of the Einstein-Maxwell equations to successfuly retrodict the mass and radius of the proton. The reason everyone failed in their old attempts to do this was that they used the wrong value of G. DSR tells you specifically what value of G to use and the happy retrodiction is available for your study [website: Technical Notes: "Modelling Subatomic Particles...].

So let's be clear buddy, I do not ignore well-tested physics like General Relativity and Classical Electromagnetism. You ignore the discrete self-similar paradigm.

My dark matter predictions were published in The Astrophysical Journal [322, 34-36, 1987]. You might look it up.

My complaint is that people who act like they have no functioning right hemispheres have controlled physics for decades and filled countless theoretical physics journals with millions of incomprehensible equations which offer little or nothing in the way of useful and/or accurate understanding of nature. String theory is just the archetype of this truly mad and pervasive excursion that theoretical physics has been on.

FIRST COME THE CONCEPTS! And to generate conceptual advances you need TWO well-functioning hemispheres, with an emphasis on a powerful right hemisphere. Know what I mean? Probably not.

Yours in science,

Robert L. Oldershaw

www.amherst.edu/~rloldershaw

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Steve Dufourny wrote on Oct. 7, 2009 @ 07:17 GMT
Florin ,

Still one post deleted .It's not serious .

Thanks for the Euclid demonstration ,like Bernouilli or Euler ,these limits ,physicals are different than a mathematical infinity ,the primes and naturals must be adapted ,if not it's an error ,simply .

About Goedel ,it's a beautiful axiomatisation ,a beautifull essay towards the unknew .Interesting.

Best Regards,and good luck for the contest

Steve

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Terry Padden wrote on Oct. 7, 2009 @ 11:55 GMT
Florin

I find much to agree with in your essay, but I have to say your claims that you are writing about a TOE are ridiculous.

The "ultimate" challenges facing physics are Emergence and Consciousness. Surely a TOE, if there is such a thing, can handle them. Could you explain what the scope of your "TOE" is and how these are covered by it ?.

You make clear your work derives from that of Emile Grgin - but in his essay he does not mention a TOE. He focuses on unification of QM & GR. In his response to me he makes clear his Quantions are not ultimate structures, and in no way suggests they will enable a TOE.

The unification of QM & GR has been with us for 30 years it is an immediate problem - not an ultimate one. The TOE proponents of a previous generation abandoned their ridiculous TOE claims when everyone realised they were ridiculous and brought only discredit to the proponents and to physics. Why do you want to revive this discredited nonsense. It only devalues your work and that of Grgin.

Also re your axiomatics. Yuri Manin is one of the greatest living mathematicians often called onto to present to leading mathematical conferences keynote addresses that layout the challenges facing mathematics today. A quote from one of them is featured near the end of my essay. To paraphrase. Like TOEs in physics, in maths the day of axiomatics / formalisms is over - MEANING is what matters. I think this is always true of physics.

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NN wrote on Oct. 7, 2009 @ 13:41 GMT
Florin, your essay is a beauty of sorts and very popular both with he public and the community. Thus you may be running short of time, as i await your response to my latest post of Oct 03; 4:47 am. Please do not feel pushed, respond only if you find my post as of some use to you in your essay text.

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Author Florin Moldoveanu wrote on Oct. 7, 2009 @ 13:59 GMT
Dear Narendra,

Sorry if I did not answer your questions completely. To your post on Oct 03; 4:47 am, I replied on your site on Oct. 3, 2009 @ 14:53 GMT and you answered back on Oct. 4, 2009 @ 09:26 GMT. (I wish FQXi would have had a simple ID number instead of the time stamp to keep track of the threads of discussions).

I thought I have completely answered your question, but please ask your question again so that I will not digress on a tangent you are not interested in.




Author Florin Moldoveanu wrote on Oct. 7, 2009 @ 15:00 GMT
Terry,

I also find much to agree in your essay, but I think you misunderstood what I say about the TOE.

Let me try to clarify: I do not know if a TOE does or does not exist. It would be nice if it did, but we cannot start from there. However, physics axiomatization does exist, and this is the right place to start. The very title of my essay does not say: “Heuristic rule for...

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Author Florin Moldoveanu wrote on Oct. 7, 2009 @ 15:03 GMT
Steve,

Thank you for your kind words.




Robert L. Oldershaw wrote on Oct. 7, 2009 @ 23:57 GMT
Florin,

Saying that I ignore "all that we already know about gravity and electromagnetism" is provably false.

This only shows that you have little understanding of Discrete Scale Relativity.

For example I uniquely use the Kerr-Newman solution of the Einstein-Maxwell equations to successfully retrodict the mass and radius of the proton. The reason everyone failed in their previous attempts to do this was that they used the wrong value of G. DSR tells you specifically what value of G to use. The successful retrodiction is available for your study [website: Technical Notes: " Subatomic Particles...”].

So let's be clear, I do not ignore well-tested physics like General Relativity and Classical Electromagnetism. On the other hand, you ignore the well-documented discrete self-similar paradigm.

On another issue, my dark matter predictions were published in The Astrophysical Journal [322, 34-36, 1987]. You might look it up.

My complaint is that people who act like they have no functioning right hemispheres have controlled physics for decades and filled countless theoretical physics journals with millions of incomprehensible equations which offer little or nothing in the way of useful and/or accurate understanding of nature. String theory is just the archetype of this truly mad and pervasive excursion that theoretical physics has been on.

First come the concepts! And to generate useful conceptual advances you need two well-functioning hemispheres, with an emphasis on a powerful right hemisphere.

Simplex signilum very,

Robert L. Oldershaw

www.amherst.edu/~rloldershaw

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Author Florin Moldoveanu wrote on Oct. 8, 2009 @ 01:10 GMT
Hello Frank,

We had exchanged many messages in the past, and I thought my position was clear. I did not see anything different in your questions from what you asked before. Let me repeat my position again: 1. unification of electromagnetism with gravity is wrong, as we already know that electromagnetism is unified first with the weak force. 2. Unification in dreams is not a mathematical explanation.

Florin




Author Florin Moldoveanu wrote on Oct. 8, 2009 @ 01:24 GMT
Robert,

It is true, I do not understand Discrete Scale Relativity, but that was not my criticism. Postulating a fractal structure I would expect that the pattern of atomic physics and galactic physics to occur again at even higher scales much larger than galactic distances. After all, a self-similar fractal pattern should be repeating itself.

My contention is that there is nothing beyond the galactic scale resembling your patterns because the atomic and galactic patterns are generated by the 2 infinite range interactions: electromagnetism and gravity. So either your pattern does repeat above the galactic scales, or it is not a fractal. But if you do not call it a fractal, then you should explain the origin of your best fit parameters. If you can manage to put them on a solid explanatory foundation, then your dark mater predictions will be taken much more seriously.

Florin




Robert L. Oldershaw wrote on Oct. 8, 2009 @ 05:08 GMT
Hi Forin,

Very interesting.

You contend that "there is nothing beyond the galactic scale resembling your patterns because the atomic and galactic patterns are generated by the 2 infinite range interactions: electromagnetism and gravity".

Fine, but consider two things.

1. Your contention that EM and GR are infinite range interactions is purely an assumption. This has never been tested, and in fact is technically untestable. Right there you are on shaky ground.

2. Your logic also implies that EM+GR can generate atomic, stellar and galactic structure, but not higher level structure!! Oops, I think you've got a logical disconnect there, my friend. What physical mechanisn would permit discrete self-similar atomic, stellar and galactic structure, but suddenly cut this off above the galactic scale?

People who understand Discrete Cosmological Self-Similarity have not been able to falsify it over 3+ decades of trying. Those who do not have an adequate understanding of the new paradigm are hardly likely to be more successful.

Bottom Line: Empirical evidence trumps theoretical assumptions. Every time.

Simplex signilum veri,

RLO

www.amherst.edu/~rloldershaw

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Author Florin Moldoveanu wrote on Oct. 8, 2009 @ 20:57 GMT
Hi Robert,

You contend that is impossible to determine if EM and GR have infinite range.

Your first your argument is incorrect. We know that the photon has zero mass, and while it will be never possible to detect a single graviton, we know gravity works to at least the size of the observable universe. However, all this is irrelevant as we definitely know that the strong and weak force have a much smaller range and for my argument we can replace “infinite range” with “very large range”.

For your second point, you may be right, but you contradict your first point: if EM and GR do have only a finite range, then there will be definitely a cut-off.

But all this is only a fruitless discussion of many ifs. Bottom line is that pushing a new paradigm is always an uphill battle. In this day and age one person cannot do it all by himself, and you need collaborators to join in your quest. For that you need to address all the questions critics will raise. A simple statement that empirical evidence trumps it all is insufficient even if you are right.

Please feel free to ignore my advice, but this is not what I am doing for my paradigm battle. In my case Gödel’s theorem is the first thing that comes to mind when someone thinks about axiomatizing physics and I take this challenge head-on from the second statement of the abstract.

My overall impression of your theory from the very limited amount of time I devoted trying to understand it is that you may be onto something, but your explanation for it is over the top.

Even if you are right and I am dead wrong, trying to convince me of your point of view will not make me start working in your theory and is a waste of time. A much more efficient use of time is to take my honest impression (which may be wrong) and try to address my concerns (which I think are probably shared by many other people). Of course, you may think that I am not a typical physicist and that my views do not reflect the general perception of your theory by the general physics audience, but you have to decide this for yourself.

Florin




Robert L. Oldershaw wrote on Oct. 9, 2009 @ 01:37 GMT
Hello Florin,

1. Consider your 2nd paragraph:

"Your first your argument is incorrect. We know that the photon has zero mass, and while it will be never possible to detect a single graviton, we know gravity works to at least the size of the observable universe. However, all this is irrelevant as we definitely know that the strong and weak force have a much smaller range and for my argument we can replace “infinite range” with “very large range”."

You pepper your arguments with absolutes that are assumed but cannot be tested. For example, zero mass photon or infinite range EM/GR. You proceed as if we have much more guaranteed-to-be-true knowledge than we really have. Well-known problems in physics like the hierarchy problem and the vacuum energy density crisis demonstrate quite clearly that there are serious mistakes somewhere in our current set of theoretical assumptions. But if you treat this set of assumptions as "empirical facts" then you might be blind to the critical changes in our thinking that are required for advance.

2. Yesterday you argued that the infinite range of EM+GR ruled out metagalactic self-similarity. Today you argue that a finite range for EM+GR would rule out such structure. My, my, you certainly have all bases covered! Methinks the theoretician speaks with forked tongue.

Bottom Lines: These discussions are for the benefit of others, Florin. Know what I mean?

The abstract theoretical axiomatic approach to making discoveries has not worked in the past and is unlikely to work in the future. A quote from Maxwell may be appropriate here.

“I have no reason to believe that the human intellect is able to weave a system of physics out of its own resources without experimental labour. Whenever the attempt has been made it has resulted in an unnatural and self-contradictory mass of rubbish.” James Clerk Maxwell

No, my friend, if you study the history of physics you will find that the fundamental advances by Democritus, Spinoza, Galileo, Faraday, Darwin, Einstein, etc. follow the same patterm. (1) Study nature with a passion for the real thing, not some abstract representation of it, (2) identify a pattern or relation that appears to unify previously unrelated concepts, (3) develop the critical empirical clues into a coherent paradigm, and finally (4) apply mathematical and analytical techniques to formalize and extend the conceptual paradigm.

Sorry, my friend and colleague, but "same as it ever was".

Yours in science, which dares to question any assumption,

RLO

www.amherst.edu/~rloldershaw

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Steven Oostdijk wrote on Oct. 9, 2009 @ 17:13 GMT
Dear Florin,

In your conclusions you end with the statement:

"When experiments are no longer needed or possible, we will enter a post Gallilean era when physics would no longer rely exclusively on experiments as the ultimately judge of success. Math never depended on experiments and whenever physics is experiment independent, it should be done more like math: with increased rigour and safeguarding a diverse approach towards research directions."

So, my conclusion out of that statement would be that according to you what is ultimately possible in physics is to replace the physics with math (and get rid of these nasty true or false experiments) :) ?

Good luck with the contest!

Steven Oostdijk

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Author Florin Moldoveanu wrote on Oct. 10, 2009 @ 01:11 GMT
Dear Steven,

With apologies to Robert and Frank for answering you first (and I do not know where Frank’s message went, I did not reported as inappropriate myself), here is the answer.

First I want to say that I am glad someone noticed my very last statement, because it is very important. There are 2 ideas in it.

If the axiomatization approach is to become successful and explain much more than today, then math is indeed going to play a much more important role. But there is another road leading there and this is due to the very weak nature of gravity. This is what happens already today in string theory which does not offer any true experimental prediction, and therefore math takes the center stage instead.

Now I respect the string theory for its insights, but I disagree with its dominant role in theoretical funding which starves out other approaches and here we are competing at FQXi for only token recognition while we should be able to get decent grants from traditional sources. What I say in my statement is that if what you do is experiment independent in physics (and this includes myself), then the research grants should be evenly divided up in a similar fashion with what happens in math today.

String theory had its roots in traditional high energy physics with valid claims for the lion’s share of resources, but the virtual monopoly on funding it inherited survived to this day despite the lack of experimental predictions and this is just not fair. This is a hot acrimonious topic and I tried to find some argument everyone can agree with while making the case for the FQXi mission and diversity (or at least that was my intention).

PS: due to the overwhelming number of late entries, I did not had a chance yet to read your essay, but I will do it (hopefully) shortly.




Robert L. Oldershaw wrote on Oct. 10, 2009 @ 17:10 GMT
"this is due to the very weak nature of gravity"

Sigh, another unfortunate bias among theoretical physicists, and one which has no empirical justification. It has just been repeated so often that no one questions it anymore. Very unscientific, in my opinion.

Gravitation is strong enough to keep your body on this Earth, even though it is not strong enough to prevent a mind from floating off into the abyss of abstraction.

What if the strength of gravitation is scale dependent like t'Hooft and I claim? Then most of your agrument collapses.

If we base our arguments on towers of assumptions, are we not setting ourselves up for a big fall?

RLO

www.amherst.edu/~rloldershaw

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Author Florin Moldoveanu wrote on Oct. 10, 2009 @ 18:57 GMT
Robert,

Flamboyant statements are a poor substitute for solid judgment. Also you cannot pick and choose which experimental facts you have to explain. Third, assuming a victimization posture of not being understood by the theoreticians who are not questioning enough proven theories may help you carry on in your quest against the opposition, but it is not good science.

Also it is really hard to continue this discussion with you while you continue to display this unprofessional cowboy attitude. I already told you my opinion about your theory earlier. You can accept it, or ignore it, it makes no difference to me.




Steven Oostdijk wrote on Oct. 10, 2009 @ 21:06 GMT
Dear Robert and Florin,

""this is due to the very weak nature of gravity"

Sigh, another unfortunate bias among theoretical physicists, and one which has no empirical justification."

I completely agree with Robert. Gravity scales. But it scales linearly, so you will find that even a proton, electron or photon would measure 9.8m/s^2 gravity at their surfaces.

Steven Oostdijk

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Author Florin Moldoveanu wrote on Oct. 10, 2009 @ 23:12 GMT
Dear Steven,

Can you please elaborate on how gravity scales linearly? Do you mean Newtonian gravity is not inverse proportional with squared distance, but only with distance?

Thanks,

Florin




Robert L. Oldershaw wrote on Oct. 11, 2009 @ 20:58 GMT
Florin,

In this discussion, promoting Discrete Scale Relativity has been a secondary concern.

The primary goal was to promote a very general scientific philosophy: If you want to understand nature, you should study nature, not Platonic artifice.

When the discussion deteriorates, it should end.

RLO

www.amherst.edu/~rloldershaw

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Steve Dufourny wrote on Oct. 13, 2009 @ 13:13 GMT
Hi Florin ,all,

You say

"Gravity scales. But it scales linearly, so you will find that even a proton, electron or photon would measure 9.8m/s^2 gravity at their surfaces."

I agree too .

Indeed we are under specific local system ,here our Earth and its mass ,the code of the center is relevant too.

If the gravity is the mass ,of course we must adapt the different steps of the spherical system.

the distance ,r is too very important about the gravity ,

all bodies interacts ,attracts ....we can interpret the gravity at many scales ,Earth ,sun,galaxy,super groups,universe,quantum systems and mechanics of rotations .

Even our moon has a rule of balance,of complemenatrity .If we raise ,take off only one particle ,all will be chaotic and in all senses .The gravity ,this evolutive mass is the equilibrium between all ,even the space .

The quantum gravity or the galactical gravity is the same link ,the mass and the rotating spheres for me .The gravity has a cause ,the evolution and the rotating spheres ,the rotation is proportional with the mass in a physical point of vue of course .

The gravity always changes ,due to the evolution and the very weak polarisations .

But of course we can't perceive these decimals about the increasing of mas ,it's always a question of relativity in fact.

Best Regards

Steve

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Author Florin Moldoveanu wrote on Oct. 14, 2009 @ 02:50 GMT
Dear Steve,

I did not say that gravity scales linearly, but if you agree with it, maybe you can clarify it for me because I do not really understand what it means.

Thanks,

Florin




Steve D wrote on Oct. 14, 2009 @ 17:16 GMT
Hi Dear Florin ,

hihihi well said .I didn't say too that it was an affirmation of you .

Let's return at this gravity if you want Florin ,I d like go a little more far .

It exists a cause ,even causes in a global point of vue ,universal about our gravity or gravitIES .Our Universe has a specif mass ,and this mass probably evolves due to the evolution in this line time ,which is constant furthermore this time.

You know Florin ,for me the gravity is all .All is linked by this simple fact ,the gravity and all is in equilibrium ,fortunally .All spherical systems ,physical have a mass and a center ,coded since the beginning .It's these centers too which are relevant like all.

The gravitational fields are all linked in a beautiful music in harmony ,evolutive.

For a stability of these mass systems ,a specific system and its combinations is necessary .Thus the synchronisation is importaznt about the stability .These synchronisations of interactions is under specific frequences ,and these frequences are linked with the rotating spheres for me .Thus the gravity has many interpretations in function of the local system where r and the rotations more the spheres are different .The mass doesn't change ,evolves but doesn't change.

I am curious ,in resume ,

for you what is the origin of the mass ,thus the gravity .

Sincerely

Steve

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Steve Dufourny wrote on Oct. 14, 2009 @ 17:26 GMT
Dear Florin ,

How is the diffusion of light ?,in spherical distribution

how are the gravitational waves or fields ,....it s the same in fact with the local parameters and variables of course .

The only difference is the superimposings with the gravity ,

Perhaps,it is just a question of sense ?

Sincerely

Steve

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Carl Lumma wrote on Oct. 16, 2009 @ 20:24 GMT
Florin,

You state that "Within an axiomatic system in math, the amount of information is restricted by the original axioms." but I think (depending on the definitions used) this is precisely what Godel's incompleteness results disprove. Can you demonstrate otherwise?

-Carl

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Mark Stuckey wrote on Oct. 17, 2009 @ 00:21 GMT
Florin,

I would like to discuss the first of your principles and your paper, physics.gen.ph/0704.3074. I'm not sure we have the same understanding of the nature of the paradox associated with CTC's in GR, so let me articulate mine.

Suppose we are going to roll a ball into the mouth of wormhole along a CTC such that, assuming the ball follows the CTC, the ball collides with itself and cannot enter the wormhole. Clearly this is a contradiction, but keep in mind that GR demands all masses (like the ball) in its solutions be represented by the stress-energy tensor (SET). Now it may well be the case that this ball is too small to affect the geometry of the CTC, but nonetheless, it must be represented in the SET. Typically, no contradictions occur so we don't bother with the SET for the ball, it just follows the curve in question without incident (we could construct a SET for the ball, but it doesn't effect the solution). However, in this case, we see that no SET can be constructed for the ball moving along the CTC, thus we do not have a solution of Einstein's equations. So the "paradoxical question" is, what WILL happen when I roll the ball along this trajectory? And the answer is, we don't know because GR is the only theory we have that tells us about the curvature of spacetime and it doesn't provide a solution for that situation.

Let me stop here and ask whether your understanding of this situation matches mine. If so, then we can discuss the need for "infinite forces" as called for in your 0704.3074 paper. If not, we need to discuss our different understandings.

Thanks,

Mark

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Author Florin Moldoveanu wrote on Oct. 17, 2009 @ 02:37 GMT
Carl,

A better restatement of this is to say that the algorithmic information content of any axiomatic system in Chaitin’s sense is finite. I should have cited Chaitin here, this was an oversight. Algorithmic information theory (AIT) was inspired by Gödel’s incompleteness theorem, and Chaitin arrived at it by considering Berry’s paradox instead of the standard Liar’s paradox, but as Gödel points out in his proof, any antinomy can be used and AIT is a close cousin of the incompleteness theorem. Chaitin has a popular way of saying the same thing: “you cannot obtain 20 pounds of theorems from only 10 pounds of axioms”, or something along those lines.

I also want to point out why is the deformability principle (or infinite complexity) necessary. The first principle guarantees ontology. The second one is saving the world from the frozen fate of mathematical structures. A software program, a cartoon character on TV may be made compatible with the first 2 principles. But to distinguish between a brain in the vat case and the real world, then infinite complexity is needed, otherwise there is no guarantee we are not all just characters in someone’s a computer game.

Florin




Author Florin Moldoveanu wrote on Oct. 17, 2009 @ 04:27 GMT
Mark,

Let me first construct the background for the argument in my paper.

Over time there were a bit of back and forth arguments between the supporters and the opponents of time travel:

1. Friedman, Novikov, Thorn, and others considered the idea.

2. Polchinski countered with an inconsistent self-collision of a billiard ball for traversable wormholes.

3. Friedman...

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Carl Lumma wrote on Oct. 17, 2009 @ 07:03 GMT
Hi Florin,

>A better restatement of this is to say that the algorithmic information content

>of any axiomatic system in Chaitin’s sense is finite.

I believe this is still backwards. Chaitin shows that every axiomatic system contains theorems (strings) that can't be proven (compressed) with the axioms given -- their information content exceeds that of the axioms. If they could be proven their information content would be reduced.

By the way, there is hardly a need to specify whether we mean Chaitin AIC, or Shannon or Boltzmann/Gibbs entropy, since they are all equivalent. The difference is how they tend to be applied. With Boltzmann entropy we tend to assume the universe is chosen directly from all possible configurations of its particles. Under this assumption, we find that a very unlikely configuration was chosen. I take this as evidence that the assumption is wrong. If we instead assume, as the algorithmic information theory folks seem to do, that the universe is produced through a computational process, then low entropy states are actually more probable, since they appear sooner or more often whenever the computation is in any way (time, space etc) resource constrained.

-Carl

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Author Florin Moldoveanu wrote on Oct. 17, 2009 @ 14:17 GMT
Hi Carl,

I think we agree on what Chaitin proved, but not on its interpretation. Let’s just stay with the plain incompleteness theorem. This shows that the math is infinite because you can always construct new statements which are not provable. In my interpretation, while syntactical correct, those statements are not part of the axiomatic system because they cannot be proved. So are those statements inside or outside the axiomatic system? This is irrelevant because the real world behaves differently from mathematical world: all events in a continuous event manifold are “decidable” because they can be observed. The difference between reality and math is: "infinite" numbers of provable statements vs. "finite" number of provable statements. For event manifolds this implies a freedom that is only compatible with SO(p,q) as Rau showed.

(I put the finite and infinite in quotations because we need a rigorous mathematical definition and I think AIC can do that. Regardless of this, Rau's result is still valid, but I take it only as a starting point for future stronger results.)

Florin




Mark Stuckey wrote on Oct. 17, 2009 @ 16:12 GMT
Dear Florin,

Thanks for your reply. I suspect we do have different takes on the nature of this "paradox." You write, "Now your argument corresponds to item 2, the Polchinski paradox. Concerning the need to represent the ball in the stress-energy tensor you say, 'This is OK, but the typical counter-argument is that the self-collision can occur far away from the mouths of the traversable...

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Author Florin Moldoveanu wrote on Oct. 17, 2009 @ 20:19 GMT
Dear Mark,

GR equations are local equations and there is no such thing as global consistency build into them. As long as locally one distinguishes between past and present, then locally all is OK including the SET. However, globally causality can be violated in many ways in GR: wormholes, warp drives, infinite strings, rotating cylinders, etc. If your contention is with the SET, then one can choose a simpler case of a Tippler’s cylinder. If the cylinder rotates fast enough then it is tipping the local Minkowski light cones by a frame dragging mechanism to the point that a CTC can be formed (and no billiard ball can perturb it). Now in this case locally everything is well defined but the Polchinski paradox occurs on a global scale. The paradox is inescapable either on a local or on a global scale, pick your poison. If local physics is well defined, then the Polchinski paradox ensues on a CTC. If by unknown physics (presumably in a complete and final quantum gravity theory) inconsistent self interactions are forbidden as you seem to imply, then the local classical physics pays the price. (And with it also quantum mechanics in the range of the validity of the correspondence principle.)

So now let me try to restate what I think your argument is. I believe that you contend that an inconsistent SET forbids an inconsistent self-interaction. This is incorrect because a consistent SET can only guarantee a well behaved local evolution and not a global one. This is the difference between local and global hyperbolicity. There is a potential loophole in my argument against your position: the block interpretation of space-time and Barbour’s end of time. But the block interpretation is wrong as it cannot account for free will (on the philosophical point of view) or for the freedom to choose what to measure (from the QM point of view). I can elaborate on those points or on why I believe Barbour is wrong to base his analysis on a timeless Lagrangian.

Florin




Anonymous wrote on Oct. 18, 2009 @ 01:26 GMT
Florin,

I believe we're getting closer to understanding each other. You write, "So now let me try to restate what I think your argument is. I believe that you contend that an inconsistent SET forbids an inconsistent self-interaction." An inconsistent SET can't be constructed, so if you're trying to describe a self-inconsistent situation in some local region of spacetime, it can't be done with a SET. That's simply a mathematical articulation of the proposed self-inconsistency. If you can create the SET for the ball throughout its trajectory, you don't have any inconsistencies. There are solutions whereby the ball exits the wormhole, hits and knocks itself into the wormhole at just the right angle so as to exit along the trajectory so as to exit and hit itself ... . Another example can be constructed with objects that pass through themselves (no self-interaction), so that it doesn't knock itself off course. A SET exists for these situations, and I wouldn't say they contain self-inconsistency. I'm talking about the situation as I described it previously whereby there is at least one problematic region in which you cannot construct the SET for the situation.

Mark

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Frank Martin DiMeglio wrote on Oct. 18, 2009 @ 14:02 GMT
Hi Florin:

How would/does your essay account for/address the following:

Time has 3 parts -- past, present, and future. Any TOE must not only address the integrated extensiveness of experience in general, but it must address this as well. You cannot have a TOE whereby time is dimininished, in other words. The integrated extensiveness of being/thought/experience must address the integrated extensiveness of time. The totality of time must be understood in conjunction with, and inseparable from, the present. Physics, to date, has failed miserably at this.

Undoubtedly, this is an important post. Please respond. Thanks. Frank

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Mark Stuckey wrote on Oct. 18, 2009 @ 14:50 GMT
Florin,

Let me clarify one more item. You write, "GR equations are local equations and there is no such thing as global consistency build into them. As long as locally one distinguishes between past and present, then locally all is OK including the SET." I'm not claiming the self-inconsitency arises due to a violation of causal stability. I'm looking at situations which involve the...

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Jonathan J. Dickau wrote on Oct. 19, 2009 @ 03:14 GMT
Greetings Florin,

I just noticed that you were one of the authors in Vol. 1 no. 1 of Quantum Biosystems, where I also appear. I was wondering where I had seen your name before, and now I don't have to wonder. But I will have to look at your essay, as well.

My contest essay is entitled The Possibility for Answers from Physics, and uses my earlier QBS paper as a reference.

All the Best,

Jonathan J. Dickau

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Author Florin Moldoveanu wrote on Oct. 19, 2009 @ 15:37 GMT
Mark,

Sorry for not answering earlier, I was away yesterday. First an easy point. I do no know what Fig. 7 shows, but I believe it has to do with the multiplicity of solutions that Echeverria, and Klinkhammer studied in detail. But conceptually this is not a problem of GR, it has more to do with the classical mechanics’ three body problem. Maybe I am saying it backwards. Because of Echeverria’s, and Klinkhammer’s results, the three body problem can be proved to be not solvable; in any case this is a classical mechanical problem, and not a GR specific issue.

Back to the CTC solutions of GR, I am still not clear about your point. Do you think time travel is possible or not? My position is that it is not possible and all GR solutions exhibiting CTCs are unphysical. One can go about proving it in several ways. If you want to start from a divergence-free SET, this is not what I considered in my paper, but this is an equally valid starting point. As I was saying in my paper on the bottom of page 5, a CTC case with self-consistent interaction is similar with a phase space behavior. I conjecture that this will uniquely lead to a symplectic and not a metric manifold, but there is no proof yet. (And because of this lack of proof I did not pursue this way of proving the impossibility of CTC spaces.) In phase space one has only global invariants similar with a CTC space with consistent self-interaction and this is at odds with the usual freedom allowed by a metric space.

In general, in a closed system, global self-consistency is against local freedom.

Florin




Author Florin Moldoveanu wrote on Oct. 19, 2009 @ 15:41 GMT
Frank,

You say: "The totality of time must be understood in conjunction with, and inseparable from, the present. Physics, to date, has failed miserably at this."

Present is a part of time in both Newtonian physics and special relativity. I do not understand in what way physics has failed.

Florin




Author Florin Moldoveanu wrote on Oct. 19, 2009 @ 15:50 GMT
Greetings Jonathan,

It’s a small world after all. With so many entries now, all becomes a blur and I have to re-read your paper to refresh my memory. Good luck to you in this contest.

Best Regards,

Florin Moldoveanu




Mark Stuckey wrote on Oct. 19, 2009 @ 19:12 GMT
Florin,

Concerning the indeterministic solutions, I've attached Figure 7 mentioned previously, along with another such figure (citations are given in attachment). In FIG. 7, the ball can roll between the mouths of the wormhole undisturbed or it can hit itself, coming from the left mouth, knocking itself into the right mouth which is identified with the left mouth at an earlier time, so it exits the left mouth to hit itself, etc. In this second scenario the ball coming from the left mouth goes up after the collision. A divergence-free SET can be constructed for either case, so they are both solutions to GR. The question is, which will occur when I start the ball rolling? It's indeterministic.

Returning to the issue of self-consistency, I don't need to explain my point since your posit that CTC spacetimes are unphysical renders it moot. I don't think you can prove this in the context of GR since some of these situations do constitute solutions, i.e., SETs can be constructed for them. However, that doesn't mean such solutions are physical, so if you want to posit their nonexistence and explore the consequences, so be it. That's akin to what we did in arXiv paper, where we posit the boundary of a boundary principle for self-consistency.

I'll have to reread your essay with this understanding in mind.

Thanks,

Mark

attachments: CTCs_Indeterministic_Solns.pdf

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Anonymous wrote on Oct. 19, 2009 @ 19:33 GMT
Greetings Florin,

I have begun reading, but must set it aside for now. I'm up to IIIc, at this point, and have found it very interesting. Regarding the Intro, perhaps another difficulty of deriving Physics directly from Math is that Mathematics itself has become so fragmented. And of course there is a definite problem where Math, Physics, and Engineering sometimes all use the same term, but differently.

I've enjoyed what I read so far, and when I get a chance I'll digest the rest and post additional comments. I have some thoughts on how the choice of Gödel (where to begin his proof) may have influenced the outcome. There is a hierarchal aspect that creeps into any axiomization process, owing to the fact that levels of abstraction need to be introduced sufficient to represent the important aspects of what's being studied.

Perhaps I'll see something relating to this, when I read the rest of your essay. Either way, it seems germane to the conversation and will probably come out in future forum comments.

All the Best,

Jonathan

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Jonathan J. Dickau wrote on Oct. 19, 2009 @ 19:36 GMT
Oh Well,

Yes that was my post above. I guess my login expired.

More later,

Jonathan

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Author Florin Moldoveanu wrote on Oct. 20, 2009 @ 01:16 GMT
Mark,

Thank you for the image. I am still digesting your paper, but the boundary of a boundary idea looks like the index theorems. Is this your approach?

Thanks,

Florin




Author Florin Moldoveanu wrote on Oct. 20, 2009 @ 01:28 GMT
Greetings Jonathan,

I am glad you find the essays interesting, I am looking forward to reading your comments after you are done.

Gödel’s theorem was a great inspiration for me as his proof can be translated almost one to one in the proof for the necessity of time as the only way to avoid inconsistencies in nature. The difference is at the end of the proof: in math Gödel chooses incompleteness to avoid inconsistency, in nature we choose inconsistency because events are observable (decidable). All event manifolds where the corresponding Godelization technique holds have closed causal loops. The only way to avoid inconsistency in nature is to forbid all causal loops. And this is equivalent to have global hyperbolicity, or time.

Best Regards,

Florin




Mark Stuckey wrote on Oct. 20, 2009 @ 17:34 GMT
Florin,

Let me respond to your question, "the boundary of a boundary idea looks like the index theorems. Is this your approach?" I assume you're referring to the Atiyah-Singer index theorem. We are proposing the action be constrained topologically by the boundary of a boundary principle (BBP), so one would expect this constraint to manifest itself when the index theorem is applied to the corresponding diffy q's, i.e., those obtained via the least action principle. I don't know that this would help us find solutions to our eigenvalue problem since we already constrain our solution space per experimental outcomes in a clear fashion via the path integral formalism.

The reason I mentioned our use of the BBP is that it strikes me as a local counterpart to your requirement of global hyperbolicity. Both are related to the nature of time and what Albrecht and Iglesias characterize as "the central role of quasiseparability," i.e., the need to construct trans-temporal objects. Of course, global hyperbolicity is a more stringent requirement than the BBP, since solutions to EE's always satisfy the BBP but are not always globally hyperbolic, e.g., the two solutions shown in FIG. 7 of the previous attachment. We chose to base the fundamental level on the BBP for other reasons as well, e.g., it is a tautology easily constructed from boundary operators of the spacetime chain complex of the graph and the difference operator so constructed mirrors that for coupled harmonic oscillators on the graph.

Mark

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Jonathan J. Dickau wrote on Oct. 21, 2009 @ 01:35 GMT
Hello Florin,

Thank you for this very insightful and well thought-out essay. You spell out nicely, the way in which we must remain always on the realist side of the Platonic - Math driven - approach. I really like the way you have connected Gödel's proof with relativity and light cones, demonstrating there is a zone of true but unknowable facts - in our cosmos.

I like your explanation of the composability principle, that was nice. And the connection with Quantions was interesting. Some of the statements in the final wrap-up seem to detract from your earlier message, though. Perhaps if you explained that in Cosmology, there are always realities that - while observable - will remain forever beyond the reach of experiment, the closing comments would fly. It would seem, however, that you are suggesting one day Physics will have superseded the need to answer to or explain experimental results, and this would not be entirely positive.

You are wise to assert that axiomization must be heuristic, but this demands that explaining what is actually observed will forever remain important, even paramount. The fact that some people had more faith in the models than in the data is what brought down Wall Street and almost crashed the world's economy. When the Gaussian Copula function was first introduced, it was hailed a a major advance in risk estimation, but it was fatally flawed.

The consequences for axiomization errors in Physics may not crash the world economy, but many dire consequences could emerge - if Physics has no error-correcting mechanisms. This is especially so once we pass our models on to engineers to build things with. So we must be sure they are grounded in reality. I've got to think more on this essay's premise.

But I must commend you as you explain yourself well, and have done important work showing there may indeed be an answer to one of Hilbert's most thorny problems. I'll likely have more comments but that's all for now.

All the Best,

Jonathan

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Author Florin Moldoveanu wrote on Oct. 21, 2009 @ 04:23 GMT
Mark,

Indeed, I was referring to the Atiyah-Singer index theorem. The topological constraints do help, but I do not think they are powerful enough. In general I agree with your relational point of view, but I am not very comfortable with the block idea.

Florin




Author Florin Moldoveanu wrote on Oct. 21, 2009 @ 05:49 GMT
Hello Jonathan,

Thank you for your comments. The best kept secrets are hiding in plain sight, as it was the link between incompleteness and relativity. It took me two years to fully understand Gödel’s theorem and many dead ends of trying to translate it to physics, but after finding the conceptual mapping all fell neatly into place. In retrospective, the proof now seems trivial, but...

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Mark Stuckey wrote on Oct. 21, 2009 @ 16:35 GMT
Dear Florin,

I've reread your essay in light of our conversations. It hangs together nicely now that I understand you're positing, not claiming to prove, global hyperbolicity. Now I can address my primary concern.

Many in the foundations community believe "The problem of quantum mechanics is unlikely to be solved in isolation; instead, the solution will probably emerge as we make progress on the greater effort to unify physics" (Smolin, The Trouble with Physics, p 10, 2006). Naturally we also believe "This is probably the most serious problem facing modern science" (ibid, p 9), or we wouldn't be studying foundational issues. With these biases in mind let me ask, how do you see your three principles bearing on, say, EPR-Bell phenomena, i.e., correlated, space-like separated experimental outcomes that violate Bell's inequality? The choices are usually characterized as nonseparability (constitutive non-locality) or (causal) non-locality (could also be both, of course). Naively, it seems your first principle is more in accord with nonseparability since non-locality would force a preferred frame (absolute simultaneity) to provide a causal connection between space-like separated outcomes ("provability"). A constitutively non-local structure seems better suited for maintaining the "provability" of EPR-Bell phenomena. Of course, you could relax the notion of causation as is done in backwards causation quantum mechanics, i.e., adopt statements like "A and B are causally related" rather than "A causes B" or "B causes A." You could also deny "provability" is necessary to explain EPR-Bell phenomena and provide something else altogether, but let me stop speculating and let you reply :-)

Mark

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Jonathan J. Dickau wrote on Oct. 21, 2009 @ 18:31 GMT
Hello again Florin,

I haven't looked yet to see if you've made a response to my comments, and I'm writing these comments off-line now, because I have more thoughts to share. What you are attempting to do is monumentally difficult, so you are to be applauded. I have spent some time considering related questions, and wish to offer my perspective. You may determine the value of my observations to your quest, for yourself.

I've become a big fan of Constructivism in Math and Logic, because it forces you to consider what is essential. A lot of Math and Mathematical Physics is rife with both hidden and explicit assumptions - String Theory is a good example. Constructive Math forces you to answer questions like "if we need 10 dimensions, for our theory to work, how does it propose they came to be?" It may well be that there were an infinitude of dimensions prior to the possibility for measurement, which coalesced into an array more compact over time, but we don't know. Constructive Math says a space has no specific dimension apart from the array of objects and observers (or fields) which may inhabit it, and which allow a determination of dimensionality. Does this make sense physically? I'm not sure.

In my view; there are big connections of the process of cognition, and the process by which the exploration of any field of Science becomes a means for its formalization leading to accurate and complete axiomization. As my earlier comment stated, I feel there is a necessity for some level of hierachality to arise in the formal systems we adopt, to account for all of the levels of abstraction necessary to describe the phenomena we are attempting to characterize. The trick is to make that explicit, rather than trying to sneak it in 'under the carpet.'

My first impression is that you have done us all a service, but also that your work is incomplete, or tries to make things just a little too simple. I shall look at any comments after posting this, and have another look at your paper as there are still some things I am trying to understand. I'll raise any questions in my next post.

All the Best,

Jonathan

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Author Florin Moldoveanu wrote on Oct. 22, 2009 @ 04:20 GMT
Dear Mark,

Let me explain how I see the QM problems. From my perspective, QM does not have any problems; it is the emergence of classical mechanics that is the (only remaining) issue.

In nature, we encounter observables which can be measured at the same time. Therefore observables form an algebra. Associated with observables are generators which describe the time evolution....

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Author Florin Moldoveanu wrote on Oct. 22, 2009 @ 04:30 GMT
Hello Jonathan,

I will not comment yet on your latest post to avoid starting too many threads of discussion, but I am looking forward to your comments after reading my prior reply.

Best Regards,

Florin




Owen Cunningham wrote on Oct. 22, 2009 @ 05:21 GMT
Hello Florin,

Jonathan mentioned your paper in one of his comments on my paper, so I just got around to reading much more thoroughly what I had only briefly skimmed weeks ago. I am very impressed and agree with most of your conclusions.

Robert Oldershaw and I had a run-in on his paper's forum thread, and it ended in stalemate despite the fact that he and I fundamentally agree. (This...

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Mark Stuckey wrote on Oct. 22, 2009 @ 15:01 GMT
Florin,

Thanks for your detailed reply. It doesn't appear you are familiar with the "problem of QM" since you reply to "the problems with QM," which all agree don't exist. What you say is the "problem," i.e., "the emergence of CM," is certainly viewed as the most reasonable first step to a solution -- admitting CM is not fundamental. We also agree that spacetime is the point of correspondence. You write, "In standard QM space-time are outside concepts and Bell's inequality violations appears puzzling, but this is only because the usual framework of discussion starts from space-time, a non-unitary structure. The real mystery is space time itself, but this is only an artifact of the limit process from relativistic QM to non-relativistic QM." I'm not sure I understand this statement. Are you claiming the classical spacetime structure of QFT (M4) can somehow resolve the issue? The spacetime structure of QFT introduces yet more problems, most prominently IR and UV-inequivalencies and divergences, so I have to believe you're talking about something fundamental to QFT (strings, LQG, etc.). Would you specify exactly what modifications to the M4 spacetime structure of QFT you are proposing? Again, for example, those of us in foundations take a hint from violations of Bell's inequality, considering causal or constitutive non-locality, but I assume your biases lead to alternatives.

Thanks,

Mark

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Author Florin Moldoveanu wrote on Oct. 22, 2009 @ 16:41 GMT
Dear Owen,

I do say, Jonathan speaks highly of me in your thread, and I not sure I really deserve that. I did correspond with Robert and it was only after reading his web page that I did realize the value of his ideas. It was unfortunate we did not manage to continue the discussion and it ended on rather bad terms. He is definitely onto something, but in my opinion he is approaching the discussions on too inflexible terms and he is only doing himself a disservice. I only gave him my honest appraisal, take it or leave it. But hey, we are all grownups and everyone does what he thinks is best to himself, and I wish him luck in his efforts.

Regarding the fractal idea, it is a fruitful idea in a rather large region of validity. As a TOE however, the fractal idea is an unproductive way of putting squared pegs in round holes; it is not a cogent way of understanding all that it is already known.

I will read your essay in more details, but I have to give you a disclaimer. I am not a believer in computation as a core feature of nature. The main reason is that computability is a concept invented by humans billions of years after the Big Bang, and it is not widespread all around us. The stuff physics tries to describe is ubiquitous all around us: space, time, elementary particles, electromagnetic waves, etc. Computation is not. (ignoring the latest hype of Windows 7 – ha, ha.) (By the way, I hope Windows 7 will be much better than Vista, otherwise I will get a Mac next time.)

Back on serious territory, there is a loophole in my argument and it comes from quantum mechanics which can be understood in an information setting framework, and therefore the jury is still out on this.

Another argument against computability is the Turing test of proving intelligence. To this day a computer cannot even remotely qualify to pass this test. (One roadblock is the serial nature of the computers vs. the massive parallelism of the brain, but even massive parallelisms are not enough; otherwise newborns would solve quantum mechanics problems the day they are born.) Let’s suppose for the sake of argument that a million years from now computers will become so powerful that we cannot tell them apart from humans. Then, the situation described in “The Matrix” can be a conceivable reality and no one would then be able to distinguish between reality and a brain in the vat case. In fact we could all be some computer simulations inside someone’s computer which in turn could be yet again another simulation in a higher reality, ad infininum in a truly fractal structure. And I find this 1. personally unpalatable, and 2. very unlikely.

In summary, I will read your essay, but chances are that I may not agree with it. It is a fact that I was wrong in the past multiple times and I am not the holder of absolute truths and do not be discouraged if I will not agree.

Regards,

Florin




Owen Cunningham wrote on Oct. 22, 2009 @ 20:35 GMT
Hi Florin,

I am grateful for your willingness to put your cards on the table with regard to the computationality, or lack thereof, of nature. I am a (fervent) believer that computation is a core feature of nature, and I will now make a few observations that I hope at least somewhat weaken your conviction to the contrary.

Your first objection is that "computability is a concept...

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Author Florin Moldoveanu wrote on Oct. 23, 2009 @ 03:17 GMT
Hi Owen,

I simply cannot pass on an excellent discussion, so I will try to reply to your post before a careful reading of your essay. I will try to answer paragraph to paragraph, but most of the time I will not copy your original text to simplify the discussion. I hope it will be clear.

On your first rebuttal on the existence of mathematical structures before they were discovered, I...

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Author Florin Moldoveanu wrote on Oct. 23, 2009 @ 05:13 GMT
Mark,

I am not getting your point in your first few sentences but let me try to explain it in a different way.

Relativistic QM is based on quantionic algebra, while the standard non-relativistic QM is based on complex numbers.

When the Compton length times the gradient of \psi / psi is much smaller than 1, relativistic QM reduces to standard non-relativistic QM and the Zovko rule becomes the Born rule. For a plane wave the rule above reduces to the usual non-relativistic limit of small speeds: v/c




Author Florin Moldoveanu wrote on Oct. 23, 2009 @ 05:39 GMT
Mark,

I am not sure where the rest of my answer went, it got truncated and I did not save it in a file and I have to write it again. Sorry for the delay.

@FQXi

the text file after a double smaller than sign got truncated.




Author Florin Moldoveanu wrote on Oct. 23, 2009 @ 20:48 GMT
Mark,

Second time’s the charm.

There is nothing wrong, incomplete, or strange about QM if one considers the composability principle as the starting point. QM comes in 2 flavors: relativistic QM and standard non-relativistic QM.

Relativistic QM:

- is based on quantions

- uses the Zovko rule

- is the only non-unitary representation of abstract...

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Frank Martin DiMeglio wrote on Oct. 23, 2009 @ 22:36 GMT
Florin:

Shroedinger suggested "a new type of physical law" in response to the perplexities of life. Do you have any suggestions/ideas on what that might be?

What would be the applicability/limitations of mathematics in regard to same?

Thanks. Frank

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amrit wrote on Oct. 24, 2009 @ 11:26 GMT
"Heuristic rule. Identify all mathematical properties of

the physical world that are universally valid in the real

world and are not universally valid in the abstract world

of mathematics."

My comments: Physical world has no mathematical properties, physical world has only physical properties. What is valid in physical world is always valid in mathematical world. For example 1 plus 1 aple is 2 aple in physical world. In math world 1 + 1 = 2.

What is valid in abstract math world is not alwys valid in physical world. Hawking explained inflation phase as multiplication of negative gravitational and positive mass energy with mathematic. He sad that as -1 + 1 = 0 also sum of gravitatrional energy and mass energy in the universe is zero. In inflation both energyes are multiplaying. This explanation is against first low of thermodinamics. So in math -1 + 1 = 0 but this does not mean that energy can be created out of nothing.

Physics canot be explained with mathematics. Physics can only be described with mathematics. Awakened observer is aware if this descriptions are corresponding to the physical world or not. He distinquish clearly between models of the world and world itself.

Heuristic rule is contradicting itself.

yours amrit

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Author Florin Moldoveanu wrote on Oct. 24, 2009 @ 13:56 GMT
Frank,

I am not aware with Schrödinger’s suggestion and therefore I cannot comment on it. On the other hand Wigner spoke on the unreasonable effectiveness of mathematics in the natural sciences. I agree with Wigner and I hope that my essay shows way this is so.

Thanks,

Florin




Author Florin Moldoveanu wrote on Oct. 24, 2009 @ 14:28 GMT
Amrit,

You say: “What is valid in physical world is always valid in mathematical world.” I agree.

You say: “What is valid in abstract math world is not alwys valid in physical world.” I do not agree.

It is not always apparent right away how a new mathematical structure applies in nature, and there is a time lag between the discovery of new math and the recognition on where and how it applies in nature, but history of math is full of examples of realizations of how mathematical discoveries have a physical relevance.

You also state: “Physics canot be explained with mathematics. Physics can only be described with mathematics.”

This to me looks like meaningless hair splitting philosophy. If you describe it, and agrees with experiments, and make new predictions validated by experiments, then you explain it.

“Awakened observer is aware if this descriptions are corresponding to the physical world or not.” Again, this sounds just like philosophy playing with words. Can you extract mathematical consequences from it?

“He (Awakened observer) distinquish clearly between models of the world and world itself.”I agree, but again can you extract mathematical consequences from it?

“Heuristic rule is contradicting itself.” No. Only your (semantic) model of my heuristic rule is contradicting itself. Is it as you said, you have to distinguish between the model and the real thing.

If from the heuristic rule I prove that 1 = 2, then the heuristic rule is inconsistent. If on the other hand I prove from it that space time had 128 dimensions, then it is just wrong, a fruitless fantasy.

A lot of people find quantum mechanics distasteful, but the fact remains that QM is validated by experiments. You may find my heuristic rule distasteful based on your philosophical ideas, but the ultimate judge is agreement with experiments, and so far all its mathematical consequences were validated by experiments. This is not a guarantee that the heuristic rule will continue to generate mathematical consequences validated by nature in the future, but it looks darn good for now.

Yours Florin




Mark Stuckey wrote on Oct. 24, 2009 @ 15:09 GMT
Florin,

Thanks for your detailed replies, I've enjoyed our exchanges. Let me respond to specific excerpts.

"There is nothing wrong, incomplete, or strange about QM if one considers the composability principle as the starting point. QM comes in 2 flavors: relativistic QM and standard non-relativistic QM."

Again, everyone agrees there is nothing wrong with QM. Most agree, however, that QM (causally and/or constitutively non-local) is incompatible with CM (causally and constitutively local), yet both work very well in their respective domains, so we've a situation akin to the late nineteenth and early twentieth centuries with EM and CM, resolved by SR. How you choose to label this situation is semantics, but if you believe physics should be integral as well as coherent, you acknowledge this incompatibility is a problem. I don't see anything in your approach to resolve it.

"Non-relativistic QM is based on complex numbers, used the Born rule, The wavefunction lives in a Hilbert space."

You can Wick rotate the Feynman path integral to a Euclidean path integral so that statistical analysis via a partition function replaces the Born rule. Of course, the wave function can be considered to reside in spacetime in the path integral approach since future boundary conditions are employed.

"The measurement problem is unsolvable in standard non-relativistic QM because one can prove that there are no allowed discontinuities in probabilities there."

The MP is resolved by those interpretations using future boundary conditions, e.g., path integral approaches and backwards causation.

"All QM interpretations except Copenhagen and Rovelli (which is a stronger version denying any ontological value to the wavefunction), are misguided and they are rooted in classical mechanics preconceptions."

I can disprove this statement with a counterexample -- RBW is constitutively non-local which is in discord with CM's constitutive locality.

"With the exception of the measurement problem (which can be proved that it is not solvable in this context), non-relativistic QM is fully understood at this time."

Again, the MP can be resolved, but to say that QM is fully understood assumes you can live with the lack of integrity created by CM and QM. Many cannot, thus foundations is a thriving area.

"You already presented a good argument in your paper about why Haag's theorem is irrelevant in the IR range and why the Stone- von Neumann theorem violation is physically irrelevant."

We did not argue that UV inequivalence is physically irrelevant. Quite the contrary, it points towards the need for physics fundamental to the Standard Model. That is what is meant by "QFT as an effective theory."

Looking forward to your next response!

Mark

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Frank Martin DiMeglio wrote on Oct. 24, 2009 @ 19:33 GMT
Hi Florin:

This is a very important post Florin, and it has very clear relevancy/bearing upon your essay. Your clear and responsive reply is much appreciated.

In follow-up to your prior reply, how does your essay/ideas account for the following? -- You must admit that this post is very relevant to the mathematical feasibility of any possible TOE, correct? If not, why (specifically...

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Author Florin Moldoveanu wrote on Oct. 25, 2009 @ 00:18 GMT
Mark,

I too enjoy this exchange, and although we do not yet seem to be on the same page, we are converging.

“Again, everyone agrees there is nothing wrong with QM.”

Then let me quote your earlier post:

“Many in the foundations community believe "The problem of quantum mechanics is unlikely to be solved in isolation; instead, the solution will probably emerge as...

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Author Florin Moldoveanu wrote on Oct. 25, 2009 @ 00:52 GMT
Hi Frank,

You are not asking questions that you did not ask in the past. Therefore my answers are still the same.

You have to derive mathematical consequences from your ideas. Just stating something it does not make it true; you need a proof.

The bottom line is that your approach is not physics.

Florin




Frank Martin DiMeglio wrote on Oct. 25, 2009 @ 06:36 GMT
Florin, you do not have the conceptual mastery/understanding/knowledge of experience in general to be properly and competently discussing the possibility of a TOE.

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amrit wrote on Oct. 25, 2009 @ 10:00 GMT
Hi Florin

You did not comment Hawking explanation of inflation with math. This is where what is correct in math cannot be always correct in physical world.

yours amrit

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amrit wrote on Oct. 25, 2009 @ 10:02 GMT
PS

What is valid in abstract math world is not alwys valid in physical world. Hawking explained inflation phase as multiplication of negative gravitational and positive mass energy with mathematic. He sad that as -1 + 1 = 0 also sum of gravitatrional energy and mass energy in the universe is zero. In inflation both energyes are multiplaying. This explanation is against first low of thermodinamics. So in math -1 + 1 = 0 but this does not mean that energy can be created out of nothing.

pleace comment

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Author Florin Moldoveanu wrote on Oct. 25, 2009 @ 13:34 GMT
Dear Amrit,

I am not aware of the specific statement Hawking made and that is why I did not comment on it. However, it looks correct to me, and I think you meant the second law of thermodynamics, but to cover all ideas, I will comment on the first, second, and zero laws of thermodynamics.

Let’s take a simpler system than the entire universe. Let’s consider our solar system. We need a lot of rocket energy to escape the solar attraction and send a spaceship to a nearby star. This is because gravitational energy is negative due to gravity’s attractive nature. Kinetic energy is positive on the other hand.

Now back on the inflation period. What is the total energy of the entire universe? Any answer is arbitrary, and let’s pick zero. (In fact current measurements support this idea.) As the universe started evolving, elementary particles started to be formed and you get a big positive energy because of this. This was counterbalanced by the negative potential energy of gravity. The first law of thermodynamics states that the total energy is conserved, so +1-1 = 0 and there is no contradiction with a zero total energy.

Second law of thermodynamics: entropy or disorder can only increase. This means that compared with today, the early universe must have had an incredible amount of low entropy. How is this possible? The answer is yet again gravitational. The maximum gravitational entropy is in a black hole and it is proportional with its surface. In the beginning there were no black holes and if you compute the total entropy then and now you will see that the total entropy then (including gravitational entropy) was indeed lower than the total entropy now.

But how about the zero low of thermodynamics? Should we just expect a “thermal death” of the universe where everything will evolve towards a common low temperature? Normally yes, but there are objects in this universe of negative specific heat, that is they get hotter when they lose energy. What are they? They are the stars? And how is this possible when ordinary objects get colder when losing energy? Yet again the answer is gravity.

Yours,

Florin




Lawrence B Crowell wrote on Oct. 25, 2009 @ 21:58 GMT
I notice there is a bit of a debate about inflation and Hawking radiation. Hawking Gibbon radiation acts upon the cosmological horizon in much the same way it does with radiative decay of a black hole. The universe is approaching asymptotically a de Sitter vacuum as dark energy approach 100% of energy in the spacetime. From this classical attractor point the spacetime will quantum mechanically...

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Frank Martin DiMeglio wrote on Oct. 25, 2009 @ 22:15 GMT
Hi Florin. Your understanding of the ultimate nature of sensory experience, reality, and cosmology is basically and significantly deficient, and the following proves it.

Compared to the blackness of space, the increased transparency/invisibility of space in astronomical/telescopic observations is very important. This allows us to see farther. But this also means, again, that space is becoming increasingly invisible/transparent. This occurs in dreams, as space is increasingly invisible in dreams; in fact, the experience of space in dreams is both invisible AND visible. (This is why you may or may not touch what you see in the dream as well.) Astronomical observations, to a significant extent, are interactive creations of thought. My essay talks about this.

The reduction in the range and extensiveness of feeling in dreams and the increase in the invisibility/transparency of space therein not only relate to the sensory experience [therein] being more like thought, but this also relates to/is consistent with the relative reduction in the brightness/feeling of the red Sun (including the redshift). Astronomical/telescopic observations have significant similarities with dreams.

Note the transparent space/sky around the larger and red [setting] sun.

The line (or feeling) of gravity is altered/reduced -- in comparison with the Sun being overhead, when it is brighter -- so the Sun appears differently (and is not as bright) when it is in front of us. This is consistent with the reduction of gravity/feeling/brightness in the dream, with the increased invisibility/transparency of the space therein, and with the eyes being (basically) locked forward. (Telescopic/astronomical observations make the objects larger, or they could not be seen at all.)

(Note that thoughts are relatively shifting and variable, so dream vision is also relatively shifting and variable.) In relation to the increased transparency/invisibility of space, is there not a uniformity of gravity/acceleration (that would provide an additional binding energy)regarding the outer stars accelerating more than they should be (in, say, spiral galaxies)? Consider objects near Earth in the invisible/transparent space/sky.

Dreams make thought more like sensory experience in general, thereby unifying gravity and electromagnetism/light. Note that the Earth is in a relatively smaller space (the transparent/invisible sky) compared to that of the Sun.

The setting Sun looks more like the Earth because it feels more like the Earth WHEN SEEN. (And because it is also seen in/with a transparent/invisible sky.)

The integrated extensiveness of being and experience go hand-in-hand.

The world requires and involves man.

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Mark Stuckey wrote on Oct. 26, 2009 @ 01:47 GMT
Florin,

After reading our exchanges Silberstein said, "You guys are talking past one another." You're working in the algebraic regime and I in the geometric. The measurement problem is intractable for you and easily solved for me. Locality is a central mystery for me and is a non-issue for you. I think our biases preclude meaningful conversation between us.

Thanks for the discussion, it was fun :-)

Mark

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Author Florin Moldoveanu wrote on Oct. 26, 2009 @ 04:15 GMT
Mark,

I do agree: it was fun. But algebra and geometry are very similar. And locality was a big mystery for me as well. Locality is not a standard QM concept in its unitary incarnation. Relativistic QM solves this mystery because of its non-unitary representation which does included the orthogonal group. The classical Lie groups are all about what is preserved under their transformation, and locality is only possible under the orthogonal group. Perform the limit from relativistic QM to non-relativistic QM and all sorts of “paradoxes” arise, like EPR. Those are very hard to accept in standard non-relativistic QM setting, but all the mystery disappears in the relativistic case.

I do not believe in backward causation, but a proof is a proof and I think I do have the proof for the no go theorem of solving the MP in nonrelativistic QM, and you claim to have the proof to the contrary. Regardless of our biases, at most one of us is right and maybe we are both wrong.

I am in the process of preparing a paper about QM where I hope I will make my case clear. Do you have a paper I can read where the proof of the MP is presented? (If you are right, it will at least space me the embarrassment to try to publish something wrong.)

Thank you,

Florin




Author Florin Moldoveanu wrote on Oct. 26, 2009 @ 04:23 GMT
Lawrence,

Thanks for your feedback. I think I told you in the past about Segal’s Chronometric Cosmology ideas and that while interesting, it did not looked very believable. I recently discovered this link: http://www.astro.ucla.edu/~wright/segal_errors.html which I find it interesting.

Regards,

Florin




Mark Stuckey wrote on Oct. 26, 2009 @ 15:50 GMT
Florin,

"Locality is not a standard QM concept in its unitary incarnation. Relativistic QM solves this mystery because of its non-unitary representation which does included the orthogonal group."

I don't understand how it is that one needs to resort to relativistic QM (RQM) to explain experiments in perfect accord with NRQM. Anything in RQM that needs to be invoked to resolve this...

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Lawrence B. Crowell wrote on Oct. 26, 2009 @ 17:39 GMT
The chronometric universe is not what I was referring to, at least as I understand it. The universe started out with low entropy probably because the initial state of the universe occupied a very small number of states or a small sub-Hilbert space. The existence of the cosmological horizon does mean there is a thermal signature to the vacuum state. The horizon means there is unidirectionality in the transmission of information: we can receive information from the past and far away, but we can't send a signal to the future of these sources. So the de Sitter spacetime or vacuum is not quantum mechanically stable. This means the spacetime can adjust the cosmological constant to a smaller value through the emission of radiation. That radiation has a huge wavelength > r = sqrt{3/Λ}. So the cosmological horizon will over time recede away. This process might also involve a tunneling process, where a part of that vacuum energy enters into another region or a nascent cosmology.

George Ellis wrote a paper somewhat related to the problem of measurement. I wrote a post there last week, where I indicate a possibility for how gravity plays a role in the emergence of a measurement outcome and the classical or macroscopic world. Ellis offers what might be called a top-down perspective. In some manner what we might call an existing universe is one which has classical content.

Cheers LC

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Lawrence B. Crowell wrote on Oct. 26, 2009 @ 19:29 GMT
The connection between classical and quantum physics is in the standard sense a replacement of Poisson brackets with commutators. There is one little hitch though. In classical mechanics there is no Poisson bracket between the Hamiltonian and time. Similarly with quantum mechanics there is no commutator between the Hamiltonian and a time operator. There have been proposals for a time operator, but so far no such idea has been presented with has satisfied the physics community. Yet in quantum physics by extension with wave mechanics there is an uncertainty relationship between energy and time. This is a hole in the standard or canonical quantization idea.

This is made more evident with relativistic quantum field theory. Time is defined on Cauchy surfaces according to equal time commutators. So time is defined as a set of imaginary clocks set by a coordinate condition on an initial spatial surface. Yet this differs from the relativistic invariant concept of time as a proper interval. So there are two notions of time in our physics. So in effect the bridge between these two areas of physics involves a subtle relationship between these two concepts of time that we really do not understand.

Cheers LC

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Frank Martin DiMeglio wrote on Oct. 26, 2009 @ 22:53 GMT
Hi Florin:

How do you see your essay/mathematical approach as accounting for/addressing the following:

Schroedinger was puzzled by life enough to suggest "a new type of physical law." -- p. 258 -- See Paul Davies book The Fifth Miracle. Also see De Duve: "Life and mind emerge...as natural manifestations of matter, written into the fabric of the universe." -- p.252 thereof. And Darwin: "The principle of life will hereafter be shown to be a part, or consequence, of some general law" -- p.252 hereof. Look at the words "GENERAL law"!

From Jonathan Dickau (referring to my ideas), and I quote him in the following two paragraphs:

"I just re-read your second post above and it made a bit more sense of something you were saying in the earlier post. Your statement at the end "How space manifests as electromagnetic/gravitational energy is a central and very valuable physical idea." is right on. Perhaps the key, as you say, is to recognize that there is both an attractive and repulsive component at work - which changes the effective action at different levels of scale. This makes unification simpler."

"We end up 1) Balancing/unifying scale and 2) Balancing attraction and repulsion in conjunction with space manifesting both gravitationally and electromagnetically. (Think wave/particle)."

This post is very important, and it is undoubtedly relevant to your assertions/essay. I would appreciate a reply. Thank you.

FQXi -- do not delete this entry.

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Author Florin Moldoveanu wrote on Oct. 27, 2009 @ 03:52 GMT
Lawrence,

I was discussing the chronometric ideas as a side item only. In QM time is not an operator because energy is bounded from below and this precludes a hermitian observable for time. Still people introduce the “time of arrival” idea to explain the energy-time uncertainty inequality.

Florin




Author Florin Moldoveanu wrote on Oct. 27, 2009 @ 04:06 GMT
Mark,

I've got a copy of your "Why quantum mechanics favors adynamical and acausal interpretations such as Relational Blockworld over backwardly causal and time-symmetric rivals. Studies in History & Philosophy of Modern Physics 39(4), 736-751 (2008)." paper. I will get back to you after I will read it carefully.

Florin




Owen Cunningham wrote on Oct. 27, 2009 @ 17:12 GMT
Hi Florin,

I'm posting a copy of this message in both your and my forum.

I have read and enjoyed your most recent posts and know I owe you a response, but recent personal events have conspired to keep me away from physics for at least another few days. I will reply as soon as I can.

Again, thanks for your time and interest.

- Owen

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Mark Stuckey wrote on Oct. 27, 2009 @ 17:23 GMT
Florin,

The paper you have is the most philosophical of our work. If you want a refutation of backwards causation, then that's the paper. If you want to see the physics behind our interpretation (due largely to A. Bohr, Mottelson, Ulfbeck, Kaiser, etc.), then read the FoP paper cited previously. If you want to see our interpretation of QFT and our graphical path integral approach, see 0908.4348. We would love to have your feedback on RBW, but I don't know that it will bear on your program.

Mark

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Author Florin Moldoveanu wrote on Oct. 28, 2009 @ 04:22 GMT
Mark,

I have finished reading your paper (and quant-ph/0205182). Very interesting stuff overall. What I would like to read next is to see how exactly you are completely solving the measurement problem in RBW. Do you have a suggested paper on that?

Regarding RBW itself, I agree with the R part, but not with the BW part which I think it is an over-generalization. The arguments you use for the bloc-world, acausal and adynamical interpretation, I can use myself to justify the Bayesian interpretation of the wavefunction collapse. In mathematics, in an axiomatic system, any result which is derived from axioms is acausal and adynamical. All mathematical theorems are already there the moment one selects the axioms.

In my essay I mention that QM can be obtained by 3 axioms: composability, consistent reasoning about a physical system, and a technical separation axiom. It is the consistent reasoning part which leads to unitary groups and the Bayesian interpretation. The variants of Hardy’s experiment and the EPR state can also be explained as consistent reasoning about all available evidence (including the “D” click). And Bayesian reasoning is just like obtaining a theorem in mathematics: acausal and adynamical.

I have still to read about how you unify relativity with QM in the RBW framework, but I have to say I am very skeptical: relativity demands orthogonal groups and there are no orthogonal groups in nonrelativistic QM. Also I do not quite see how you can claim to solve the measurement problem completely inside RBW. Bayesian interpretation, and decoherence solve part of the problem. In my opinion, the remaining part is to provide a mechanism for the emergence of superselection rules.

Florin




Mark Stuckey wrote on Oct. 28, 2009 @ 18:54 GMT
Florin,

For our resolution of the measrument problem see Stuckey, W.M., Silberstein, M., Cifone, M.: Reconciling spacetime and the quantum: Relational Blockworld and the quantum liar paradox. Foundations of Physics 38(4), 348-383 (2008). Again, it does not address the MP per your requirement of a dynamical approach. We use the path integral approach which includes future boundary conditions so we can work in spacetime but it is inherently a BW view since one is supplying a specific outcome for the calculation. Are you familiar with the path integral approach to physics? As we show in our FQXi essay, it is very different than the "causal" approach of differential equations. Maybe you should read our essay to decide whether you want to go further down this rabbit hole :-) If so, then you can try the FoP paper.

Our unification of relativity and QM is via an underlying discrete structure so we intend to make correspondence with GR via Regge calculus. See Figure 8 of QFT paper and associated text for an explanation. The continuum approximation of our result will not be a differentiable manifold because it will be constitutively non-local as explained therein. One has to ignore this non-locality to obtain the GR spacetime, thus GR is only an approximation. Your critique is based on the assumption that we expect to recover GR exactly, while we expect to recover GR plus additional non-local structure via discrete mathematics.

Sorry, this is a lot of info about RBW posted on your thread. Maybe we should take such questions to my thread in the future. Let us strive to keep your thread about your approach :-)

Mark

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Jonathan J. Dickau wrote on Oct. 28, 2009 @ 21:35 GMT
Hello again Florin,

I re-read your essay, and I must say I'm even more impressed. It is elegant, how you are able to reduce such a complex process (or problem) to a few simplicities. I still feel that it is somehow a little too simple, but I'm not really sure that I have an objection as such. There's more to say, but I'm away at a conference, and my time at the library is about at an end.

I will re-visit this thread when back home, this weekend, and comment more extensively.

All the Best,

Jonathan

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Author Florin Moldoveanu wrote on Oct. 29, 2009 @ 03:53 GMT
Mark,

I’ve read “Stuckey, W.M., Silberstein, M., Cifone, M.: Reconciling spacetime and the quantum: Relational Blockworld and the quantum liar paradox. Foundations of Physics 38(4), 348-383 (2008).”, but I did not double check the math myself. I think I understand now your position, but I believe that there is a case where your RBW interpretation cannot fully answer the measurement problem: what happens after decoherence?

All the examples you give, I can explain them in the Bayesian formalism just fine. But in this interpretation, it is clear that one cannot explain the emergence of superselection rules as Bayesian gain of knowledge, because this is outside the traditional non-relativistic QM which incidentally can be obtained by the Bayesian interpretation. Proving superselection rules from Bayesian interpretation amounts to inconsistency.

One thing that looks suspicious is the K4-NRQM because this clearly does not satisfy the Lorenz transformation, but again, I did not double checked your math and I am not sure to what degree you are using this. I am very familiar with the path integral approach, but I have never worked in this area myself.

About the BW interpretation, I simply cannot agree with it. In this interpretation there is no freedom and all future history is pre-determined. Non-relativistic QM is perfectly compatible with this interpretation, but not relativistic QM. (Check out A. Connes and C. Rovelli, Von Neumann algebra automorphisms and time-thermodynamics relation in general

covariant quantum theories, arXiv:gr-qc/9406019 (1994).) A RBW interpretation is time independent and this runs aground of the Tomitza-Takesaki theorem which provides a God-given time parameter.

Florin

PS: I had also posted this on your thread and we can continue the RBW discussion there.




Anonymous wrote on Oct. 29, 2009 @ 04:06 GMT
Hello Jonathan,

My approach is indeed very simple, and the conceptual aspects are really straightforward, but wait till you see the math that comes with it. My biggest worry is that I simply do not have enough time to master the entire math which is relevant for my approach.

I am looking forward to your comments.

Best regards,

Florin

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Owen Thomas Cunningham wrote on Oct. 29, 2009 @ 20:20 GMT
Hi Florin,

I just posted a response to your comments on my thread (517). Looking forward to your reply.

Thanks,

Owen

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Frank Martin DiMeglio wrote on Oct. 31, 2009 @ 05:31 GMT
Hi Florin:

I had posted to you previously:

Time has 3 parts -- past, present, and future. Any TOE must not only address the integrated extensiveness of experience in general, but it must address this as well. You cannot have a TOE whereby time is dimininished, in other words. The integrated extensiveness of being/thought/experience must address the integrated extensiveness of time. The totality of time must be understood in conjunction with, and inseparable from, the present. Physics, to date, has failed miserably at this.

Your reply was:

Frank,

You say: "The totality of time must be understood in conjunction with, and inseparable from, the present. Physics, to date, has failed miserably at this."

Present is a part of time in both Newtonian physics and special relativity. I do not understand in what way physics has failed.

Florin

My question is/was: How do you see General Relativity in relation to my paragraph above?

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Lawrence B. Crowell wrote on Nov. 1, 2009 @ 00:53 GMT
I have been away from here for a while. Just a few comments that I have. The nonexistence of a time operator is I think related to the fact that general relativity is not directly quantizable. I think that, as I allude to in my essay (which is a sketch of sorts really) that the underlying system in the Jordan exceptional matrix is a Skyrmion field theory that is abelian. This is quantized. Spacetime emerges as a classical or semi-classical field theory at lower energy.

There are two notions of time, one in relativity which is the proper interval. The other in quantum field theory which is defined by equal time commutators on a spatial surface, which is chosen in a coordinate condition. So quantum field theory requires that time is something "bolted down" on spatial surfaces. This is a fundamental departure between general relativity and quantum field theory.

Cheers LC

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Author Florin Moldoveanu wrote on Nov. 2, 2009 @ 14:23 GMT
Hi Owen,

I replied on your thread and we can continue the discussion there.

Thanks,

Florin




Author Florin Moldoveanu wrote on Nov. 2, 2009 @ 14:42 GMT
Lawrence,

“The nonexistence of a time operator is I think related to the fact that general relativity is not directly quantizable. I think that, as I allude to in my essay (which is a sketch of sorts really) that the underlying system in the Jordan exceptional matrix is a Skyrmion field theory that is abelian. This is quantized. Spacetime emerges as a classical or semi-classical field theory at lower energy.”

I found this hard to believe. Standard QM does not have anything to do directly with gravity (unless Penrose is right). Also time is related to the Lie part of QM, and not the Jordan part.

Cheers,

Florin




Lawrence B. Crowell wrote on Nov. 2, 2009 @ 16:19 GMT
Standard QFT is set up according to equal time commutators on a spatial surface. In special relativity this is a rather straight forward procedure. For curved spacetime this results in nonunitarity or unitarily inequivalent representations of states. This is seen in the Bogoliubov transformation. So going back to the special relativity case this does mean that a coordinate condition is established globally, or a frame is chosen, and the wave dynamical equations integrated from there. These are coordinate times specified for each of the "infinite" number of harmonic oscillators defined by the partial differential wave equation. In the case of curved spacetime there are of course hyperbolic transformations between local frames which determine connection coefficients. This makes the QFT in curved spacetime "odd."

Gravitation only really tells us that one definition of time is physically realistic. This is proper time, or the invariant interval. This is different both qualitatively and quantitatively from the definition of time for quantum wave dynamics.

Cheers LC

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Steve Dufourny wrote on Nov. 7, 2009 @ 11:13 GMT
Hi Lawrence ,Florin,Frank ,Owen ,Jonathan ,...

It is a beautiful thread .

Dear Florin ,

Happy to see your scores ,good luck .

But I have an ? ,you say

I found this hard to believe. Standard QM does not have anything to do directly with gravity

I agree it is hard to beleive indeed .All is dependant and linked .The cause of the gravity comes from the interior and not from the exterior in my opinion but of course all thinks like he wants and interprets in function of his datas and tools .Perhaps some synchrnizations are possible between the maths and physics .There perhaps the axiomatization will become synchronized with reals .

In all case your method is relevant ,congratulations .

Like several about these extrapolations .I am persuaded what if yoyu work all in team ,your results shall be better .For exemple ,and I forget some people of course ,Let's imagine if You ,Florin ,Lawrence ,Ray,Jason,Lisi,Girn,georgina,...focus on one system .I am persuaded that the results shall become very interestings.The complementarity is fundamental ,the ideas of several are better than the ideas of only one .

In all case I wish all the best ,good luck .

Regards

Steve

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Author Florin Moldoveanu wrote on Nov. 8, 2009 @ 00:42 GMT
Hi Steve,

Thank you for your kind words. Gravity is just a harder problem, but I have no doubt the solution will be found.

Regards,

Florin




Emile Grgin wrote on Nov. 9, 2009 @ 23:30 GMT
Hi Florin,

I like your idea by which time solves the antinomies in mathematics. Let me rephrase it: Let's say that in a system of axioms it is possible to derive the implication "A implies notA" for some proposition A. In the absence of time (as is the case in mathematical logic), the implication is immediate, meaning that A and notA coexist, which is implossible. But with the sightest delay in the implication (as is the case in the electronic implimentation of logic) A and notA alternate. Only one of them holds at any instant, and we have a square wave.

Reards, Emile.

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Author Florin Moldoveanu wrote on Nov. 10, 2009 @ 06:03 GMT
Emile,

I am glad you liked it. The concept of time is a bit more complicated than simply avoiding antinomies. In logic, there is this branch called paraconsistent logic which has major applications in computers for example.

Because in nature only a handful of mathematical structures are unique/distinguished/used by nature, we do not need to eliminate all math antinomies, but only a small subset, those corresponding to liar’s paradox. One key to the proof is the realization that global consistency conditions impose unphysical consequences on local physics, and therefore only global hyperbolic space-time is free of contradictions.

I am thinking that there must be some categorical proof of the statement that global consistency is against local freedom, because we encounter this in other domains besides CTC spaces.

In human societies for example, totalitarian closed societies impose global constraints on individuals violating their (local) human rights. In phase space, a symplectic structure does allow for closed evolution curves, but on a symplectic manifold one does not encounter the same freedom as on a metric manifold. There, arbitrary coordinate changes do not preserve Hamilton’s equations, and a sympectic manifold has only global invariants while a metric manifold can have local invariants.

Because nature is not one giant mathematical structure, but it is made out of many mathematical structures, there is an inherit freedom of how to combine them and it is this freedom that demands the existence of time. This picture is consistent with Barbour’s ideas and with the LQG approach.

Still, in a CTC space, paradoxes can not be avoided, and an ill defined Cauchy problem does not become well defined by itself. The existence of time and non existence of CTC spaces should be a consequence of something else. The natural mechanism for the emergence of globally hyperbolic time is QM. There are enough mathematical results showing that one no longer needs to postulate global hyperbolicity and time, but the time problem will be fully solved when we will have a sensible quantum gravity theory.

Regards,

Florin




Lawrence B. Crowell wrote on Nov. 12, 2009 @ 19:21 GMT
A CTC spacetime only makes sense if the spacetime is compartmented such as the Taub-NUT spacetime. There a region with closed null curves partitions the spacetime into achronal region and a CTC region. The spacetime is similar to a black hole metric, but where time serves the role of the radius and horizon length. A spacetime, or region of a spacetime, with CTC means there does not exist Cauchy surfaces of data which are spacelike everywhere. This is likely not physically realistic, unless this region is bounded by a horizon or is separated from a chronal region by some geodesic incompleteness.

Cheers LC

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Author Florin Moldoveanu wrote on Nov. 13, 2009 @ 15:29 GMT
Lawrence,

A Cauchy surface is essential to Born’s rule as was pointed out by Jacobson otherwise the expectation values are not well defined. Whenever interactions are present, a CTC space leads to loss of coherence and Boulware and Hawking showed that in separate papers. (It is easy to se why: a particle is emitted at one point in space-time, travels around a CTC loop, acquires a phase difference and is re-absorbed at the point of creation breaking coherence and unitarity).

Florin




Lawrence B. Crowell wrote on Nov. 13, 2009 @ 18:38 GMT
A quantum particle on a CTC can also in effect be duplicated. It comes back to some epsilon distance from its point of emission and emerges as two particles. This is a cloning procedure, which of course can't be unitary. A spacetime region with CTCs is at best a region bounded by some horizon, or null geodesic incomplete boundary region. The non-chronal region with CTCs then might act as a tunneling region or as a source for quantum fields emitted into a chronal region. The bottom Taub-NUT region, or the timelike interior region of a Kerr-Neumann-Nordstrom black hole metric are examples of this. Yet, we the exterior observers do not directly observe backwards casual regions, or observe information propagated back in time.

Cheers LC

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Author Frank Martin DiMeglio wrote on Dec. 12, 2009 @ 17:06 GMT
Hi Florin.

FQXi -- Stop deleting my posts.

What are the limitations/possibilities of mathematics in regard to the below?

Your essay is going to have to address the following. There is no [legitimately] getting around this. Also, how do your see your essay as being consistent or inconsistent with the following please?

Since dreams make thought more like sensory experience (including gravity and electromagnetism/light) in general, the idea of "how space manifests as electromagnetic/gravitational energy" is not only demonstrated in dreams (as I have shown), but this idea is then ALSO understood to be NECESSARILY central to an improved understanding of physics/experience in general.

According to Jonathan Dickau, my idea of "how space manifests as electromagnetic/gravitational energy" is "right on" as a central and valuable idea/concept in physics.

Also, how do you account for the following:

Do you understand the GIGANTIC significance of the following three statements taken together?:

1) The ability of thought to describe OR reconfigure sense is ultimately dependent upon the extent to which thought is similar to sensory experience.

2) Dreams involve a fundamental integration AND spreading of being, experience, and thought at the [gravitational and electromagnetic] MID-RANGE of feeling BETWEEN thought AND sense.

3) Dreams make thought more like sensory experience IN GENERAL (including gravity and electromagnetism).

Now, also consider the following:

These are the essential parameters/requirements regarding the demonstration/proof of what is ultimately possible in physics.

1) Making thought more like sensory experience in general.

2) Space manifesting as gravitational/electromagnetic energy.

3) Balancing/uniting scale.

4) Exhibiting/demonstrating particle/wave.

5) Repulsive/attractive.

What is ultimately possible in physics cannot (and should not) be properly/fully understood apart from this great truth:

The ability of thought to describe OR reconfigure sense is ultimately dependent upon the extent to which thought is similar to sensory experience.

This is a very important post, and it is very relevant to your essay claims.

FQXI -- DO NOT DELETE THIS POST.

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Author Florin Moldoveanu wrote on Dec. 16, 2009 @ 14:28 GMT
Errata:

Page 5, second paragraph, line 4:

Change “background invariance” to “background independent”

Page 5, second paragraph, line 10:

Change “approached” to “approach”




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