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

What are the various ideas for modified theories of gravity?

Clifton, Timothy, Pedro G. Ferreira, Antonio Padilla, and Constantinos Skordis. "Modified gravity and cosmology." Physics reports 513, no. 1-3 (2012): 1-189. arXiv.org preprint

Can Litvinov et alia provide a decisive test of the alleged Fernández-Rañada-Milgrom effect? If dark matter has positive gravitational mass-energy and zero inertial mass-energy, then an empirical test might soon disconfirm (or confirm) the hypothesis that dark-matter-compensation-constant = sqrt((60±10)/4) * 10^-5 .

Litvinov, D. A., V. N. Rudenko, A. V. Alakoz, U. Bach, N. Bartel, A. V. Belonenko, K. G. Belousov et al. "Probing the gravitational redshift with an Earth-orbiting satellite." Physics Letters A (2017), arXiv preprint

Beck gives the estimate 110±2 micro-electron-volts for the axion rest mess (putting c = 1).

Beck, Christian. "Axion mass estimates from resonant Josephson junctions." Physics of the Dark Universe 7 (2015): 6-11. arXiv preprint

1.10±.02 * 10^-4 eV is a more precise estimate than 1.2 ± 1.0 * 10^-4 eV and Beck arrived at his estimate by alternate routes of reasoning and evidence.

Consider 3 hypotheses:

Hypothesis 1: If Wolfram's cosmological automaton has a timing mechanism that displays itself in some dramatic physical way, then dark-matter-compensation-constant is likely to be nonzero.

Hypothesis 2: If time is finite, then Einstein's field equations need a Koide cutoff.

Hypothesis 3: If energy-density cannot approach +в€ћ, then Einstein's field equations need a Lestone cutoff.

Does string theory with the infinite nature hypothesis imply supersymmetry and no MOND? Does string theory with the finite nature hypothesis imply MOND and no supersymmetry? Is MOND the key to overthrowing the anthropic principle?

Anthropic principle, Wikipedia

"The anthropic principle is an observation, not an explanation."

-- Burton Richter

"Theory in particle physics: theological speculation versus practical knowledge." Physics Today 59, no. 10 (2006): 8.

Any scientific theory might be falsified. Here are 3 alternate theories for the dark matter problem:

Vagnozzi, Sunny. "Recovering a MOND-like acceleration law in mimetic gravity." arXiv preprint arXiv:1708.00603 (2017).

Chanda, Prolay Krishna, and Subinoy Das. "Static structure of chameleon dark Matter as an explanation of dwarf spheroidal galactic core." arXiv preprint arXiv:1702.01882 (2017).

Burrage, Clare, Edmund J. Copeland, and Peter Millington. "Radial acceleration relation from screening of fifth forces." arXiv preprint arXiv:1610.07529 (2016).

González Alvarez, Juan Ramón, "Modified Newtonian Dynamics and Dark Matter from a Generalized Gravitational Theory" (2011)

"MOND may very well entail loss or replacement of some cherished principles; but which?"

-- M. Milgrom, page 10 of 2008 arXiv preprint

"The MOND limit from spacetime scale invariance." The Astrophysical Journal 698, no. 2 (2009): 1630. arXiv preprint (2008)

Anyone who wants to pursue string theory with the finite nature hypothesis, might want to consider the following two publications:

According to Wolfram (1986), "Continuum equations are derived for the large-scale behavior of a class of cellular automaton models for fluids. The cellular automata are discrete analogues of molecular dynamics, in which particles with discrete velocities populate the links of a fixed array of sites. Kinetic equations for microscopic particle distributions are constructed. Hydrodynamic equations are then derived using the Chapman-Enskog expansion. Slightly modified Navier-Stokes equations are obtained in two and three dimensions with certain lattices."

Journal of Statistical Physics, November 1986, Volume 45, Issue 3-4, pp 471-526 "Cellular automaton fluids 1: Basic theory" by Stephen Wolfram

Bredberg, Keeler, Lysov, and Strominger (2012) presented a construction which "is a mathematically precise realization of suggestions of a holographic duality relating fluids and horizons which began with the membrane paradigm in the 70's and resurfaced recently in studies of the AdS/CFT correspondence."

Irene Bredberg, Cynthia Keeler, Vyacheslav Lysov, and Andrew Strominger. "From Navier-Stokes To Einstein." Journal of High Energy Physics 2012, no. 7 (2012): 146. (arXiv.org preprint)

Why am I fixated on the nonzero dark-matter-compensation idea? First, the idea seems to me to be compatible with the preponderance of the empirical evidence. Second, the idea seems to me to be the only way of betting against Einstein once without betting against Einstein twice. If any one of my three suggested modifications to Einstein's field equations is empirically wrong, then I would bet 100% on Einstein and back the idea of MOND-compatible dark matter particles that have variable effective mass depending upon nearby gravitational acceleration.

I have suggested that Heisenberg's uncertainty principle is always empirically valid whenever measurement is possible, but Einstein's equivalence principle fails empirically in 4 different ways.

According to Einstein,

"A little reflection will show that the law of the equality of the inertial and gravitational mass is equivalent to the assertion that the acceleration imparted to a body by a gravitational field is independent of the nature of the body. For Newton's equation of motion in a gravitational field, written out in full, it is:

(Inertial mass) cdot (Acceleration) = (Intensity of the gravitational field) cdot (Gravitational mass).

It is only when there is numerical equality between the inertial and gravitational mass that the acceleration is independent of the nature of the body."

Equivalence principle, Wikipedia

Consider 4 hypotheses:

(1) Dark matter has positive gravitational mass-energy but zero inertial mass-energy.

(2) Dark energy has negative gravitational mass-energy but zero inertial mass-energy.

(3) As energy-density approaches a cosmological maximum, the equivalence principle fails due to the Lestone cutoff. (Leptons and quarks have nonzero virtual cross sections.)

(4) As energy-density approaches a cosmological minimum, the equivalence principle fails due to the Koide cutoff. (The transfer of energy from the boundary of the multiverse into the interior of the multiverse nears completion as energy-density approaches a cosmological minimum. There are 3 generations of fermions because Wolfram's cosmological automaton generates 64 dimensions of uncertainty which are equivalent to 16 dimensions of virtual boson paths plus 48 dimensions of virtual fermion paths. )

Consider 6 hypotheses:

(1) String theory is the only mathematically plausible way of unifying quantum field theory and general relativity theory.

(2) String theory (with the infinite nature hypothesis) predicts supersymmetry.

(3) String theory (with the infinite nature hypothesis) implies that the equivalence principle is valid for ordinary matter and dark matter.

(4) Einstein found the correct mathematical formulation for the equivalence principle.

(5) String theory (with the infinite nature hypothesis) implies that, after quantum averaging, Einstein's field equations are 100% correct.

(6) String theory (with the infinite nature hypothesis) predicts Einstein's field equations.

Are the 6 preceding hypotheses empirically valid? Consider some ideas of J. D. Bekenstein:

"Literally taken the MOND recipe for acceleration violates the conservation of momentum (and of energy and of angular momentum) ..." (page 2)

"... What principles should the relativistic embodiment of the MOND paradigm adhere to? ...

° Action principle ...

° Equivalence principle ...

° Positivity of energy ...

° Relativistic invariance ...

* Causality ...

° Departure from Newtonian gravity ..." (pages 4-5)

"Tensor-vector-scalar modified gravity: from small scale to cosmology" by Jacob D. Bekenstein, submitted in 2004 & revised in 2005, arXiv.org

I suggest that empirically successful MOND does indeed imply that gravitational energy is not conserved and that string theory with the finite nature hypothesis is empirically valid. (If dark-matter-compensation-constant were equal to zero, then Wolfram's cosmological automaton would not have a uniform timing mechanism.)

According to Edward Witten, "String theory forces general relativity upon us ..."

"Unravelling string theory", Nature, December 2005

Many string theorists seem to think that Milgrom, McGaugh, Kroupa, Sanders, and Scarpa are somehow deluded -- but are these string theorists correct? I conjecture that string theory with the finite nature hypothesis implies real MOND and no supersymmetry, while string theory with the infinite nature hypothesis implies pseudo-MOND and supersymmetry. What do I mean by "pseudo-MOND"?

Can the string landscape explain the empirical successes of Milgrom's MOND? Consider 4 hypotheses:

(1) After quantum averaging, Einstein's field equations are 100% correct.

(2) All dark matter particles are WIMPs with D-brane charges.

(3) Within the string landscape there is a D-brane shock wave that makes it appear that Einstein's field equations are slightly wrong (due to D-brane charges acting detectably upon some WIMPs but non-detectably upon other WIMPs.)

(4) In the standard form of Einstein's field equations replace the -1/2 by -1/2 fake-function, where the fake-function seems to be there because the pro-MOND astrophysics are unaware of the D-brane shock wave acting upon some of the WIMPs.

Are the pro-MOND astronomers and astrophysicists suffering from some type of N-ray delusion?

N ray, Wikipedia

Is MOND empirically invalid?

"Lessons from the Local Group (and beyond) on dark matter" by Pavel Kroupa, 2014, arXiv preprint

Are there paradoxical multiverse quantum jumps, D-brane shock waves, or multiverse wormhole strikes that somehow mimic MOND? I say that the empirical evidence favors Milgrom, McGaugh, Kroupa, Sanders, and Scarpa -- however MOND does not make sense in terms of string theory. Imagine that the string landscape makes sense in terms of quantum field theory. There might be gradients of D-brane charges within the string landscape -- if the gradients are sufficiently lopsided there might be a multiverse quantum jump (MQJ) of gravitational energy from one alternate universe to another. The alternate universes might be classified into 3 main types: the negative CC universe, the zero CC universes, and the positive CC universes. An MQJ might not be small -- it might amazingly large. Think of Einstein's field equations with one side derived from the geometrical tensor and the other side consisting of the energy-momentum tensor. Imagine an analogy between a lightning strike and a MQJ. The ground of the lightning strike corresponds to weird MONDian WIMP particles. Because the pro-MOND astronomers fail to realize that the weird MONDian WIMP particles exist, they have altered the wrong side of Einstein's field equations. The MQJ should be incorporated into the energy-momentum energy according to the true nature of the MONDian WIMP particles. By attempting to model a MQJ that roughly matches MOND, string theorists might find new dualities, new types of compactification, or a new paradigm.

Consider this hypothesis: The empirical successes of MOND are the first empirical confirmation of string theory. How so? String theory with the finite nature hypothesis implies MOND (i.e. Fernández-Rañada-Milgrom effect), while string theory with the infinite nature hypothesis somehow allows pseudo-MOND to happen. According to Glashow, "The new theory must incorporate the old theory and say something new."

Viewpoints on String Theory, Sheldon Glashow, NOVA, Elegant Universe, 28 October 2003

I suggest that the most important "something new" is either MOND or pseudo-MOND.

Let us assume that string theory with the infinite nature hypothesis is correct.

Professor Bekenstein has enumerated the 4 alternatives:

"Mild failures aside, it is clear that there is a broad range of masses, 10^6 -- 10^11 MтШЙ, in which systems adhere to MOND in their systematics. This must be telling us something; logically there are the following possibilities. a) MOND is merely an efficient summary of the way DM is distributed in the said systems? b) MOND reveals the dependence of inertia on acceleration for small accelerations? c) MOND betrays hitherto unknown forces particularly effective at astronomical scales? d) MOND encapsulates departures from standard Newtonian-Einsteinian gravity theory at the mentioned scales?"

"Tensor-vector-scalar-modified gravity: from small scale to cosmology", J. D. Bekenstein, arXiv preprint, 2012 (quote from p. 4)

Kroupa has ruled out (a) -- explaining MOND requires a new paradigm for the foundations of physics. (b) is the dark fluid approach. Think of MOND chameleon particles having variable effective mass depending upon nearby gravitational acceleration -- the dark fluid causes the variable effective mass. (c) is the holographic approach. The weird unknown force derives from the multiverse via the holographic structure of the multiverse. (d) is the Einstein-Hilbert-Bekenstein action approach. Because MOND is empirically valid, at least one of the 3 approaches (b), (c), (d) should work. My guess is that all 3 approaches can be made to work by sufficiently complicated tweaking.

Consider the following 2 publications:

Volovich, I. V. "D-branes, Black Holes and SU(в€ћ) Gauge Theory." arXiv preprint hep-th/9608137 (1996)

Faddeev, L. D. "New variables for the Einstein theory of gravitation." arXiv preprint arXiv:0911.0282 (2009)

Are Faddeev's "24 components in torsion" related to the 24 in the Ramanujan tau function?

Ramanujan tau function

What is fundamental? What were the most fundamental discoveries and inventions of the past? What are the most fundamental questions? Are experiments more important than theories? What are the most important experiments in the history of science? What are the most important questions in the history of science? What are the most fundamental questions? Are questions more important than answers?

Consider 3 opinions:

Opinion 1. In 1900 the 2 most important questions were:

How can chemistry be explained in terms of physics? How does the sun produce so much energy?

Opinion 2. In 1950 the 2 most important questions were: How can electronic computers be improved? How can biology be explained in terms of chemistry?

Opinion 3. In 2000 the 2 most important questions were: How can robots be improved? How can consciousness be explained in terms of molecular biology?

Are the 3 preceding opinions wrong?

Do dark matter particles exist? Is there a unified theory of mathematics and theoretical physics? Consider the following conjecture:

Dark matter particles exist if and only there exists a proof for the Yang-Mills and mass gap problem.

Yang-Mills existence and mass gap, Wikipedia

Are the RAR (radial acceleration relation), the BTFR (Baryonic Tully-Fisher Relation), and MOND 3 logically equivalent formulations?

Wheeler, Coral, Philip F. Hopkins, and Olivier Doré. "The radial acceleration relation is a natural consequence of the baryonic Tully-Fisher relation." arXiv preprint arXiv:1803.01849 (2018)

Acedo, Piqueras, and Moraño (page 13) compared their orbital model to the Juno spacecraft data:

"We see that the agreement is very good but the model systematically underestimates the altitude of the spacecraft as if some outwards anomalous radial acceleration were acting upon Juno during its approximation to the perijove."

"A possible flyby anomaly for Juno at Jupiter", L. Acedo, P. Piqueras, J. A. Moraño, arxiv.org, 2017

Is the alleged Fernández-Rañada-Milgrom effect confirmed by the Juno spacecraft data?

How might supersymmetric vacua in string theory be used to make a prediction for the fine structure constant?

Douglas, Michael R., Bernard Shiffman, and Steve Zelditch. "Critical points and supersymmetric vacua I." Communications in mathematical physics 252, no. 1-3 (2004): 325-358.

Lestone's theory of virtual cross sections might be applied to the string landscape if the following 4 hypothesis are correct:

(1) Leptons and quarks have nonzero virtual cross sections.

(2) Virtual photons, virtual gravitons, and virtual gluons travel in the string landscape interstitium, which has 1 temporal dimension and 9 spatial dimensions.

(3) When gravitational spacetime is nearly flat, virtual photons travel in a 4-dimensional approximation to the string landscape interstitium and there is a semi-classical approximation that yields an approximate value for the fine structure constant, representing an expectation value derived from the string landscape.

(4) Measurement causes probabilistic clouds of virtual photons, virtual gravitons, and virtual gluons to condense into real particles.