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FQXi FORUM
October 16, 2019

CATEGORY: Trick or Truth Essay Contest (2015) [back]
TOPIC: String Theory and Milgrom's Modified Newtonian Dynamics (MOND) by David Brown [refresh]
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Author David Brown wrote on Jan. 9, 2015 @ 22:27 GMT
Essay Abstract

String theory might be the ‘only game in town’ for the unification of quantum field theory and general relativity theory. In 1983 the Israeli astrophysicist Mordehai Milgrom challenged Newtonian theory in terms of non-relativistic astronomical phenomenon associated with hypothetical dark matter. Over 30 years later the challenge remains controversial and unconvincing to most string theorists.

Author Bio

David Brown has an M.A. in mathematics from Princeton University and was for a number of years a computer programmer.

Download Essay PDF File

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Philip Gibbs wrote on Jan. 10, 2015 @ 09:55 GMT
David, this is a nice start for the contest. It is interesting that MOND explains some features of galaxy dynamics that dark matter might not, but it fails with galactic clusters. MOND is incompatible with general relativity but string theory predicts GR, so it is not hard to see why string theorists would reject MOND. I think you would have to say more about how you see string theory being modified to get their attention.

You ask "(1) To what extent does string theory unify physics
 

and mathematics? (2) To what extent can physics an
d mathematics be unified?" These are interesting questions, but what do you think the answers are?

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Author David Brown replied on Jan. 10, 2015 @ 14:35 GMT
Phil Gibbs: I, along with many scientists or would-be scientists, owe you a great debt of gratitude for providing vixra.org . People say I am a crackpot and they are correct. My method is to generate hundreds of crackpot ideas and see if any provide testable predictions which might be correct. J. Christian has pointed out (correctly) that I am an incompetent physicist. I am not like Newton who...

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Philip Gibbs replied on Jan. 11, 2015 @ 09:45 GMT
David, you raise some interesting questions which is why I am always happy to see anyone get involved in science. I like your quotes from Crick.

The questions about unifying maths and string theory are very important. My view is that this is central to future progress. In my essay I speculate that a structure leading to string theory emerges from a principle of universality in mathematics. The work of Nima Arkani-Hamed is the most obvious lead towards understanding the fundamentals of string theory (see e.g. his recent short talk https://www.youtube.com/watch?v=C9LwPkijT10 ) There are also people looking at the application of n-category to string theory such as John Baez and Urs Schreiber. I find the abstraction hard to follow but I am sure it will emerge as important work and I think that a very general n-categorical structure could be what unifies maths and string theory.

Keep asking good questions!

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Author David Brown replied on Jan. 11, 2015 @ 11:42 GMT
"The questions about unifying maths and string theory are very important." To what extent can string theory plumb the depths of nature? At the U. of Chicago, Professor Chandrasekhar said to me, "Nature is deeper than any scientist's theory." One might divide mathematics into 6 major areas: algebra/category theory, mathematical analysis, applied mathematics/differential equations/numerical...

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Anonymous wrote on Jan. 18, 2015 @ 00:08 GMT
David,

I enjoyed your article, and especially some of your quotes. I believe good quotes are particularly relevant for essays. Particularly Witten's observation that "there is not yet any proof that the theory is relevant to physics." In my current essay I refer to this as a map that does not point to any territory. Also liked Gross's remark that "String theory is part and parcel of quantum field theory."

By the way, based on remarks of his that I've read, I'm amazed that Witten responded to you. Congratulations!

Of your three basic alternatives I would favor the second, that Newtonian-Einstein gravitational theory is correct but appears wrong because of neglect of non-linear mechanisms. The flat rotation curves are real, but MOND appears to be a 'patch' to explain them. That's just my opinion. Your suggestion that string theory could solve the problem is interesting.

Like Philip, I too like your (first) quote from Crick. My essay treats a specific case in point. I invite you to read my essay and leave an opinion.

Best regards,

Edwin Eugene Klingman

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Author David Brown replied on Jan. 18, 2015 @ 13:12 GMT
Edwin: Thank you for you congratulatory sentiment. Is MOND more than a 'patch'? Is the MOND acceleration constant actually an important constant of nature — even if such a constant is not precisely defined to more than 20% ? In connection with the "dark-matter-compensation-constant" there are the questions: (1) Is such a constant consistent with the empirical facts? (2) If such a constant is consistent with the empirical facts, then what does the constant really mean in terms of the foundations of physics? Is Milgrom the Kepler of contemporary cosmology? Those researchers who are interested in the preceding question should consider a further question: Should physicists consider the problem of attempting to prove, under plausible physical hypotheses, that the Anderson-Campbell-Ekelund-Ellis-Jordan flyby anomaly formula is approximately equivalent to replacing the -1/2 in the standard form of Einstein’s field equations by -1/2 + dark-matter-compensation-constant ?

"Anomalous Orbital-Energy Changes Observed during Spacecraft Flybys of Earth" by Anderson et al., PhysRevLett, 2008

Regards, David Brown

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John C Hodge wrote on Jan. 22, 2015 @ 18:07 GMT
Another model for the unification of quantum field theory and general relativity theory is Scalar Theory of Everything model correspondence to the Big Bang model and to Quantum Mechanics .

Spiral galaxy rotations curves also have an asymmetry that other models do not attempt to explain. Because ``accepted’’ physics has tried and failed (including MOND) to explain the asymmetric rotation curves, these seem ripe for a forum like FQXi. My model is Scalar potential model of spiral galaxy HI rotation curves and rotation curve asymmetry .

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John R. Cox wrote on Jan. 25, 2015 @ 20:25 GMT
David,

Very provocative in posing the questions. Also good reference articles and abstracts listing for the inquiring minds. Mond is an 'outsiders' pursuit, but does ask us to discover a correct question. I have amused myself from time to time with the notion that in the future all those solutions^500 might be seen as a naively obtained inventory of radial fluctuations of energy seeking equilibrium as an ideal spherical rest mass. Good luck, for what its worth my rating is as an amateur. jrc

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Gary D. Simpson wrote on Jan. 27, 2015 @ 23:12 GMT
David,

A pretty good read with lots of thoughtful questions. The answers can only be had through experiment and observation as you note in some of the comments.

Best Regards,

Gary Simpson

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Author David Brown replied on Jan. 28, 2015 @ 00:50 GMT
Gary,

Thank you for your comments on my essay. In your essay "Calculus - Revision 2.0" page 7, you wrote, "It is only through the comparison between prediction and experiment that we can hope to understand." Physics without prediction is unsatisfactory. String theorists need to find a way to eliminate, or at least drastically constrain, the string landscape. My guess is that Milgrom's MOND is the key to eliminating the string landscape and to making decisive, testable predictions with string theory. String theorists need to incorporate MOND into string theory. Consider the problem of attempting to prove, under plausible physical hypotheses, that the Anderson-Campbell-Ekelund-Ellis-Jordan flyby anomaly formula is approximately equivalent to replacing the -1/2 in the standard form of Einstein’s field equations by -1/2 + dark-matter-compensation-constant.

"Anomalous Orbital-Energy Changes Observed during Spacecraft Flybys of Earth" by Anderson et al., PhysRevLett, 2008

Anyone interested in the foundations of physics might find to worthwhile to consider the preceding problem.

— David Brown

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Amrit Srecko Sorli wrote on Jan. 29, 2015 @ 08:06 GMT
string theory has no bijective epistemological correspondence with physical world. It is a pure fantasy.

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Author David Brown replied on Jan. 29, 2015 @ 12:00 GMT
Amrit Sorli (Foundations Of Physics Institute): In your essay "Application of Bijective Function of Set Theory in Physics" you wrote, "Mathematics is the useful tool of physics. However out of pure mathematical laws we cannot deduce physical laws." The logical possibilities seem to be vastly greater than the physical possibilities. My guess is that vibrating strings at or below the Planck scale are a reality, in some sense. According to Burton Richter, "... Progress in physics almost always is made by simplification. ... To the Landscape Gardeners I would say calculate the probabilities of alternative universes, and if ours does not come out with a large probability while all others with content far from ours come out with negligible probability, you have no useful contribution to make to physics. ..."

Is "Naturalness" Unnatural? Presentation at SUSY '06, Prof. Burton Richter, Stanford University, 14 June 2006

I maintain the Milgrom Denial Hypothesis: The main problem with string theory is that string theorists fail to realize that Milgrom is the Kepler of contemporary cosmology. Why do I maintain this hypothesis? String theory seems to be the mathematics of quantum gravity, while Milgrom, McGaugh, Kroupa, Pawlowski, and others have empirical evidence that gravity is Milgromian, whatever that might turn to be in terms of string theory. If string theory is merely a mathematical fantasy it has certainly been a productive fantasy for mathematics. The mathematical unification of quantum field theory and general relativity theory might, by logical necessity, be some form of string theory or M-theory.

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Akinbo Ojo wrote on Feb. 9, 2015 @ 09:30 GMT
Dear David,

I just read your essay and the refreshing ideas proposed. Your essay should score highly even though to your question: Does dark matter exist? My answer is Yes, it does and not only that it exists right there inside your office and laboratory. If you are inclined to discuss the proof, we can take this further.

Best regards,

Akinbo

Please note: I share your skepticism about string theory.

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Author David Brown replied on Feb. 10, 2015 @ 12:34 GMT
Dear Akinbo,

In your essay “Does the division of extension mean the same in mathematics as it does in physics?” (page 5), there is the statement: “It appears that without the addition of some further ingredient into our physics, there are subtle nuances to what we call discrete and how it can be fundamentally expressed." I guess that, more specifically, one or more new physical hypotheses need to be introduced into string theory in order to explain dark matter and the space roar. My quantum theory of gravity has several basic assumptions: Dark matter is virtual mass-energy that has positive gravitational mass-energy and zero inertial mass-energy. Dark energy is virtual mass-energy that has negative gravitational mass-energy and zero inertial mass-energy. Nature is finite and digital, more-or-less as described in Wolfram’s “A New Kind of Science”, Chapter 9. The Koide formula, Lestone’s heuristic, and ‘t Hooft’s superstring determinism are necessary for understanding the foundations of physics. The Fernández-Rañada-Milgrom Effect, the Space Roar Profile Prediction, and the 64 Particles Hypothesis are empirically valid. According to the Gravity Probe B science team, my quantum theory of gravity has already been refuted. (I dispute the Gravity Probe B science team’s interpretation of their own experiment.) In any case, I affirm the Milgrom Denial Hypothesis: The main problem with string theory is that string theorists fail to realize that Milgrom is the Kepler of contemporary cosmology. Why do I affirm this? The mathematic evidence supports string theory, and the empirical evidence supports Milgrom’s acceleration law (according to the work of Milgrom, McGaugh, Kroupa, and Pawlowski).

— D. Brown

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Member Tim Maudlin wrote on Feb. 11, 2015 @ 18:36 GMT
Dear David Brown,

I am so somewhat surprised that you link the question of dark matter with string theory so strongly. MOND was proposed as a way to account for the flat rotation curves of stars in galaxies, and is not committed to any particular account of the nature or origin of the dark matter. And cosmological observations of gravitational lensing effects have become much more exact and sophisticated since 1983. The Bullet Cluster has been cited as fairly direct evidence for dark matter. Do you have results that show how to account for these observations without dark matter, and just with a modification of the gravitational dynamics?

Regards,

Tim Maudlin

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Member Tim Maudlin replied on Feb. 11, 2015 @ 18:38 GMT
Sorry: I meant that the dark matter explanation of the rotation, as opposed to MOND, is not committed to any particular account of the dark matter, and in particular not to string theory.

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Author David Brown replied on Feb. 12, 2015 @ 00:00 GMT
Dear Tim Maudlin,

In your essay “How Mathematics Meets the World” there is the statement, “The puzzle is why the language of mathematics should be such an effective tool for describing the physical world.” My guess is that the solution to the puzzle is: Nature is finite and digital with string vibrations confined to 3 copies of the Leech lattice. Why is string theory likely to be ‘the only game in town’? Google “mystery magic matrix witten”. What is the empirical evidence for MOND? Google “kroupa pawlowski milgrom new paradigm”. Does the Bullet Cluster show that dark matter particles exist? See:

Milgrom's perspective on the Bullet Cluster, The MOND Pages

What is the empirical evidence for the Fernández-Rañada-Milgrom effect? See:

Does the Rañada-Milgrom Effect Explain the Flyby Anomaly?

My thinking is that the empirical evidence favors MOND, the mathematical evidence favors string theory (or M-theory), and the Fernández-Rañada-Milgrom effect is likely to be the string theoretical interpretation of MOND. I claim that an easy scaling argument demonstrates that the alleged effect is approximately equivalent to MOND. If in the standard form of Einstein's field equations the -1/2 is replaced by -1/2 + dark-matter-compensation-constant, gravitational lensing works approximately as well merely because the dark-matter-compensation-constant is very small in comparison to 1/2.

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Sujatha Jagannathan wrote on Feb. 16, 2015 @ 08:23 GMT
You've taken a controversial subject of choice.

Thumbs Up!

Sincerely,

Miss. Sujatha Jagannathan

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Author David Brown replied on Feb. 21, 2015 @ 10:31 GMT
Dear Miss. Sujatha Jagannathan:

In your essay “Trick or Truth: The Mysterious Connection Between Physics and Mathematics”, you state: “The puranic view asserts that the universe is created, destroyed, and re-created in an eternally repetitive series of cycles.” My theory assumes that the preceding idea is basically correct but my theory is based upon Wolfram’s atheistic, materialistic theory as expounded in “A New Kind of Science” (see NKS Forum, Applied NKS). However, according to the Space Probe B science team, my theory has already been ruled out. (If the 4 ultra-precise gyroscopes malfunctioned in the manner suggested by the Space Probe B science team, then I agree that my theory is wrong.) In any case, I think that Milgrom is the Kepler of contemporary cosmology (on the basis of empirical evidence accumulated by Milgrom, McGaugh, Kroupa, Pawlowski, and others). What MOND really means is unclear even to Milgrom.

— D. Brown

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basudeba mishra wrote on Feb. 18, 2015 @ 09:34 GMT
Dear Sir,

We have discussed relativity critically in our essay. Since GR is also an inverse square theory, if MOND is correct, GR would also need modification. But for this modified versions to work, some sort of unseen or “dark” presence is a must, which looks a lot like dark matter. It won’t be described by particles in the way that dark matter is described - it may be described in...

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Author David Brown replied on Feb. 21, 2015 @ 12:25 GMT
Dear Basudeba Mishra,

In your essay “Reasonable Effectiveness of Mathematics”, you state “The validity of a physical statement is judged by its correspondence to reality.” Judging whether a physical theory corresponds to empirical reality depends upon the fairness of the empirical tests. I claim that the string theorists fail to realize that the empirical game is rigged against MOND...

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Theodore St. John wrote on Feb. 24, 2015 @ 11:36 GMT
David Brown,

Nice work on your essay. Short and sweet but you obviously put a lot of thought into it. Most of these essays are very thought provoking but some are hard to read. I went a different route and wrote what I consider a more entertaining twist - sort of a blend of Knights of the Round Table and Lord of the Rings (See Doctors of the Ring - The Power of Merlin the Mathematician to Transform Chaos into Consciousness). It is based on a model that I am trying to get published, which I posted at http://vixra.org/abs/1402.0045 called the space-time-motion model. I invite you to read it and let me know what you think (email to stjohntheodore@gmail.com). Of course, I also invite you to read and rate my essay if you get the chance.

Respectfully,

Ted St. John

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Author David Brown replied on Feb. 24, 2015 @ 12:46 GMT
Ted St. John,

In your essay “Doctors of the Ring – the Power of Merlin the Mathematician to Transform Chaos into Consciousness”, you state: “... some admit that they don’t really understand what time actually is. ... The problem with trying to answer the question why is there only one dimension of time is: How can we be so certain that there is only one dimension of time if we don’t even know what it is? True, it only takes one number to describe time, but not because it is a one-dimensional entity; it’s because everyone agreed upon a single time standard in order to describe motion.” Fernández-Rañada and Tiemblo-Ramos suggested that atomic time might be different from astronomical time — I say that atomic time is guaranteed to be different from astronomical time because the work of Milgrom, McGaugh, Kroupa, and Pawlowski shows that some revision is needed in the current paradigm of cosmology. The physicists have agreed upon a single time standard based upon empirical findings, quantum field theory, and general theory relativity — their time standard well works amazingly well for the most part. However, Milgrom’s MOND, the space roar, and the photon underproduction crisis demonstrate that something is wrong somewhere in physicists’ current understanding of the foundations of physics. — D.B.

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Mary Ann Slaby wrote on Mar. 13, 2015 @ 03:52 GMT
I liked the approach, however a cohesive relationship was not put forth.

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Author David Brown replied on Mar. 13, 2015 @ 12:10 GMT
Dear Mary Ann Slaby,

In your essay "What is the Mysterious Connection Between Physics and Mathematics?", you wrote: "The mysterious connection between physics and mathematics resides in the calculus developed by Newton and Leibniz." Riemannian geometry generalizes calculus, and presumably the non-commutative geometry of string theory is the generalization of Riemannian geometry that works...

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Jose P. Koshy wrote on Mar. 19, 2015 @ 14:32 GMT
Dear David Brown,

I claim I am doing 'independent' research in theoretical physics. My few papers are available at vixra. When I learned from your reply to Philip Gibbs that you love 'crackpot' ideas, I thought it will be good to go through your essay. You have put forth some relevant questions.

I consider Dark matter a myth. What I propose is finite gravity with a speed dependent G. The present G is actually the G of Earth for its present speed.; it can be theoretically deduced from 'G' of electrons. The universe as a whole has a certain G which increases with expansion; the present G of the universe is 1.4194x10-3. Using this G, the present Earth- Moon distance can be accurately predicted. What do you think? A crackpot idea! Visit my site finitenesstheory.com for more details.

Kindly go through my essay A physicalist interpretation of the relation between Physics and Mathematics.

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Author David Brown wrote on Mar. 19, 2015 @ 15:33 GMT
Dear Jose P. Koshy,

In your essay you wrote, "The Standard Model of particles is a set of interpretations based on QM. Similarly, the ΛCDM model of the universe is a set of interpretations based on GR. These models are still incomplete, and require further refining." According to Kroupa, the ΛCDM concordance cosmological model has been ruled out. A theory of "finite gravity with speed dependent G" contradicts what I call the Fernández-Rañada-Milgrom effect, i.e., the -1/2 in the standard form of Einstein's field equations should be replaced by -1/2 + dark-matter-compensation-compensation, where this constant is approximately sqrt((60±10)/4) * 10^-5 . Note that Milgrom's acceleration law does not suggest "speed dependent G" but some modification of Newtonian gravitation which is acceleration dependent. On the empirical evidence, I could be wrong about everything except the Milgrom Denial Hypothesis. No matter what the future holds, I predict that a few ideas now deemed 'crackpot' will triumph — however, these ideas will be very few in number and it is very unclear what the ideas will be.

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Joe Fisher wrote on Mar. 30, 2015 @ 15:16 GMT
Dear Mr. Brown,

I thought that your engrossing essay was exceptionally well written and I do hope that it fares well in the competition.

I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.

All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.

Joe Fisher

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Author David Brown replied on Mar. 30, 2015 @ 20:01 GMT
Dear Joe Fisher,

In your essay "WHY THE REAL UNIVERSE IS NOT MATHEMATICAL", you wrote, "... it must be re-emphasized here that all appearances are deceptive. The real Universe is not apparent and this is why it is not mathematical." If mathematics is that part of human thinking that is precise, then I personally believe that mathematical thinking is a particular type of electromagnetic field and therefore is at least a component of the real universe. On page 2 of the "Meaning of Relativity", 5th edition, Einstein wrote, "The only justification for our concepts and system of concepts is that they serve to represent the complex of our experiences; beyond this they have no legitimacy." The gravitational theories of Newton and Einstein are correct over broad ranges of experimental tests — beyond empirical testing, the true nature of reality is perhaps fundamentally a question of subjective opinion or philosophy.

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Jayakar Johnson Joseph wrote on Apr. 5, 2015 @ 15:42 GMT
Dear David,

As there is inconsistency between QM and cosmology, MOND is imperative; in that Gauge anomaly is causal for this inconsistency that invalidates Gauge theory. While this Gauge anomaly is a Vector gauge anomaly then that Gravitational anomaly invalidates General relativity. This is causal for the Gravity anomaly of Planets that is more pronounced with the observations of Galaxy clusters and their Superclusters.

Thus, further developments on MOND emerges with the theory of Tensor–vector–scalar gravity and its extension, Bi-scalar tensor vector gravity theory; while MOG is developed on Scalar–tensor–vector gravity theory.

All these incompleteness indicates that, redefining the Causality of gravitation is much imperative with string theory. Thus we may recommend for the modifications in string theory, in that a string-segment itself is to be considered as an eigen-rotational matter with energy, that is an alternative to the fermionic field.

Thus, Gravitation between micro objects is a tensor derivative of a string-matter or collective tensor derivatives of few string-matters between invariable scalar structures of micro objects; whereas the Gravitation between macro objects is the resultant collective tensor derivatives of the string-matter bundles exists between that invariable scalar structures of macro objects, in time.

With best wishes, Jayakar

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Author David Brown replied on Apr. 5, 2015 @ 17:12 GMT
Dear Jakayar Johnson Joseph,

In your essay "Before the Primordial Geometric origin: The Mysterious Connection between Physics and Mathematics" you wrote, "Though it may be obvious that our Universe is Mathematical, because of Initial singularity, the only possibility to explore the initial conditions of the Universe is with Gödel's incompleteness theorems that have inherent limitations." It might be possible to detect gravitational waves generated in the very early stages of the Big Bang. In my personal opinion, Gödel's first and second incompleteness theorems suggest that the mathematical concept of infinity is somewhat unsatisfactory — to know what we really mean by "infinity" we might have to add infinitely many new axioms to Peano Arithmetic. One of my ideas is to replace the -1/2 in the standard form of Einstein's field equations by -1/2 + dark-matter-compensation-constant, where this constant is approximately sqrt((60±10)/4) * 10^-5 — however, if the Gravity Probe B science team is correct, this idea has already been ruled out. If some "eigen-rotational string matter continuum paradigm" accurately describes empirical reality, there needs to be some MOND-compatible prediction, perhaps along the lines of TeVeS or some similar theory.

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Thomas Howard Ray wrote on Apr. 13, 2015 @ 14:14 GMT
David,

You say that string theorists fail to recognize that Milgrom is the "Kepler of contemporary cosmology," and yet I interpret Witten's reply to you, as favorable to that idea. He gives credit to the observational cosmologists, and credit to the mathematical cosmologists.

Just as Kepler's laws cannot be derived from first principles -- they are themselves first principles -- frameworks that explain frameworks, in a metamathematical and metaphysical way, are inductive hypotheses, and prior to the method of deduction from theory that characterizes rational science.

Like Witten (and Newton), I like to begin with a mathematically complete idea and make my conclusions from that structure, by theorem-proving. That doesn't obviate any hypotheses from observation that might crop up from serious researchers -- yet why should one trust any inductive conclusion? As that sage Yogi Berra put it, "If you don't know where you're going, you might end up somewhere else."

I got interested in Milgrom's research a few years ago after reading John Moffat's *Re-inventing Gravity.* I liked the book and the ideas in it -- in the end, though, I come back to my "center" in the fundamentals of field theory, and in agreement with Witten that "general relativity cosmology forces itself on us."

My current essay is part of my attempt to reconcile field theory with cosmological initial conditions, which brings quantum field theory (and therefore string theory) back to center stage.

Nice job of raising important questions -- my highest mark to you.

Best,

Tom

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Author David Brown wrote on Apr. 13, 2015 @ 17:09 GMT
Dear Thomas Howard Ray,

In your essay “Science of the Possible, or the Probable?” (page 4), you wrote, “What quantum theorists know and seldom talk about, is that Bell’s Inequality— the formal mathematical statement of Bell’s theorem— is only locally real. The issue of nonlocality arises in the proof of the theorem, and that proof is only by way of double negation.” In my...

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Thomas Howard Ray replied on Apr. 14, 2015 @ 02:38 GMT
David,

I find the claim -- "axiomatization of physics (Hilbert's 6th problem) implies that nature is fundamentally both finite and digital" -- to be self-contradictory.

Finite sets are continuous in principle, physically and mathematically. One can derive parts from the whole; the converse is not true, because the sum of the continuous whole is greater than that of its discrete parts. Take the simple arithmetic theorem -- that a point may simultaneously map to any set of points, provided that it is far enough away. That point at infinity has to exist, physically (and locally, i.e., in every measured time interval), or else Minkowski space-time and special relativity are falsified.

The basic logical completeness of a generalized field theory (even including number fields) persuades me that nature is recursive. In my essay discussion forum -- in a recent attachment -- I demonstrated a continuous digital recursive function corresponding to the simplest prime number sequence.

Tom

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Author David Brown replied on Apr. 14, 2015 @ 12:48 GMT
Tom,

Einstein and Leonardo da Vinci apparently believed that nature is infinite. According to Leonard da Vinci, "La natura è piena d'infinite ragioni, che non furon mai in isperienzia." (Nature is full of infinite reasons, which people have never realized.)

"Finite Nature is the hypothesis that ultimately every quantity of physics, including space and time, will turn out to be discrete and digital; that the amount of information in any small volume of space-time will be finite and equal to one of a small number of possibilities." — Edward Fredkin, "A New Cosmogony"

Can quantum information be explained in terms of Fredkin-Wolfram information below the Planck scale? Perhaps not. However, even if nature is infinite, the amount of actual data accumulated by scientists will probably always be finite. Google "witten milgrom" for more information on how the Copenhagen theory of measurement might be replaced by a Fredkin-Wolfram theory of measurement.

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Thomas Howard Ray replied on Apr. 14, 2015 @ 14:57 GMT
"Einstein and Leonardo da Vinci apparently believed that nature is infinite."

Not Einstein. General relativity describes a universe "finite and unbounded."

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