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?
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?
'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.
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.
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.
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.
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.
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.
'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.
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 observed using electron scattering and this is what convinced physicists of the quark model; before that the bootstrap theory was in fashion.
"To hide this error, they invented konfinement". This is extremely well understood to the point that proving it has now become a graduate student homework problem.
"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." The problem is that QED and the Standard Model DO explain all current experimental data. That is why we need more powerful accelerators to generate new data that may be at odds with the current theories. So your theory has to first reach the same level of prediction as QED and QCD. Then we may consider predictions for new experiments.
"QCD is not a logical theory in general because confinement do not follow logically from theory. It is a mathematical model only." Yes it does follow logically from theory from the non-Abelian local symmetry group.
"QCD has a major problem - it is not possible to unify QCD with gravitation and other interactions." This is true.
"It is the main cause why QCD must fall." Yes, we already know the Standard Model and QCD is not the final word in describing reality, but gravity is extremely weak compared with the other forces and we could not even detect gravitational waves created by violent cosmic events, let alone the ones occurring at the atomic and subatomic levels.
"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."
Unlikely. If they glue the nucleons, than they cannot explain the weak force which is responsible for particle disintegration - the opposite of gluing.
"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."
Did you seek criticism from Smolin or other loop quantum gravity people?
'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.
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.
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
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.
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?
Sorry, I make errors in hurry. The previous post is my post.
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.
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
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.
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.
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)
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
With respect to the zitterbewegung I worked a numerical analysis of it. The attached file is a one dimensional representation of zitter motion.
Cheers LCAttachment #1: 1_zitterzag.gif
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.
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
PS, on my site I mentioned today in a rather long post zitterbewgung in refrence to scaling principles. LC
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.
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. As we know, all the attempts that have been done during the last two thousand years failed. As a consequence of this radical failure metaphysics was regarded as scientifically meaningless.
The main reason for this radical failure was the transcendent character of the One. It was described as being beyond every description and formalization. At the first sight a foundation that is characterized in this way seems to be in fact no serious object of science, especially of physics.
But just this impression is a fatal error, because it prevents us from a deep and penetrating understanding of the universe. If the One is truly the ultimate basis of our universe, then we have unavoidably to include it in our research. But how can we deal with it?
We have to turn around our usual philosopichal perspective: Instead of dealing with something, that cannot, in principle, be described in physical terms, we have to ask: How must the Universe look like if it is based on something that is of transcendent character?
If we follow this line of reasoning systematically we can discover that transcendence is a highly restrictive condition with respect to the structure of the Universe. That the universe is mathematically describable, has its origin just in the fact that its ultimate basis is withdrawn of all mathematical describability. That is at least my conviction.
But this foundation has an inconvenient property as far as physics is concernd. That is the reason why I am writing this post. Actually there is an ontological equivalent ot Gödels Incompleteness Theorem.
I found that the universe must have a certain kind of a radical non-dual structure, if it shall base on a transcendent foundation. It seems that there is even concrete evidence that our universe does really have such a structure.
Let us suppose for a moment that the assumption of such a radical non-dual structure is really true. This truth would suggesting that the One is really existing. But could we prove this truth? No, we could not provide any proof, just because the One is, in principle, of transcendent nature.
And this would be in fact the last word about the very core of the universe. Although the One would be physically recognized as the ultimate foundation of the Universe, we could never prove it.
That is the inconvenient message of a modern metaphysics.
H.Hansen
More details see Taming of the One.
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 LCAttachment #1: EffetTunnel.gif
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).
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.
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.
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.
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
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.
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
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.
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.
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
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.
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?
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 blog post. I needed to reduce wear and tear on fingers.
I have been giving the matter of quantions some study. I am not entirely decided about their status as yet. My sense is they are an interlinking between two complex number or quaternions in a way which defines norms differently. This might have something to do with S-matrix. So I will outline some aspects of S-matrix theory and black hole complementarity, and then try to make possible links to quantions.
The holographic principle and black hole complementarity are generalizations of the S-matrix. Susskind's treatment of strings falling onto a black hole according to a distant observer treats the S-matrix on a domain which is causally defined on an infinite domain of support according to the tortoise version of the radial Schwarzschild coordinate
r* = r - 2m ln|r - 2m|
The S-matrix requires an infinitely extended domain by which fields are causally related, which is "manufactured" by this coordinate. In these coordinates the string exhibits a range of strange behavior, which I am not going to review again in great detail. Yet the string ends up covering the black hole horizon and is frozen their according to this distant observer. To an infalling observer on a commoving frame with the string none of this is the case, but rather the string enters the black holes with no apparent change and then exhibits tidal forces of an extreme nature near the interior of singularity. The string is a form of S-matrix theory, and the two cases reflect the existence of two S-matrices, each according to state space elements which are incommensurate with each other, or according to noncommutative operators. This is one way of looking at the so called black hole complementarity principle. There is then a superposition of the string in these two bases of states, and for this reason the distant observer may see the string frozen above the event horizon and also "burned up" by Hawking radiation made of quanta scattered from the string according to the infalling observer's frame.
The ordered S-matrix defines each vertex, or particle, and its neighbor. In a linear chain a general state is an S-matrix channel of the form
|φ> = |p_1, . . . , p_i, . . . , p_j , . . . , p_n>
This state or S-matrix channel is related to but distinction from the channel
|φ'> = |p_1, . . . , p_j, . . . , p_i, . . . , p_n>
The particles or vertices p_i and p_j have exchanged their neighbors, which means some "relationship" structure to the amplitude has been fundamentally changed. The S-matrix is written according to S = 1 - 2πiT, so two states or channels |p_1, . . ., p_n> and |q_1, . . . , q_n> are related to each other by the S-matrix as
(p_1, . . . , p_n|Sjq_1, . . . , q_n> = (p1, . . . , p_n|(1 - 2πiT)|q_1, . . . , q_n>
= (p_1, . . . , p_n|q_1, . . . , q_n> - 2πi(p_1, . . . , p_n|T|q_1, . . . , q_n>:
For the < | the in channel and | > as the out channel p_n and q_1 are neighbors, and neighbors through the T-matrix. This eliminates an open vertex in the chain. The vertices or particles p_1 and q_n are the open elements in the chain and defines an "anchor" for the chain, and are thus defined as neighbors in this manner.
A four point function and the transition matrix defined by vertex operators T = V(p_1)ΔV(p_3) will contruct the Euler-beta function for coherent states of the S-matrix. This is the connection of course between string theory and the old bootstrap or S-matrix theory. Now for two S-matrices, which pertain to the different domains of causality on a black hole this theory is made more difficult. The S-matrix is a braiding operation of sorts between elements of a quantum group G. So we might model this as a commutator structure (braiding) between two elements a and b \in G. So we might denote this as ab --- ba. Now let us assume the states we observe are super-positions of incommensurate states involving two quantum groups G and G'. We will then have a structure of the sorts (ab)c --- a(bc), that exist in an associahedron I_2(5) with a homotopy structure. This homotopy then connects to a K-theoretic field theory, which I discuss in my paper
http://www.fqxi.org/community/forum/topic/494.
I will not belabor this part of the things, until later or somebody takes an active interest in what I am suggesting here.
The black hole complementarity principle. The complementarity is an odd structure, for Hawking radiation is due to a Bogoliubov transformation between basis elements. In this setting the theory of spacetime is classical and the fields scatter off the black hole or spacetime with an event horizon. The response of the black hole or spacetime is a metric back reaction, which is a classical response to a quantum scattering. Yet black hole complementarity has demonstrated that quantum information is preserved for the case of a BZT black hole in an anti-de Sitter spacetime. So a connection between the quantum principles of unitarity (or maybe more generally modularity) and a classical field theory which exhibits thermal physics (black hole entropy and Bekenstein bounds etc) exists within this AdS/CFT setting. Yet we do not as yet understand how quantum information is preserved. We just know that it is.
So the quantumal rules of Grgin seem to segue into the picture here. The permitted multiplication rules
(fαg)αh (gαh)αf (hαf)αg = 0
gα(fσh) = (gαf)σh fσ(gαh)
(fσg)σh − fσ(gσh) = agα(hαf)
Connects the Jordan exceptional algebra to a quantum algebraic system. The associator is then by the homotopy equivalence mapped to a quantum group as a system of permutations (related permutahedra) with one set of norms determined by the underlying permutative rules or associahedra and the other by standard rules of complex conjugation in quantum mechanics. So the associator is [f, g, h]σ = agα(hαf) which induces the map between the octonions and the quantion group. This seems like an interesting problem to develop.
Cheers LC