String Theory and Milgrom\'s Modified Newtonian Dynamics (MOND) by David Brown

"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 analysis, geometry/topology, set theory/mathematical logic/theoretical computer science, and probability/statistics (see https://math.berkeley.edu/research/areas). In the future, each of these 6 major areas might have a formulation in terms of string theory.

In reply to an email request for criticism concerning my essay, Professor Edward Witten has kindly provided the following comments:

"Dear Mr. Brown,

I think the best answer to your question is that the opinions of string theorists about MOND are not very important, what is more important are the opinions of astronomers who really know well all the data. However, I can see a lot of obvious reasons that people are skeptical about MOND. For example, gravitational lenses were discovered after MOND was put forward, and dark matter appears to participate in lensing as one would expect in General Relativity. The universe is a complicated place with a lot of colliding galaxies, clusters of galaxies, large scale structure etc. General Relativity gives a description of all this that appears to work as far as we can test it, which is a lot although not everything one would want to test. MOND is a sort of one-galaxy-at-a-time description so it is probably hard to apply MOND to a lot of things. Finally, one really has to stand on one's head to reconcile MOND with what is well-established about relativistic physics, and the results are pretty obscure and far-fetched looking. None of these comments, however, have anything at all to do with string theory. They are just based on physics that is much better-established and down-to-earth."

Let us assume my quantum theory of gravity ("Wolframian string theory") is empirically wrong. Through study of the work of McGaugh and Kroupa, I strongly believe 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. My guess is that the majority of experts on dark matter are incorrect and that Milgrom, McGaugh, Kroupa, and Pawlowski are correct. Consider 2 quotations:

"Unthinking respect for authority is the greatest enemy of truth." - Einstein

"Theorists almost always become too fond of their own ideas, often simply by living with them for so long." - Francis Crick, "What Mad Pursuit", page 141

The empirical evidence backs Milgrom, McGaugh, Kroupa, and Pawlowski, in so far as my judgment has any validity whatsoever.

"... get into specific details." From McGaugh's MOND PAGES, "When we measure the amount of luminous mass (stars and gas) in these systems and apply Newton's Law of Gravity, the observed mass falls well short of the amount required to explain the observed orbital speeds. This is the mass discrepancy. There are two logical possibilities to explain the observed mass discrepancies:

Either Most of the Mass in the Universe is Invisible (Dark Matter), or Dynamical Laws must be Modified (MOND).

There are significant challenges to both ideas. Issues for MOND:

Can a modified force law explain all observations?

Can a satisfactory theory encompassing both General Relativity and MOND be found?

Issues for Dark Matter:

Does the stuff we call Dark Matter really exist?

Can a dark matter based theory explain the MONDian phenomenology observed in rotation curves?

Why should the mass discrepancy only appear at a particular acceleration scale?"

It appears to me that there are 2 basic alternatives: (1) Newtonian-Einsteinian gravitational theory is 100% correct but appears to wrong for some unknown reason (weird quantum effect based upon the string landscape?) OR (2) Newtonian-Einsteinian gravitational theory really is significantly wrong. For the 1st alternative I posted some dubious speculations at NKS Forum Applied NKS. What if the 2nd alternative is true?

What is the simplest interpretation of Milgrom's MOND? The answer might be that the law of conservation of gravitational energy is false. Consider Einstein's "The Meaning of Relativity", 5th edition, page 84. Concerning the fundamental geometric tensor, Einstein wrote "3. Its divergence must vanish identically. ... it may be proved that this third condition requires a to have the value -1/2." I say that Milgrom is the Kepler of contemporary cosmology and that the constant a should be -1/2 dark-matter-compensation-constant, where this dark-matter-compensation-constant is some very small positive number to be determined by experiment. I claim that an easy scaling argument shows that this idea is approximately equivalent to MOND. I suggest that the Gravity Probe B science team misinterpreted their own data, and that a good value for the hypothetical dark-matter-compensation-constant can be found by analyzing the Gravity Probe B data under the assumption that the 4 ultra-precise gyroscopes functioned to within design specifications. The reanalysis should decisively disconfirm or confirm my simplistic idea. My idea is that Einstein's equivalence principle is 100% true for mass-energy that is implicitly or explicitly measured and 100% false for virtual mass-energy. My guess is that dark matter is virtual mass-energy that has positive gravitational mass-energy and ZERO inertial mass-energy while dark energy is virtual mass-energy that has negative gravitational mass-energy and ZERO inertial mass-energy. By assuming that nature is finite and digital and that string vibrations are confined to 3 copies of the Leech lattice, it might be possible to justify the preceding speculative idea.

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

Dear Mr. Fisher: The idea that "... reality must already be fully unified in order for it to be realistic ..." might be true in that nature's reality has no need of validation by mathematical theories. According to L. E. J. Brouwer, "Mathematics is nothing more, nothing less, than the exact part of our thinking." Reality is what it is, no matter what I think. My conjecture, what I call the Milgrom Denial Hypothesis, i.e. the main problem with string theory is that string theorists fail to realize that Milgrom is the Kepler of contemporary cosmology, involves the assumption that Milgrom, McGaugh, Kroupa, and Pawlowski are empirically correct and the assumption that string theory, in some form, can explain dark matter. I am not entirely sure that string theory can explain dark matter. According to Edward Witten, "... string theory has proved to be remarkably rich, more so than even the enthusiasts tend to realize. It has led to penetrating insights on topics from quark confinement to quantum mechanics of black holes, to numerous problems in pure geometry. All this suggests that string theory is on the right track; otherwise, why would it generate so many unexpected ideas? And where critics have had good ideas, they have tended to be absorbed as part of string theory, whether it was black hole entropy, the holographic principle of quantum gravity, noncommutative geometry, or twistor theory."

"Unravelling string theory" by Edward Witten, Nature, vol. 438, 22/29 December 2005

From an operational viewpoint, I say that string theorists must somehow incorporate Milgrom's MOND into string theory -- the empirical evidence suggests this.

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.

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

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.