Is Milgrom’s MOdified Newtonian Dynamics (MOND) fundamental for philosophy, science, and the physical interpretation of string theory? by David Brown

Essay Abstract

This essay raises questions concerning what is fundamental in physics. There is a brief discussion of Milgrom's MOdified Newtonian Mechanics with two possible interpretations: one possible interpretation in terms of string theory with the finite nature hypothesis and another possible interpretation in terms of string theory with the infinite nature hypothesis.

Author Bio

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

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The electromagnetic effects of axions (1-spheres with virtual cross sections) and leptons (2-spheres with virtual cross sections) might suggest that some form of electromagnetic uncertainty might be approximated by (axion mass)/(electron mass).

Can the proton charge radius puzzle be resolved in terms of electromagnetic effects from axions?

Proton radius puzzle, Wikipedia

Axion, Wikipedia

According to Graf and Steffen, "If the Peccei-Quinn (PQ) mechanism is the explanation of the strong CP problem, axions will pervade the Universe as an extremely weakly interacting light particle species."

"Thermal axion production in the primordial quark-gluon plasma" by Peter Graf and Frank Daniel Steffen, 2011

According to Derbin et al., "If the axions or other axion-like pseudo scalar particles couple with electrons then they are emitted from Sun by the Compton process and by bremstrahlung ...:

"Search for solar axions produced by Compton process and bremsstrahlung using the resonant absorption and axioelectric effect" by A. V. Derbin, et al., 2013

What is the magnitude of the uncertainty in determining the fine structure constant?

Fine structure constant, Wikipedia

Hanneke, Fogwell, and Gabrielse (2008) estimated 1/(fine structure constant) as: 137.035999084(51)

Hanneke, D., Fogwell, S., & Gabrielse, G. (2008). New measurement of the electron magnetic moment and the fine structure constant. Physical Review Letters, 100(12), 120801.

.000000051/137.035999084 = 3.72... * 10^-10

(electron mass) * 3.72 * 10^-10 = 1.901 * 10^-4 eV/c^2

P. J. Mohr, B. N. Taylor, and D. B. Newell (2015) estimated 1/(fine structure constant) as: 137.035999139(31)

"Fine structure constant" in CODATA Internationally recommended 2014 values of the fundamental physical constants, National Institute of Standards and Technology

.000000031/137.035999139 = 2.262... * 10^-10

(electron mass) * 2.262 * 10^-10 = 1.156 * 10^-4 eV/c^2

How might the proton radius puzzle be related to uncertainties in determining the fine structure constant?

In the article "The Rydberg constant and proton size from atomic hydrogen" Beyer et al. (2017) stated (p. 80), "Line shape distortions caused by quantum interference from distant neighboring atomic resonances have recently come into the focus of the precision spectroscopy community ... To the best of our knowledge, this effect has been considered in the analysis of only one of the previous H experiments and was found to be unimportant for that particular experimental scheme ... The effect was found to be responsible for discrepancies in the value of the fine structure constant α extracted from various precision spectroscopy experiments in helium ... The root of the matter is that natural line shapes of atomic resonances may experience deviations from a perfect Lorentzian when off-resonant transitions are present."

Beyer, Axel, Lothar Maisenbacher, Arthur Matveev, Randolf Pohl, Ksenia Khabarova, Alexey Grinin, Tobias Lamour et al. "The Rydberg constant and proton size from atomic hydrogen." Science 358, no. 6359 (2017): 79-85.

Are axions a likely source of off-resonant transitions? Could the older experiments for determining the proton charge radius have failed to eliminate axion interactions as a source of inflating the value of the proton radius? Could the 2017 experiment by Beyer et al. be failing to take into account axion interactions? What might happen if experiments for measuring the proton charge radius were performed at 4 different levels of shielding -- on the surface, in a slightly deep mine, in a moderately deep mine, and in a very deep mine -- to check for possible axion production of off-resonant transitions? By assuming a precise value for the axion mass could the 2017 experiment by Beyer et al. be modified for axion detection?

If most of the proton charge radius puzzle can be explained by uncertainty in estimating the finite structure constant due to unexpected axion detection, then (1.2 ± 1.0) * 10^-4 eV/c^2 might be a plausible estimate for the axion mass.

"If nature is described by some finite structure then how big does that structure have to be?" The preceding is a crucially important question -- unfortunately, at this stage, my only answer is an extremely crude, wild guess. Let us assume that classical information reduces to quantum information reduces to Fredkin-Wolfram information. How much classical information is there in the observable universe? How many cubic millimeters might there be in the observable universe? According to Wikipedia, one plausible estimate for the number of the cubic millimeters in the observable universe might be 3.57 * 10^89

Observable universe (Size), Wikipedia

If nature can be described by Wolfram's cosmological automation, then how many bits of Fredkin-Wolfram information might be involved in the complete description of Wolfram's cosmological automaton? Let us define googol = 10^100, googolplex = 10^(googol), googolplexplex=10^(googolplex). As a wild guess, it seems to me that the number of bit of classical information in the observable universe might be at the googol level, the number of bits of quantum information in each particular universe in the multiverse might be at the googolplex level, and the number of bits of Fredkin-Wolfram information needed to describe the hypothetical finite structure of the multiverse might be at the googolplexplex level. In order to accurately describe Wolfram's cosmological automation, 4 steps might be necessary: (1) Write down 4 or 5 simples rules that completely describe Wolfram's automaton. (2) Using the 4 or 5 simple rules, derive empirically satisfactory approximations to quantum field theory and general relativity theory. (3) Make new predictions using Wolfram's automation. (4) Empirically verify the new predictions. Can this be done? I don't know.

It might be plausible to assume that the physical universe is an infinite surface in some mathematical model. At the present time, it seems to me that the vast majority of string theorists believe that our universe is infinite. If nature is infinite, then it is plausible to assume that physics has infinitely many degrees of freedom. If nature is finite, then nature might have only 78 degrees of freedom. Consider 3 copies of a model of 26-dimenional bosonic string theory, yielding 78 dimensions of bosonic waves. There might be a boson/fermion duality theorem derivable from Wolfram's cosmological automation. There could be 6 "barks" or "big quarks" each carrying a barkload of 12-dimensions of information, yielding 72 dimensions controlled by Fredkin's 6-phase clock, thus 78 dimensions of fermionic information. Each 12-dimensional barkload might represent 4 dimensions of spacetime, 3 dimensions of linear-momentum density, 3 dimensions of angular-momentum density, 1 dimension of quantum-spin density for matter, and 1 dimension of quantum-spin density for antimatter. By redundant representation of information, it might be possible to derive an 11-dimensional model of M-theory and a 12-dimensional model of F-theory -- the idea is that the interior of the multiverse would be 72-dimensional in terms of "barkload" data, and the measurable universes would all be 71-dimensional and located on the boundary of the multiverse.

I say that my 3 most important ideas are: (1) Milgrom is the Kepler of contemporary cosmology -- on the basis of overwhelming empirical evidence. (2) The Koide formula is essential for understanding the foundations of physics. (3) Lestone's theory of virtual cross sections is essential for understanding the foundations of physics. Are the 3 preceding ideas correct? Can the 3 preceding ideas be explained in terms of string theory with the finite nature hypothesis and/or string theory with the infinite nature hypothesis? Consider 2 more ideas: Fredkin's Finitary Fourfold Hypothesis: Infinities, infinitesmals, perfectly continuous variables, and local sources of randomness are figments of the imagination and never occur in nature. Wolfram's Simple Rules Hypothesis: There exist 4 or 5 simple rules that yield empirically valid approximations to quantum field theory and general relativity theory. Are the 2 preceding hypotheses correct? How might the 2 preceding hypotheses be mathematically formulated?

Is the concept of infinity empirically valid? Is there an infinite continuum of real numbers? If there is an infinite continuum of real numbers, then are there questions in physics that depend upon the truth or falsity of the axiom choice in Zermelo-Fraenkel set theory?

According to Wikipedia, "Jerry Lloyd Bona (born February 5, 1945) is an American mathematician, known for his work in fluid mechanics, partial differential equations, and computational mathematics, and active in some other branches of pure and applied mathematics. Bona received his PhD in 1971 from Harvard University under supervision of Garrett Birkhoff and worked from 1970 to 1972 at the Fluid Mechanics Research Institute University of Essex, where along with Brooke Benjamin and J. J. Mahony, he published on Model Equations for Long Waves in Non-linear Dispersive Systems, known as Benjamin-Bona-Mahony equation. He is probably best known for his statement about equivalent statements of the Axiom of Choice: "The Axiom of Choice is obviously true, the Well-ordering theorem is obviously false; and who can tell about Zorn's Lemma?"

Jerry L. Bona, Wikipedia

What are fundamental particles in physics? Consider the following 5 questions: What are the most important unsolved problems in science and technology? What are the most important unsolved problems in the foundations of physics? Is energy-density bounded away from zero? Is energy-density bounded away from infinity? In empirical reality, is gravitational energy conserved? According to the Gravity Probe B science team, my basic theory is wrong. I suggest that the 4 ultra-precise gyroscopes functioned correctly and confirmed what I call the Fernández-Rañada-Milgrom effect. In terms of string theory with the finite nature hypothesis, what have I have failed to do? I need to introduce cutoffs for energy-density with respect to the strong interactions and the weak interactions. I need to predict a rest mass for inflatons. I need to suggest plausible values for both the lower bound and the upper bound for gravitational energy-density. I need to make a complete prediction for the Space Roar Profile Prediction. WOLFRAM'S SIMPLE RULES HYPOTHESIS: I need to suggest 4 or 5 simple rules that might yield adequate approximations for quantum field theory and general relativity theory. I have, so far, failed to convince string theorists that Milgrom is the Kepler of contemporary cosmology.

"I came to the subject a True Believer in dark matter, but it was MOND that nailed the prediction for the LSB galaxies that I was studying (McGaugh & de Blok, 1998), not any flavor of dark matter. So what am supposed to conclude? ... " -- McGaugh

The MOND pages

According to all of the pro-MOND astronomers and astrophysics (so far as I am aware) the MOND acceleration constant a0 is (1.2 ± .02) * 10^-10 meters * sec^-2 ... I am confident that the error estimate is not wrong by an order-of-magnitude.

Scarpa, Riccardo. "Modified Newtonian Dynamics, an introductory review." In AIP Conference Proceedings, vol. 822, no. 1, pp. 253-265. AIP, 2006.

arXiv.org preprint for Scarpa's article

ERROR IN MY POST ... a0 = (1.2 ± .2) * 10^-10 meters * sec^-2 not (1.2 ± .02)

"... there is one non-trivial way to extend the spacetime symmetries, and that is to incorporate supersymmetry. ... in any string theory, nature always looks supersymmetric at sufficiently high energy scales. If string theory is telling us something about nature, nature is supersymmetric at some energy scale ..." -- Joseph Conlon

"Introduction to Supersymmetry" by Joseph Conlon, 2010

In terms of Fredkin's Digital Philosophy, a plausible slogan is: "A complete infinity is either a mathematical convenience or a physical mistake." If supersymmetry is an approximate symmetry within Wolfram's automaton then string theorists have false confidence in their contemporary paradigm.

"Space-time is doomed--how can it emerge from more primitive building blocks? And how is our macroscopic universe compatible with violent microscopic quantum fluctuations that seem to make its existence wildly implausible?" -- Nima Arkani-Hamed

abstract of "The Future of Fundamental Physics", the LCTP Inaugural Lecture, by Nima Arkani-Hamed, 18 January 2018

Start with Kepler's laws and follow Newton's reasoning with the removal of the assumption that gravitational energy is conserved.

The result is not F = G * m1 * m2 / r^2

but instead F = ((1 - 2 * D-M-C-C)^-1) * G * m1 * m2 / r^2 , where D-M-C-C = dark-matter-compensation-constant = 0 if gravitational energy is conserved, > 0 if gravitational energy is unexpectedly large, and < 0 if gravitational energy in unexpectedly small. In the standard form of Einstein's field equations replace the -1/2 by -1/2 + dark-matter-compensation-constant to get the alleged Fernández-Rañada-Milgrom effect, where the constant is approximated sqrt((60±10)/4) * 10^-5.

IF WOLFRAM'S COSMOLOGICAL AUTOMATON REALLY EXISTS, THEN IS IT PLAUSIBLE THAT ITS TIMING MECHANISM INVOLVES A TRANSFER OF GRAVITATIONAL ENERGY FROM THE BOUNDARY OF THE MULTIVERSE TO THE INTERIOR OF THE MULTIVERSE?

In 2007, John P. Lestone of Los Alamos National Laboratory, U.S.A., suggested a possible approach to calculating the value of the fine structure constant based upon a heuristic string theory. The electron, the muon, and the tau might each consist of a 2-sphere having precisely three vibrating superstrings. In his 2007 publication "Physics based calculation of the fine structure constant " J. P. Lestone suggested that "the photon emission and absorption area A of an electron is controlled by a length scale" where the length scale is near the Planck length.

"Physics based calculation of the fine structure constant" by J. P. Lestone, 2007

Lestone introduced physical hypotheses to calculate the fine structure constant:

(a) The photon emission and absorption area A on an electron is controlled by a length scale f.

(b) The electron has a corresponding effective mean temperature T and the relationship between T and f is the same as the relationship between the Planck temperature and the Planck length.

(c) The absorption across section A/4 should be associated with a corresponding stimulated emission cross section (A/4) * exp(-epsilon), where epsilon is the energy of the incident photon relative to the temperature of the system.

(d) When a photon is absorbed by an electron there is a probability of exp(-epsilon) that a stimulated emission occurs.

(e) An electron consists of a loop of string with its length moving on the 2-dimensional surface of a nearly spherical membrane with radius f.

(f) The string's length is n times the sphere's circumference and this length is long enough so that, in a short time interval, the string can cover most of the string's surface.

(g) The finite length of the string generates an uncertainty in the effective length of the particle, and this temperature uncertainty is related to the time it takes for a signal to travel the length of the string.

Is Lestone's work a promising approach to effective calculations in string theory? What might be some of the implications of Lestone's hypothesis? Renormalization in quantum electrodynamics deals with infinite integrals that arise in perturbation theory. Does Lestone's hypothesis have important implications for renormalization? I conjecture that, EVEN AFTER QUANTUM AVERAGING, Maxwell's equations might be false at the Planck scale, because Lestone's heuristic string theory might be empirically valid. Let ρ represent the electric charge density (charge per unit volume). I conjecture that, in equation (19b) on page 23 of Einstein's "The Meaning of Relativity" (5th edition), ρ should be replaced by the expression ρ/ (1 - (ρ^2 / (ρ(max))^2))^(1/2), where ρ(max) is the maximum of the absolute value of the electric charge density in the physical universe. Polchinski (2003) offered "two general principles of completeness: (1) In any theoretical framework that requires charge to be quantized, there will exist magnetic monopoles. (2) In any fully unified theory, for every gauge field there will exist electric and magnetic sources with the minimum relative Dirac quantum n = 1 (more precisely, the lattice of electric and magnetic charges is maximal)." Are Polchinski's two general principles likely to be correct if and only if nature is infinite?

Veritas vos liberat, Wikipedia

Are most truths important? What are the most fundamental mathematical truths? What are the implications of Gödel's incompleteness theorems?

Gödel's incompleteness theorems

What is fundamentally true? What are the most fundamental questions? What are the most fundamental insights? What is important? What is unimportant? What should a person know? What should a person do? What might be the implications of Gödel's 1st and 2nd incompleteness theorems for the preceding 7 questions? There might be at least 2 fundamental responses to Gödel's incompleteness theorems: (RESPONSE 1) Peano Arithmetic and Zermelo-Fraenkel set theory need more axioms. (RESPONSE 2) The concept of a complete infinity is empirically dubious, and the concept of an arbitrarily large positive integer is an empirically dubious concept.

Are human thoughts merely natural constructions like beaver dams and termite mounds? What are the most fundamental questions? Are questions more fundamental than answers? Are experiments more fundamental than theories? What are the most fundamental goals, meanings, and purposes? As positive integers grow larger do they diminish in meaning, purpose, and significance? Are the numbers 1, 2, and 3 precisely as meaningful as the numbers 1+10^1000, 2+10^1000, and 3+10^1000? Is mathematics the language of science? Is physics the foundation of science? The general theory of relativity modifies Newton's 1st and 2nd laws of motion, but not Newton's 3rd law. In quantum theory, for every action there is an equal and opposite reaction on average, but the observer introduces uncertainty into measurements of actions and reactions.

Wolfgang Pauli called Einstein's fundamental objection to the uncertainty principle "the ideal of the detached observer" (phrase translated from the German):

" 'Like the moon has a definite position' Einstein said to me last winter, 'whether or not we look at the moon, the same must also hold for the atomic objects, as there is no sharp distinction possible between these and macroscopic objects. Observation cannot create an element of reality like a position, there must be something contained in the complete description of physical reality which corresponds to the possibility of observing a position, already before the observation has been actually made.' I hope, that I quoted Einstein correctly; it is always difficult to quote somebody out of memory with whom one does not agree. It is precisely this kind of postulate which I call the ideal of the detached observer." -- Letter from Pauli to Niels Bohr, 15 February 1955, quoted in:

page 43 of "Writings on physics and philosophy by Wolfgang Paul", edited by Charles P. Enz & Karl Meyenn, 1994

Is the ideal of the detached observer a philosophically correct concept?