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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.

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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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Dear Doug Huffman,

What assertion are you referring to?

Thank you.

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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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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.

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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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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.

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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...

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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 be so accurately described by an "abstract" system like math. For me, math is as relational as you supposed it to be. But what are the relations math deals with? Human relationships obviously deal with humans, does math therefore deal with *numbers*?

In my opinion, maths (without physics) is at first about quantities. It's about the relation between quantities and how this quantities can be transformed into one another. Therefore "rearrangement" seems quit natural for considering the nature of maths. It's about the relation between a one and the *seemingly* many. But in physics there seems to be also *qualities* in the sense of complexity and total different behaviour as consequences of total different quantities (and rearrangements) of some systems, subsystems and elementary systems. So we can surely conclude that rearrangements of quantities in some cases can abviously produce different qualities in our world, as far as human beings can conclude this out of their limited perspective that is biologically fixed. For example in chemistry, there are some fundamental entities (atoms) made out of some more fundamental entities (protons, neutrons, electrons, quarks). If you are right and nature is indeed infinite in complexity, what could this mean? Would this mean that under every "fundamental" level there exists one "more fundamental" level and so on infinitely with an infinite level of accuracy after the decimals? Well, the question is rethoric, because in yours approach the fundamentals are somewhat of math-like nature and started with bare quantities (numbers). But every number of them can theoretically be infinite in its own right. But how could this correspond to the physical world where dynamics and change govern the tide of events? More precisely: 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?

What i want to say with that is that for me it is not quite clear how the relation between quantities and qualities in our world really looks like. And now i come to my point. A mathematical statement can tell us a (relative) truth about qualities which have to be related by an equality-sign in the abstract language of maths. So the left side is equal to the right side (and in pure maths at least vice verca too). An inequality for example of the Bell-type can only tell us how the things possibly *not* are. So mathematical transformations that quantitatively equal each other are in my opinion pure tautologies and therefore could be indeed interpreted as a change of the quality of a system from human perspective. The same is truth for my own approach with ultimate reality (see therefore my essay).

But a mathematical sentence does not express a thought in the sense of qualia, creativity and mindfullness. We only use mathematical sentences to mechanically conclude from sentences that do not belong to maths to sentences that also do not belong to maths. You maybe would say that that's not true in your framework because in your framework *all* sentences belong to maths. For the latter is your perspective on the whole issue.

Well, if your perspective would be true that maths is an infinite landscape and reality as well, i would perhaps agree. But i strongly assume that the very notion of "infinity" in all its historical and philosophical facets is the biggest contradiction of all: It defines itself by saying it has no definite borders. So i would say the very notion of infinity is a totally misleading tautological concept because it only says: infinity = undefined.

Insofar as you use the very concept of infinity for your approach i would say that you use an undefined space to define your lines of reasoning by an act of (honorable) creativity. For me, the latter could be the most important ingredient of reality that could have truly qualitative properties instead of only quantitative ones. But as you in my opinion said very clearly, only time perhaps can tell us. My personal conviction is, that the whole question about the ontological and epistemic status of quantum mechanics is indeed a deep issue of the relationship between quantity and quality, hence between defined and undefined parts of ultimate reality.

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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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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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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, while Jochen Rau uses infinity to prove the necessity of orthogonal groups. In his proof, Rau allows the local physical structure on the event manifold to vary freely. It is this critical feature that helps single out the orthogonal groups and not the unitary groups for example. If you do not have this infinite local freedom, then obtaining space time as an emergent phenomenon is a very hard problem. Also, at Chaitin puts it, you cannot obtain 20 pounds of theorems from only 10 pounds of axioms. I am bypassing this algorithmic information theory limitation using the physics principles as filters. Now from Godel we know math is infinite, and reality seems infinite as well (although we do not know it for certain). The trick is how to use this observation to derive mathematical results.

Second, about the relationship between quantity and quality: I am not a philosopher, and I am not qualified to discuss this. As a physicist however, if we can make predictions that are ultimately validated by experiments, then we are making progress I can explain. Now in the conceptual area of physics, we already know the basic properties of nature and we should try to prove mathematically their unique necessity. If we achieve that, then the conceptual problems are solved. If from those results we can find the solutions to well known problems of physics like quantum gravity, then even better.

Case in point, quantum mechanics. I do not know how to explain the relationship between quantity and quality, but I can explain QM in an intuitive way without the recourse to hidden variables. Just recently I discovered Joy Christian’s claims of disproving Bell’s theorem. Very interesting papers, but I think I know where he makes a mistake. The mistake is not mathematical as his critics tried to prove so far, but conceptual in the way that he does not understand why hidden variables should commute. He is using a Clifford algebra hidden variable, and he thinks he obtains a local realistic theory, but in fact his model has a continuous state space and it is only QM in disguise in quaternionic language. He can do that because of 2 things: 1. geometric algebra can allow a representation of all classical Lie groups, and 2. there are a handful of isomorphisms between orthogonal and unitary groups SO(3)~SU(2), SU(4)~SO(6), SO(2,4)~SU(2,2). He is using the first isomorphism, but his argument will not work for SU(3) for example with no such isomorphism and his hopes to rewrite all QM in terms of hidden variables are wrong. His model is intuitive and very nice, but I think I can prove all QM is intuitive.

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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.

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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.

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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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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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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.

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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)

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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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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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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.

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Georgina,

I am looking forward to your questions.

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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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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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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.

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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.

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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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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 universe doesn't exist anymore in a far away future? I mean, our conversation at Aug. 4. 2009 seems to be a bare fact to me in the sense of an unalterable truth. What happens to this truth if the physical basis of this truth does disappear? You answered that this truth is still possible in the platonic realm, but is it still true that we both commented at each other for the case that the physical basis for that all has vanished away completely and nothing is left then - well, nothing but maths?

I do insist in this question because in that platonic realm which has the universal truth property there could be myriads of constellations that wouldn't have become actual until the universe vanishes away and are also possible and true in a certain sense. But these certain - mathematical truths - are they of the same ontological level as the actual truths? So what happens with truths as we know them after a physical universe collapses back to the "ground" where it came from? I guess your answer is that the universal truth property is the borderline of it all. But that seems to be somewhat circular for me, because the universal truth property could only be true because the universe itself is true, and the universe itself is true, because the universal truth property is true (insofar you derivate this universal truth property from the properties of the seemingly true universe in which we live).

Sorry for my insisting on your clarification, but i try to understand where all these truths come from and what/who has defined what is universally true and what not. I am aware of maths as a possible source of truth and falseness, but i am still not aware of the answer what/who inspired the breath into the equations, say exposing an if-statement that has consequences if this statement is true. Consistency alone cannot do this because consistency is a matter of fitting together some elements in a certain way that they do not contradict each other. So for example Curry's paradox:

*If* this sentence is true, then the world is made of nothing than pure maths (or cheese or whatever).

Well, therefore the world is made of nothing but pure maths or cheese because the antecedent could be true. We do not necessarily have to belive that the antecedent is indeed true, it is sufficient that it could be true.

With all this in mind i cannot conclude at this point that

"*if* we prove the necessity of time, space, quantum mechanics, Standard Model and explain the origin of the universe *then* we can really conclude with certainty that the universe is made out of nothing but mathematical relationships."

Why? Because it only says "if the universe is made out of nothing but mathematical relationships, then the universe is made out of nothing but mathematical relationships (what surely would be true in this case), but excludes the one thing that it originally wanted to explain: the origins of the universe and hence the origins of maths itself.

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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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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 future?” The short answer is NO. Only mathematical truths exist forever, and they exist within an axiomatic framework. Our discussion framework is our reality, and if this reality vanishes, so is our conversation, along with everything that ever happened in our universe. But it did happen you may say. Indeed, but if reality’s origin is mathematical, then reality is relational just like math and it requires something to have a reference to, in other words an independent observer. If there is no possible observer to witness our discussion, or its future consequences, then the existence of our conversation is an ill defined concept. We exist only in space-time; this is the canvas of reality. To ask about events in a vanished universe is the same as asking what is south of the South Pole? The universal truth property is “universal” only in reference to our reality, and not across multiple universes.

You also say: “But that seems to be somewhat circular for me, because the universal truth property could only be true because the universe itself is true, and the universe itself is true, because the universal truth property is true”. Well..., I do not know the meaning of the sentence: “the universe itself is true”. This is either metaphysics or wild speculation at best. What I do know is what I can observe around me. And what I see is that the events that make our universe have an extra property which is unlike any we have seen in mathematics. The three physics principles are true statements about our universe, and they are validated by all experiments, so this is still physics, not philosophy.

I do not derive the existence of our universe from the 3 principles. Just because I write them on paper, I cannot command them: “fly” and a new universe will form. I do not play God here. They are only used to select the desirable mathematical structures which describe out universe. The success of this program is to show that this heuristic rule generates principles which in turn will select precisely all the math which is validated by experiments and nothing else. If by working out the math consequences I predict a universe with 2 times, or a universe with 3 more elementary forces besides the ones we observe, then my heuristic rule is wrong. If I only predict the electroweak force and not the strong force, then my heuristic rule is incomplete. Only if we successfully derive exactly only the core physical characteristics of our universe, then we can fully believe the heuristic rule and extract the meaning of reality from it. (We can still do it now, but we are not yet sure of the likelihood of the correctness of our speculation). If the heuristic rule fulfills its promise, then we can say with 100% certainty that reality is based on nothing but relational mathematical objects.

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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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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.

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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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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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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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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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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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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.

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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 axiomatic...

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Sure enough let me know. I only heard about J Christian a few weeks ago.

LC

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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.

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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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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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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.

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Dear Stefan,

Let me clarify a last point. Let’s use “e” and not

$\pi$

, 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.

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Lawrence,

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

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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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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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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.

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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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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.

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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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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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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).

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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.

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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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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?

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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?"

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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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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 dies) that he can state about his world: The fact that he or she is the person he/she is and not another person with another body.

In a solipsist's world, there is no explanation for the fact, that he/she is indeed he/she and not - his aunt Daisy. To circumvent this question - the question why he not looks out "into" his/her solipsistic world through the eyes of his/her aunt Daisy and doesn't exhibit the aunt's body but all of things has his/her own body day by day -, the only way for him/her is to *deny* flatly the consistent explanation that exists in his own world: Namely evolutionary and historical accumulation of events. So to be a "real" solipsist, one has to *deny* scientific explanations (*and* therefore the fact that maths *can* predict many things in our world) or having not yet heard of those explanations or don't having very much memory at all. I think i haven't created the impression on FQXi that i do not believe in both - the ability of maths to predict things in our world and the fact of evolutionary, historical accumulation of facts in our world.

But there may be things in the universe we don't know. Nonetheless one thing i take for guaranteed: To be able to grasp and understand these things, they must be structured. Not only structured, but hierarchically structured to be comprehended by us consciously. The same would be true for the platonic landscape of mathematics. If it is structured hierachically - then maybe it could indeed exist in my opinion and in that case would have somewhat "infinite" logical deepness (the latter i would then not call "infinite logical deepness" but "intelligence"). But if it isn't structured hierachically, it would be only an aggregation of random self-assuring tautological things and each of these things would look for us humans random in respect to it's questionable existence.

Why the latter isn't the case for Pythagoras’ theorem or for Gödel’s incompleteness theorem (or pi), lies in the fact those structures to a certain degree are properties (in the sense of sub-structures) of the world we live in and this world has a historical evolution that is hierarchically structured and came into existence out of certain profound reasons we yet still don't know for sure. Therefore the mentioned mathematical theorems surely existed 5 billion years ago before Earth was formed, because our universe we live in existed 5 billion years ago before Earth was formed.

So please don't push me in a direction i don't belong to: Namely intelligent design and related issues. I believe in intelligence, but i don't believe in fairy-tales.

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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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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?

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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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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.

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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.

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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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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 inconsistent or merely incomplete just like in maths (see therefore Joe Christian's attempt or the event-based simulation concept i gave a link to at the essay-page of Lev Goldfarb). Whether they are consistent or not with our independent external reality, they remain abstract as long as they cannot be linked to human experience. But if they can be linked to human experience, they "only" make sense in a human's internal framework just like the english language does, as long as you do not assume the value of the term "sense" to be independent of conscious considerations.

In respect to the latter sentence, you are - from my position - absolutely right with your statement that the language of maths has universal independent existence. And my position is, as you have maybe already understood, that i cannot know for sure out of my limited knowledge, if maths has indeed universal independent existence or not; independent in the sense that its existence does not depend on my considerations of making sense or not for this existence.

Even if it would exist independently, i don't think that it has the omnipotent power to divide what can and does exist in general and what does not. In respect to the latter question (omnipotent power or not), it seems to me that your claim not to be a philosopher could indeed be true. I conclude that from the following words you wrote:

"Why is this physics and why it is not subjective? Because all the 3 principles are validated by all experiments performed to this date. In my heuristic rule I am asking for the differences between math and reality. This means that whatever differences are found (the 3 principles so far) they have to pass all past, present, and future experimental tests. This is why this is ultimately objective physics and not subjective philosophy. In computers there is the GIGO principle: garbage in, garbage out. If the 3 principles are invalidated by experiments, they are the garbage in and the conclusions will only be the garbage out. Next, the 3 principles generate mathematical consequences and they have already proven a large chunk of the necessity of our universe. By a leap of faith now, I am speculating that ALL core characteristics of our universe will be obtained in this way. If true, this will mean that our universe cannot be except in the way it is: it has uniqueness and this is big. If true then we have mathematically succeeded in proving that there is no God. God’s hands were tied at the moment of creation and he had no freedom into creating this universe, the blue print for the universe was already there just like the value of pi.".

This is an absolutely legitimate scientific thread. I do not criticize this thread. But i am strongly convinced that an (computer-like) exclusively deterministic-based proof can't prove the exclusiveness of determinism. That's the position of mine.

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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.

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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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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.

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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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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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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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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.

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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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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.

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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”

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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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In the attached document below I have fixed the reported typos and I have added another section.

attachments: Articol.pdf

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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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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.

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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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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.

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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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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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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.)

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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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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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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.

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Dear Florin ,

Interesting work of math .

Sincerely

Steve

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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

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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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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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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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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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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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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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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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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.

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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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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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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.

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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.)

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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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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?

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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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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?

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'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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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.

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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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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.

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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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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.

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'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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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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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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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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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.

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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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Sorry, I make errors in hurry. The previous post is my post.

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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.

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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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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.

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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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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)

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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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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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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.

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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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PS, on my site I mentioned today in a rather long post zitterbewgung in refrence to scaling principles. LC

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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.

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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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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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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).

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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.

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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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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.

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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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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.

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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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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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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 rely on a measure of absolute truth, some reliable filtering of possibilities and mathematical precision to explain everything. Which I think is the aim of this approach.It does rely on some prior assumptions and theory. Is there a danger that the very things filtered out by this approach may be the important elements that might lead somewhere significant?

You say early on ".... reasoning about a problem that would lead to undiscovered theory. This step should not rely on clever tricks or sudden inspiration but should be a systematic research programme." History has shown us that systematic research does not lead to the greatest breakthroughs but that it is often original individual thinkers outside of the mainstream of research that do this job. Systematic research leads to incremental increase in knowledge building upon existing theory. Which may be superseded when new theory emerges. Being systematic and logical only brings together those ideas that seem likely and fit existing structure. The intuitive mind does not work within these limitations and will find alternative solutions that might otherwise not be considered. How do you reconcile the innate difference between a systematic and logical approach on the one hand and originality or creativity on the other?

I'm still not sure I understand the universal truth property. It seems to me there is a difference between a mathematically true statement and any other truth. Any observation can only generate a statement that something is true beyond reasonable doubt at best. In many cases results may be merely statistically significant. However the interpretation may be based on false assumptions or incomplete evidence or use of a completely incorrect model that generates numerically correct answers. An audience of 200 can observe a rabbit being pulled from an empty hat and will agree on the observation. That does not make it true. There may also be cases where truth depends on perspective. An iridescent material may appear to be one colour to observer A, but a different colour to observer B. Without complete information the true situation can not be ascertained.

What is ultimately possible in physics? According to your article ultimately physics will cease to be an experimental science at the limits of investigation and will merge into mathematics. This merger will produce a new era of research, possibly leading to a mathematical theory of everything. I think the tacit assumption here is that because of the precision of mathematics it is considered to be a superior approach and therefore closer to truth than any theory produced by merger of physics with philosophy. That is debatable.

There will still need to be inputs to the mathematical analysis, which may be false or incomplete assumptions or evidence. There will have to be interpretations of the mathematical results which may once again be false or incomplete and lead to incorrect understanding. I do however see the appeal of attempting to construct something simple, neat and tidy, precise and unambiguous. Though I also wonder whether that neatness and precision may be overrated and might actually just be masking a further mess underneath that has not been incorporated into the model and is not even recognised.

As I said before it is not at all boring. I have only picked out those few things with which I have felt most unease. There is lots to like and I have found it very interesting to contemplate. It is not a path I would have ever considered or taken myself. Good luck with the competition and with the continuing development of this approach.

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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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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 explain. All mathematical structures are unique. Euclidean geometry is unique, Peano arithmetic is unique, complex numbers are unique, etc. Very likely all mathematical structures do play a role in reality in a way or another. But not all mathematical structures play universal distinguished roles in nature. There is only a Minkowski space or a Hilbert space. Those structures rise above all other mathematical structures and they are universally relevant to nature. Why? That is what I want to solve.

>”How do you reconcile the innate difference between a systematic and logical approach on the one hand and originality or creativity on the other?”

This is easy to answer. The hardest part in any new research program is the beginning when new relevant questions are asked that break existing assumptions and paradigms. Is simultaneity absolute? Is energy absorbed and emitted in finite amounts and not continuous? Can empty space be curved? Before those questions were asked for the very first time, the answers were considered obvious: yes, no, and no. Once the relevant new question are asked, the rest should follow effortlessly and not be subject to lucky guesses along the way. Clever proofs are a hindrance to progress, because it is almost impossible to guess right. Systematic derivations of results in small manageable steps is essential to achieving success, otherwise you get stuck midway. At that point the question becomes: am I stuck because I need this math trick I cannot guess right now, or because my original question is fruitless? Consider string theory: is the current lack of progress because the required math is too complex to guess, or is the whole approach dead wrong from the beginning and leading nowhere? The jury is out on that question. But suppose instead that no clever tricks are needed along the way after the original conceptual breakthrough occurred. This is a very good sign you are on the right track and moreover, it validates the correctness of the conceptual breakthrough.

About the universal truth property (UTP) (or event’s non-contextuality), we have to go to the very definition of what is means for something to be true? There are 2 definitions: (1) something is true if it corresponds to reality, (2) a mathematical statement is true if it can be derived from the axioms of the field. The first definition is stemming from the universal truth property which is a property of nature, while the second comes from standard mathematics. UTP does not mean that observers are having a bad day and seeing with blurry vision, but it is a mathematical idealization of perfect observers. The point of UTP is that no matter the context, the truth property of an event stays the same. This is not so in math. Take the statement 3+7=10. This statement is true in normal arithmetic, but false in addition modulo 10. Change an axiom and the truth value of the statement changes. The truth value of any mathematical statement is contextual, it depends on which axioms you are considering. Events are non-contextual. Change any point of view and the ontology of the event stays the same.

>” This merger will produce a new era of research, possibly leading to a mathematical theory of everything.”

I really do not know if or when a TOE is going to be achieved. What I am trying to do is solving Hilbert sixth problem. The heuristic rule asks for all mathematical properties of the real world that are valid in the real world, and not universally valid in math. As such, the 3 (so far) principles have to pass all past, present and future experiments. Because of this, my approach is still old fashion physics rooted in experimental verification, and not yet a hypothetical post-Galilean era approach.

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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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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.

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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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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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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.

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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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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.

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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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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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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 defined in some way by PN. So this is related to twistor theory in some way. I am not prepared to comment on whether there is some “map” or isomorphism between the two systems

I can’t help but think there is a lot more going on with physics. Witten has proposed twistor string theory, where twisters are a form of D-brane. There is also some interest in extending twistor theory into the domain of exceptional algebras. This construction leading to quantions has references to Lie-Jordan algebras and Jordan products. So I have been reading this with an eye to the prospect this might have implications which are beyond what is currently formulated. The quantion 2x2 matrix could well enough be extended to the J^2(O) matrix

|z_1 O|

|O* z_2|

and the octonion elements considered as generalizations of the elements z and z* in your equation 24. The extension to J^3(O) is by the standard BFSS matrix model with

J^3(O) = R⊕J^2(O)⊕O^2.

I see no reason why this construction can’t be extended into higher level systems. I think the composability requirement maybe satisfied for the exceptional algebra and its anti-Hermitian pair under G_2 holonomy. Further the analogue of the M(q), would be related to the characteristic polynomial det(Ω − λI) = λ^3 − (trΩ)λ^2 + tr(Ω*Ω)λ − (detΩ)I = 0, which defines the Lagrangian for the J^3 system. In an extended sense this is the same as M(q), which defines a proper interval, equivalently the Lagrangian, for a particle moving in spacetime. I am going to see if I can make this work.

The problem with restricted systems of quantum gravity is they do not contain enough information, and they run into difficulties. This happened with twistor theory and symptoms of this are evident with loop variables. I am not going to go into the reasons and history of this, but it is fairly clear this is the case. This does not mean these theories are wrong, but they are limited pieces of the puzzle. The problem with restricting a theory of quantum gravity to SO(3,1) or even SO(4,2) ~ SU(2,2), which is where both twistor theory and quantions live, is there is insufficient information. Conversely, there is this massive thing called string/M-theory which has too much. This is less of a theory than it is a sort of framework. It is my sense that ideas from theories such as twisters, LQG and maybe here with quantions provide the necessary constraints on string theory to maybe make it calculate some workable physics.

Cheers LC

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Hi Robert,

Looking forward to your comments.

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

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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.

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Connections with Hopf algebras would be interesting. This would bring things in contact with K-theory.

Cheers LC

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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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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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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 unique: there is only one Pythagoras theorem for example and only one 2D curvature-free geometry. However, only some mathematical structures are distinguished and play a special role in Nature: Minkowski space, Hilbert space, etc. Why is that? Asking for the difference between mathematics and nature singles out precisely those and only those distinguished mathematical structures. All other mathematical structures do get to play a role in nature, but not a global one.

2. Mathematical formulation. From the heuristic rule one derives physics principles which in turn have mathematical consequences. Various physical theories (like special relativity, or quantum mechanics) have many alternative axiomatizations. What I have found possible is that one can select a distinguished axiomatization using the 3 principles. The best example is quantum mechanics which becomes intuitive in the new axiomatization (work in preparation).

3. Experimental data and its critical analysis. My approach is not philosophy, but it is old fashion physics rooted in experiments. I am asking for all mathematical properties of the physical world which are universally valid in nature and not universally valid in math. Being universally valid in nature means they have to pass all past, present, and future experimental tests. I am not asking for new experiments and because of that my approach will not answer all physics questions. It is therefore definitely not a theory of everything, but only physics axiomatization. If you consider set theory as the basis of mathematics, set theory would not help you solve for example Riemann’s conjecture. I am only looking for the mathematical foundation of nature, just as set theory is the mathematical foundation of modern math. I can only speculate that maybe this would lead to TOE, I really do not know either way, but I can hope for it.

Speciality approach is a tightrope walk approach. Ignore it and you end up doing only philosophy with no predictions. Follow it too narrowly and you set yourself for dead-ends and unimportant results. There is no prescribed way of doing it, for if there were, we would invent every day brilliant new theories. You can only judge the merit of an approach only after the fact by seeing what the fruits of that approach were. I do not really know if my proposed approach will bear fruit in the end. (But I certainly do hope it will.) Only time will tell that. But what I do know is that I do ask new questions from a novel angle. Even if my approach will turn out wrong in the end, new questions will open up new ways of looking at old physics puzzles, and maybe it will play some role in solving them.

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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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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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Hello Steve,

Thank you for your good wishes,

Best Regards,

Florin

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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.

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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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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

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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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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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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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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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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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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.

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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 several...

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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 several reasons. The first reason is Goedel’s theorem. Tegmark’s response to this challenge is to consider computability as a requirement of nature, but I have serious reservations with computability as a core feature of nature. My second reason to doubt it is that nature seems to be infinite and mathematicians (who are part of nature) are discovering new axioms all the time. This is at odds with Chaitin’s results which limit the amount of complexity one can derive from a given set of axioms. If Nature is one huge mathematical structure then we should see some sort of maximum information which can be extracted from it, and this is at odds with what we observe, particularly regarding the orthogonal groups describing space-time as it was shown by Jochen Rau.

So if this in not my approach, then what is exactly my approach? Axiomatization is possible, but not as a massive single mathematical structure. Realty is made of all mathematical structures, but only some of them play distinguished roles. How can we identify them? Why is space-time 4 dimensional? Why are complex numbers appearing in QM, etc, etc? Mathematical structures are relational and abstract, devoid of ontological meaning. But physics can also be put in relational format. A trivial example is speed. More realistic example include Rovelli’s relational interpretation of QM, and LQG’s background independent approach. If there are no supernatural explanations of reality (like transcendental or God arguments), all that remains are mathematical structures as the building blocks to construct ontology. Therefore by looking at the differenced between math and reality one should extract precisely the core features of reality which in turn would select all the universal distinguished mathematical structures we see in nature: Minkowski space, quantum mechanics, etc.

The 3 physics principles: universal truth, composability, deformability (or events, interaction, infinite complexity) acts as filters of selecting the distinguished mathematical structure physicists use and experimentally confirm every day. I am not deriving them from the 3 principles, I am only eliminating all the other mathematical structures and therefore the axiomatization of physics does not result in a mathematical closed form “super structure” from which all reality is derived. This is a double negation trick which eliminates the closed form of the answer and avoids the Goedel and Chaitin roadblocks.

Regarding the global hyperbolicity, this a long discussion, but I can give you the gist. The critical observation is that there is a link between incompleteness theorem and the Minkowski space. From this one can translate the Goedel’s proof almost one to one into the proof of global hyperbolicity on arbitrary event manifolds. But event manifolds are decidable and at the end of the proof one is force to conclude that one has inconsistency for event manifolds for which Godel’s theorem translation holds (precisely the ones where global hyperbolicity is violated). This is different from Goedel because he derives incompleteness instead of inconsistency, but because of decidability, incompleteness is ruled out. The sensitive part of the proof is to prove the godelization and this works only in classical mechanics and therefore the proof is valid only in the region of the validity of the correspondence principle, and not at Plank scale. Global hyperbolicity and time are ill defined in that range anyway.

PS: I had completed the basic hyperbolicity proof right after the first FQXi essay contest and I would have loved to enter the nature of time contest and explain all this in detail, but that is life.

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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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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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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.

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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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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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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

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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

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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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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.

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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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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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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

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Florin,

Good! I am looking forward to seing it.

Emile,

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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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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.

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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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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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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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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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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.

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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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Steve,

Thank you for your kind words.

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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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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

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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

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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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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

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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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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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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.

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"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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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.

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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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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

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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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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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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

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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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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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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 incomple