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Planck unit of length not applicable,because no Gn,no Newton gravity law.
See part 3 my essay.No linear link between G and c,as in Planck unit of mass.
On the Foundational Assumptions of Modern Physics by Benjamin F. Dribus
Thanks for the clarifications, Ben. I understand your essay much better now.
Daniel
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Dear Benjamin
For better clarification my approach
I sending to you Frank 3 keen articles
http://ctpweb.lns.mit.edu/physics_today/phystoday/Abs_limits393.pdf
http://ctpweb.lns.mit.edu/physics_today/phystoday/Abs_limits393.pdf
http://ctpweb.lns.mit.edu/physics_today/phystoday/Abs_limits400.pdf
All the best
Yuri
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I send first all this links to address
'bdribus@math.lsu.edu
but get answer
'bdribus@math.lsu.edu.' on 9/17/2012 12:54 PM
Invalid recipient
Dear Yuri,
I got two out of the three articles, and I'm sure I can find the other one. I'm not sure why the first didn't come through. I don't know why you got that error message... that is the correct address. In any case, thanks for the articles; fortunately, they were easy to read, but included some information I did not know. I think I understand what you are suggesting about the relationship between the cosmological constant and Planck's constant, but don't you think that perhaps the cosmological constant is a little too small? Take care,
Ben
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http://ctpweb.lns.mit.edu/physics_today/phystoday/Abs_limits388.pdf
http://ctpweb.lns.mit.edu/physics_today/phystoday/Abs_limits393.pdf
http://ctpweb.lns.mit.edu/physics_today/phystoday/Abs_limits400.pdf
Dear Ben,
I enjoyed your comments on Brian's and my essay pages. As promised I have read and will comment on your learned fqxi contribution:
I agree with you that causality (I suppose you mean local causality, but you also refer to universes in the plural so I am left wondering) is the substrate on which to build a rational theory unifying quantum mechanics, relativity and the standard model.
Beyond this understanding, your essay is far too technical for me to follow. You couch your arguments in terms like " acyclicity, morphisms, multicategory theory, transitivity, complex Hilbert spaces" which leave be baffled. Well at least as far as Hilbert spaces are concerned Brian Swingle has thankfully dispensed with those as far as physics is concerned. As a mathematician it is wonderful that you approach physics with this background, as you just might find a new math to explain a whole range of physics - just as quaternions are now found to be useful to explain quantum interactions.
If you will forgive this image - the good wolf mathematicians huff and puff with their theories, circling around the various houses built by the little piggy physicists, and it is an excellent way to test those houses for good solid construction!
I was reminded that we should peer-rate essays as only the top 35 rated essays get read by fqxi's expert panel of judges.
With best wishes for your degree work,
Vladimir
Dear Vladimir,
I appreciate the feedback! And I was quite amused by your metaphor of the three little pigs... although I think the physicists have given mathematicians at least as much of a headache over the years with ideas like path integrals and delta functions!
As a matter of fact, as I wrote on your thread, the math I use here is simply whatever seems necessary to get the job done... the basic physical idea of cause and effect is the motivation. The length limitation for the contest makes it a bit difficult to explain things adequately and still fit in everything you want to say.
I was going to wait to rate the essays until I had read them all, but I will rate yours now just so I don't forget. Take care,
Ben
Dear Benjamin,
I am extremely sorry for the delay in replying to your query. I am glad to know that you have your original way of looking at the fundamental problems of physics and surprised to learn that you suspect too many basic assumptions of physics where as I consider as wrong only one basic assumption. On the basis of your 'causal metric hypothesis', you have tried to explain, in a novel way, the origin of the classical concepts of space-time and also the role of space and time in the quantum world. On the basis of 'causal metric hypothesis' you have attempted to unify both GR and QM leading to the theory of QG. I am also interested in knowing how you account for the appearence of continuous manifolds on the basis of 'discrete reference frames'.
Anyway, you have put too much thought in to the problems facing physics and wish you succeed in solving them in one stroke on the basis of 'causal metric hypothesis'. I rate your essay high because of its originality and want to know how you feel about mine.
Good luck and best regards,
Sreenath.
Ben,
As you said my essay was filled with ideas I can reciprocate the comment about yours. The statement you make:
"A number of existing proposals about spacetime microstructure lead naturally
to noncommutative spaces in the sense of Connes [3] via the deformation theory of Hopf algebras, 10 but noncommutative geometry is relevant more generally, and even classical spaces such as Minkowski spacetime possess important noncommutative structures."
on the top of page 7 is pretty spot on. Take a look at Giovanni Amelino-Camelia , and the reference to his paper on κ-Minkowki spacetime. You can search on down the blog comments to September 8 and see where I offer a connection to twistor theory. Giovanni's work is solid and it is regrettable that it has fallen so far down the community ranking. Spacetime is then under a certain measurement, which I think pertains to high energy processes or a very small scale is noncommutative. In my paper Noncommutative geometry of AdS coordinates on a D-brane I take a somewhat different approach to noncommutative geometry.
We do have to take pause however. The NASA spacecraft FERMI measured the time of arrival of different wavelengths of EM radiation from very distant (billions of light years) burstars. Later the ESA spacecraft INTEGRAL made similar measurements. The time of arrival was virtually identical. However, if spacetime has a foamy or noncommutative structure it is expected that shorter wavelengths of radiation will couple more strongly to this small scale structure of spacetime. The result should be there is a dispersion of EM radiation. None was observed! Experiments count more than theory.
Does this dash noncommutative geometry? Not necessarily, but it might mean something far more subtle is going on. These measurements are not directly small scale measurements. They are not experiments where particles near the Planck energy are scattered or where some Planck scale microscope looks at spacetime structure. We are actually measuring physics on a grand scale. So we are observers making a particular choice of measurement. Under these conditions we might then expect spacetime to be completely smooth with no foam or quantum noncommutative structure observed. Torsten Asselmeyer-Maluga connects exotic four manifolds (Donaldson theorem etc) with quantum spacetime. Yet this connection is with this strange business of spaces that are homeomorphic but not diffeomorphic, where this is connected to quantum amplitudes. I suggest on his website that in 11 dimensions it might be easier to consider the dual 7-manifolds with Milnor's exotic structure. We might then have some deep complementarity at work here.
The path integral issue you discuss might fit into this. The Polyakov measure in a path integral
∫(D[g, ψ]/diff(g, ψ)) exp(iS)
where one "mods out" diffeomorphisms or gauge dependencies. This gadget in some manner is generalized within this perspective. We also have to keep in mind there might be some general complementarity with noncommutivity.
The best thing about these contests is the exchange and interaction with people and different ideas and concepts.
Cheers LC
Dear Sreenath,
I appreciate the feedback! It's true that I doubt a lot of the modern assumptions, but this arises mostly from my doubt about the ultimate physical relevance of manifolds. In my mathematical work, I have come to appreciate how very idealized and mathematically convenient objects like continuum manifolds and algebraic varieties are, and it seems to me that many of the properties that make them mathematically convenient do not arise in any natural or necessary way in physics. Many people think that convenient properties such as the least upper bound property in the order theory of the continuum can be assumed without worrying about their ultimate physical reality, based on the belief that any sufficiently fine approximation will suffice for measurement purposes. However, these properties determine the symmetry groups whose representation theory governs the properties of particle states, so the difference is an important qualitative one, not simply a small quantitative one that vanishes in the limit. My approach is to begin with the concept I view as most central to scientific process, namely cause and effect, and explain as much as possible in these terms. Ultimately, it may not be enough, but it is an approach with obvious motivations and clear and simple principles, and one that has not been adequately explored.
Regarding your essay, I view it positively even though your approach is much different than mine. I don't know if your equations will turn out to be correct, but the advantage of your approach is that you go into very specific details, and it should be possible to evaluate it one way or the other in a reasonable time frame. Like mine, I think your approach is worth trying, which is really all one can ask for. Take care,
Ben
Dear Lawrence,
Thanks for the comments. I particularly appreciate your remarks about the FERMI/INTEGRAL experiments; I knew about these but don't feel very confident in interpreting the results. You're right of course that experiment is the final arbiter, but with the caveat that one must be sure what the experiment means.
Torsten's approach is fascinating and is worth understanding at a deeper level. I'll also point out that Jerzy Krol's essay is worth looking at in this regard; the two of them have been collaborating and their submissions are complementary. Jerzy discusses nonstandard models of number systems and their role in defining exotic smoothness structures.
You have the advantage of being well versed in the string/M-theoretic technology, which I am rather a novice at. Superficially, the 4d-to-7d duality of exotic structures you suggest sounds intriguing and perhaps gives another glimpse of why dimension 11 is special, although I'm not qualified to remark further on this. I do note that string/M-theory has been recently assimilating aspects of other approaches (noncommutative geometry, entropic gravity, twistor theory, etc.) in a way that suggests that the serious approaches to QG and unification may prove more amicable than previously thought. The causal theories (causal dynamical triangulations, causal set theory) seem perhaps left out of this picture to a degree, which gives me pause considering that causal theory is my own favorite approach. Take care,
Ben
Ben,
"The central new principle I propose is the causal metric hypothesis, which states that the metric properties of classical spacetime, up to overall scale, arise from a binary relation, which I will call a causal relation, on a set, which I will call a universe, and that the phase associated with a congruence class of directed paths in the con guration space of such universes is determined by the causal relations of its constituent universes"
How can you imagine let alone model causal relationships of a multiverse? Are the attributes of gravity shared between universes? I struggle with your esoteric essay.
Jim
Dear Jim,
Well, I would rather not call it a multiverse because that is often understood these days to refer to the string-theory multiverse, which means something entirely different. My "causal configuration space" is a "way of talking about the superposition principle of quantum theory in a background independent setting." For some context, in 1948 Richard Feynman showed that you could explain quantum theory by thinking of all the possible paths a particle could follow between two points in space and time. Since general relativity says that the structure of spacetime responds to matter and energy moving through it (background independence), different particle paths correspond to different spacetime structures; i.e., different "universes." So you see that in this context, "universe" doesn't mean "all that exists," it just means a particular classical causal structure.
The fact that the causal configuration space itself has a similar structure to the individual "universes" is a nice thing, in my opinion, but the relationships among the "universes" aren't "causal" in the usual sense. The point of the causal metric hypothesis is that you can describe a lot of different things (causality, spacetime "geometry," the superposition principle, etc.) by means of a single type of structure. I
I hope this helps! Take care,
Ben
Jim,
By the way, I agree with Verlinde and others that gravity is likely an entropic phenomenon. But I think it's quite possible that all the "forces" are entropic. Take care,
Ben
Thanks Ben,
The supreme example of the mathematician-physicist is Newton - and of course you are right about the 3 piggies metaphor being inexact - perhaps at the most basic level physics and mathematics are equally artificial, but in conjunction try to describe Nature the best they can. As an artist and inventor I built my physics model using geometry and physically realistic interactions. I suppose topology, knot and graph theory can all be used to describe such models, but I am satisfied with understanding how it works as a sort of mechanical linkage. (I was inspired by Kenneth Snelson's concept of tensegrity - I urged him to present his ideas about the atom in this contest and am glad he did - at age 85!)
I hope that my model can be tested by computer simulation but I had better update my research and present it more succinctly.
Following your remark about gravity and entropy: In one of the discussions of this contest I suddenly realized (and wrote) that my Beautiful Universe model explains why entropy occurs - it is the same causal local mechanism of diffusion of energy as a wave pattern in the lattice, which simultaneously explains probabilistic behavior and uncertainty! But what about solitons? how would entropy be manifested in their behavior?
Thank you for rating my essay, (as I did yours). Last year I also participated in the fqxi contest, and one participant used to sign his messages: Have fun!
Vladimir
Dear Benjamin,
Studying the question of connection of entropy and gravitation, I found Lorentz-invariant formula for entropy in the book: Fizika i filosofiia podobiia ot preonov do metagalaktik. Perm, 1999, 544 pages. ISBN 5-8131-0012-1. In short the question is described in the book: The physical theories and infinite nesting of matter. Perm, 2009-2012, 858 pages. ISBN 978-5-9901951-1-0 in such way: Using the stress-energy tensors for the substance and the gravitational and electromagnetic fields allows us to write the equations of thermodynamics explicitly in the Lorentz-invariant form. As a result the entropy, the amount of heat, the chemical potential, the work and thermodynamic potentials can be represented as tensor functions of microscopic quantities, including the electric and gravitational field strengths, the pressure and the compression function. This allows us in § 21 to find out the meaning of the entropy as the function of the system state - it is proportional to the ratio, taken with the negative sign, of the absolute value of the ordered energy in the system to the heat energy, which is chaotic by nature. The ordered energy means the energy of directed motion of the substance, the compression energy from pressure and the potential energy of the substance in the gravitational and electromagnetic fields. When the system achieves equilibrium, part of the orderly energy inevitably is converted into thermal form and the entropy obtains a positive increment. I hope it may be interesting also for Vladimir F. Tamari and others authors in the contest.
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Dear Ben,
I am in general agreement with your critique in regard to the foundational problems. My view is that the problems you have highlighted are secondary, tertiary derivatives that have emerged due to the original foundational problems that Newton (and others) introduced when he intentionally developed Mechanics on a makeshift basis as a stepping stone for what he called the "Truer Method of Philosophy".
You have quite rightly pointed out that although certain foundational problems are realized by eminent physicists, they do not know how to rectify them.
For instance you wrote in reply to Frank: "Regarding the continued use of widely doubted assumptions, the reason I mentioned this is because I wanted to make clear that I wasn't offering anything new by rejecting these particular assumptions; of course people have known for years that there are issues with manifold structure, background-dependence, etc., and plenty of people are working on these problems. I don't think that well-educated physicists continue to use these assumptions because they are trying to make them "fit a preconceived model," but rather because they don't yet know what to use in their place. .....".
This is because there is no single foundation presently. When the problems arose on the original foundation, without analyzing and rectifying them, other foundational concepts (even contradictory ones) were overlaid, while retaining some of the problematic ones (like the point mass) and this process has continued. My view is that the solution to the present crisis must begin with going back to the original foundation of Newton and rectifying its mistakes.
I have done this to a certain extent. I have not only pointed out what the foundational problems are, but I have offered solutions.
I request you to have a look at my essay and comment: http://fqxi.org/community/forum/topic/1549
Since the diagrams have not come out properly in the above pdf version, I am attaching the MS Word version also.
I will continue on this with another post making some introductory comments about my essay.
Best regards,
VirajAttachment #1: 9_A_TREATISE_ON_FOUNDATIONAL_PROBLEMS_OF_PHYSICS2.doc
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Continuing:
Hi Ben,
The following are some matters I wish to bring to your attention about the contents of my essay: http://fqxi.org/community/forum/topic/1549
1. I have listed out a number of assumptions that Newton made that have turned out to be foundational errors.
2. I have not only listed the errors, I have found a new approach to overcome these errors (guided by notions of Newton, Maxwell, Einstein) and provided accurate quantitative solutions.
3. I have discussed that these wrong assumptions of Newton have been carried over to the foundations of Quantum Mechanics and Theory of Relativity and these too are afflicted by the same problems.
To quote from the essay: "We may note that among the problematic foundational concepts created by Newton that have congenitally infected RT and QM are a) the primacy of the concepts of space and time, b) representation of bodies as mass-points without internal structure, c) consideration of centrifugal force as a pseudo-force, d) the closed system with the consequent inability to account for inflow and outflow of energy between the system and the field etc. e) Not recognizing that it is by the two quantities of energy (Mc2 and pc) fusing together to form a system that motion occurs. f) the omission of the fact that a fraction of the applied energy of motion pc gets usurped for the co-movement with the location. g) Not developing the theory with state changes of energy as the basis of its physical geometry. With these congenital foundational problems being inherent in these two progeny theories as well, it should be obvious that revamping of physics must begin from where the problems originated".
4. I have shown from Newton's writings (Preface to the Principia) that he intended to create only a makeshift theory (Mechanics) as a stepping stone until a "Truer Method of Philosophy" (a geometric theory based on the behaviour 'least particles') is found.
5. I have shown from Einstein's writings that he considered both Newtonian foundation as well as that of his own theory are based on fictitious concepts.
6. I have shown that Einstein has pointed that the 'Right Way' is yet to be found which would be based on simplest conceivable mathematical ideas connecting laws with phenomena.
7. I have shown why Einstein could not find the 'Right Way' himself which he was desperately in search of, by expanding the thermodynamic approach into whole of physics.
8. I have shown that Maxwell chartered an outline of a program for the future development of science, based on the paradigm that all phenomena are based on state changes of energy, and inflow and outflow of energy from a system (i.e. based on open systems).
9. By assimilating the intuitive notions of all the founders, in regard to the future development of physics should take, I have initiated to develop a new approach.
10. It a) provides the equation of motion for a particle at any velocity (slow or near light velocity) thus the schism in physics between Newtonian mechanics and SRT is removed. b) Explains how gamma-factors arise, c) why it requires momentum gamma-Mv for a particle to be set in motion with momentum Mv. d) provides the physical basis of the Lorentz transformation, e) the physical basis of the constancy of the velocity of light g) why physical processes slow down when a particle is in motion. h) From where the energy underlying the centrifugal force comes.
(This is all I could squeeze in within the 25,000 characters permitted by the contest. Elsewhere I have derived Lorentz force, gravitational time increase of a GPS clock, Compton scattering, explanation of Michelson's experiment by recognizing TDE changes frequency while keeping velocity constant etc.).
Hoping to hear from you.
Best regards,
Viraj Fernando
Dear Viraj,
It appears that the first few assumptions you reject ("the primacy of the concepts of space and time," etc.) are the same as mine, although we use different words (I would say "the manifold structure of spacetime," or "an independent time parameter.")
Some of the other assumptions you reject (for instance, those regarding centrifugal force and some of the statements about energy) I would expect to disappear automatically once the usual assumptions about space and time are rejected.
I had better not make any more specific remarks until I have read your essay, however. One thing I will say is that it appears as if you made an honest effort to answer the question posed by the essay contest rather than just writing down your favorite ideas about physics. You will notice that I made a similar effort. Take care,
Ben