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.
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
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?
Dear Fellow Essayists
This will be my final plea for fair treatment.,
Reliable evidence exists that proves that the surface of the earth was formed millions of years before man and his utterly complex finite informational systems ever appeared on that surface. It logically follows that Nature must have permanently devised the only single physical construct of earth allowable.
All objects, be they solid, liquid, or vaporous have always had a visible surface. This is because the real Universe must consist only of one single unified VISIBLE infinite surface occurring eternally in one single infinite dimension that am always illuminated mostly by finite non-surface light.
Only the truth can set you free.
Joe Fisher, Realist
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:
Is the ideal of the detached observer a philosophically correct concept?
"But here, I will argue that, while MOND is unconventional and inconstitent with the current cosmological paradigm, it is by no means in the category of crazy ideas. And we should recall that many constructs of modern physics, such as quarks, were at an early stage considered crazy and condemned quite viciously by renown scientists." -- Robert H. Sanders
"A historical perspective on Modified Newtonian Dynamics", 2014, (page 19) arXiv.org
Is Milgrom the Kepler of contemporary cosmology? Is the Koide formula essential for understanding the foundations of physics? Does square-root(mass) have some profound meaning in terms of the foundations of physics? Is Lestone's theory of virtual cross sections essential for understanding the foundations of physics? Is the value of the fine-structure constant a happenstance of the string landscape?
What is the most fundamental insight in quantum theory? Is it Heisenberg's uncertainty principle?
Uncertainty principle, Wikipedia
What is the most fundamental insight in general relativity theory? Is it Einstein's equivalence principle?
Equivalence principle, Wikipedia
Does string theory with the infinite nature hypothesis suggest that the uncertainty principle needs some modification based upon the string landscape? Does string theory with the finite nature hypothesis suggest that the equivalence principle needs some modification based upon Wolfram's cosmological automaton?
My guess is that the equivalence principle has 4 problems: (1) Dark energy as a weird, negative pressure suggests that dark energy has negative inertial mass-energy with respect to the string landscape. Is dark energy the result of the escape of gravitons from the boundary of the multiverse into the interior of the multiverse? Does dark energy obey the equivalence principle? (2) Does dark matter obey the equivalence principle? Does dark matter have positive gravitational mass-energy and zero inertial mass-energy? (3) Does the equivalence principle fail when energy-density becomes large enough? (4) Does the equivalence principle fail when energy-density becomes close enough to zero?
"It is seen that MOND agrees with observations over at least 6 orders of magnitude in acceleration."
-- Riccardo Scarpa
"Modified Newtonian Dynamics, an Introduction Review", arXiv.org preprint
To your number 3 and 4 questions concerning violations of the equivalence principle failing due to energy densities being close to zero or very large that is a possibility. However, the violations will still be small enough for GTR to remain valid and this hints at its robustness in our observable Universe. In the low-energy GR will work from outside galactic halos (in interstellar space) all the way to the observable gravitational endpoint of neutron star structure or similar mass black hole or the larger galactic black hole toward the center of the galaxy. That there might be a slight dynamism suggests that our Newton constant is at a hovering value and is a geometric mean of a slightly lesser Newton constant value which lies outside the galactic halo and a slightly larger Newton constant value on top of neutron star structure or a similar mass black hole (or larger). At the observable gravitational endpoint (black hole) it suggests that our metrology or way of measuring using Length, Mass and Time is no longer viable e.g. Newton constant is units m^3 k^-1 s^-2. This is where a quantum gravity is needed and GR begins to fail.This will not be observed in our physical Universe. The gravitational coupling constant is not exactly the same as the Newton constant as it is dimensionless and it exists on the exponential so that it falls out of the realm of use in the GR geometry but it is more natural than the use of the SI system of units. The gravitational coupling constant will be more important in quantum gravity than any use in GR. I wrote a paper on the use of dimensionless physics forms and I was trying to establish a pathway of eventually using the Riemann Zeta functions to obtain these numbers to get to a fundamentality, a reduction, but it is difficult to convey this to an audience where no one has established this as research to look at. As far as dark matter goes it has a bosonic character to it and maybe a way of completing a complete gauge symmetry. Perhaps it is a holographic fuzz somehow containing information about nearby baryonic matter. Since I was interested in Riemann Zeta functions applicability dark matter is more like a p-adic number fuzz (still similar to the holographic fuzz) but with the fundamentality of prime numbers. The galactic halo where normal solar system type dynamics occur (like ours with our hovering Newton constant) has a bosonic p-adic nature to it, so maybe its fractal too residing in the low-energy. What if this aspect of dark matter is what survives the intial Planck energies and survives the ride all the way down to our low-energy world and retains its fundamental character.
Dear David Brown.
I have read your essay and suggest that you read Dark Matter http://vixra.org/pdf/1303.0207v3.pdf
Quantum Mechanics claims that an electron can be both spin-up and spin-down at the same time. In my conceptual physics Essay on Electron Spin, I have proved that this is not true. Please read: https://fqxi.org/community/forum/topic/3145 or https://fqxi.org/data/essay-contest-files/Rajpal_1306.0141v3.pdf
Kamal Rajpal
Kamal Rajpal's idea "... photons with the least energy will correspond to photons with a temperature close to zero kelvin ..." (vixra.org) is likely to be correct provided that nature is finite and digital -- and might be correct if nature is infinite. Do least-energy photons exist in nature and not just in theory? Can absolute zero be approximated with arbitrary accuracy?
Observe the chicken. Why did the chicken cross the road? Because we fail to live in an alternate universe in which chickens never evolved. What is observation? What is measurement? Why does measurement exist? Consider 2 concepts:
(1) The observer creates the measurement by causing a selection among quantum possibilities.
(2) Measurement is a natural process that separates the boundary of the multiverse from the interior of the multiverse. The observer's thoughts and actions are entirely caused by Fredkin-Wolfram information.
What are other plausible concepts of measurement?
Dear David Brown,
I agree that 'zero point photons' is a theoretical concept. Thanks. The CMB photons at 2.7 K do exist.
Kamal Rajpal
What are the most fundamental questions concerning science and technology? Is reality more fundamental than language? Is applied mathematics more fundamental than pure mathematics? Are time, space, energy, and quantum information the 4 most fundamental concepts in physics? In order to unify Newton's 3 laws of motion, Newton's law of gravity, and Maxwell's equations, Einstein introduced spacetime in special relativity (1905) and in general relativity (1916). However, in general relativity, there is a concept of the fundamental geometric tensor and a concept of the energy-momentum tensor. Can spacetime and energy be unified into a single concept? Is string theory the way to mathematically unify energy with spacetime, forming a quantum theory of gravity? If there are n virtual particles that move independently, then should there be a mathematical model having n dimensions? Are the real numbers, the complex numbers, the quaternions, and the octonions the 4 most important mathematical structures? Can 9 copies of the octonions be used in explaining the foundations of physics? In any case, I say that Milgrom is the Kepler of contemporary cosmology.
"Seen in the light of evolution, biology is, perhaps, intellectually the most satisfying and inspiring science. Without that light it becomes a pile of sundry facts -- some of them interesting or curious but making no meaningful picture as a whole." -- Theodosius Dobzhansky
Is it true that biology reduces to chemistry reduces to physics? Is there a unified theory of mathematics and theoretical physics? In materials science, any valid material must pass the tests of chemistry. Can one think of science as a tree of knowledge with a trunk consisting of quantum theory, roots in the multiverse, and branches in chemistry? Is string theory a profound unifying principle for both physics and mathematics?
What are the 4 most important mathematical structures? Could the answer be the real numbers, the complex numbers, the quaternions, and the octonions?
"The octonions" by John C. Baez, Bull. Amer. Math. Soc. vol. 39 (2002)
"Division algebras and quantum theory" by John C. Baez, arXiv.org, 2011
3 copies of the Leech lattice = 9 copies of the octonions = 64 dimension of virtual particle paths 3 dimensions of linear momentum 3 dimensions of angular momentum 2 dimensions of quantum spin ???
Consider a statement made by Leonardo da Vinci:
La natura è piena d'infinite stagioni (o cagioni) che non furono mai in esperienza. (Nature is full of infinite seasons (or causes) that have never been experienced.)
Leonardo da Vinci scienziato, it.wikisource.org
Is nature infinitely complicated? Are string vibrations confined to 3 copies of the Leech lattice? Can string vibrations be interpreted in terms of 3 copies of 26-dimensional bosonic string theory with Fredkin's 6-phase clock? Is it useful to think in terms of measuring space and time with 6 particle beams, consisting of 3 electron beams and 3 positron beams? What about 3 beams of muons and 3 beams of anti-muons? What about 3 beams of tauons and 3 beams of anti-tauons?
"What are the implications of the 3-fold way?" -- John C. Baez
Does there exist a (1/3)-Koide formula that allows some quarks to have charge ± 1/3 ?
From Wolfram Alpha:
(muon mass) /(electron mass) = 206.7683
(tauon mass)/(electron mass) = 3477.48
(59^3 + 33 * 59^2 + 57 * 59 + 9 )^(1/27) - 1.59983643131952544 = 0 approx.
For a = 1.5998364, x = 206.7683, y = 3477.48,
calculate ( a^3 +(a^2) * x + a * y)/(a^3 + ( a^2) * x^.5 + a * y^.5)^2 Answer: .333333
For the polynomial x --> x^3 + 33 * x^2 + 57 * x + 9 my guess is that 33 + 26 = 59 is meaningful because of 26-dimensional bosonic string theory and the fact that the three primes 59, 59 ± 12 divide the order of the monster group. My guess is that the constant term 9 is meaningful because of Lestone's heuristic string theory.
Note that 8/5 - 1/(32 * 191) = 1.599836874 ...
For a = 1.5998369, x = 206.7683, y = 3477.48,
calculate ( a^3 +(a^2) * x + a * y)/(a^3 + ( a^2) * x^.5 + a * y^.5)^2 Answer: .333332
Note that 191 = 2 * 72 + 47 and 47, 59, 71 are the 3 largest primes that divide the order of the monster group.
Does square-root(mass) = area ?
In string theory with the finite nature hypothesis, is it possible to use quantum cohomology to calculate (muon mass)/(electron mass) and (tauon mass)/(electron mass) ?
From Wolfram Alpha:
(muon mass)/(electron mass) = 206.7683
(tauon mass)/(electron mass) = 3477.48
206.7683^(1/4) - 3 - 3^2 * 11 / 5^3 - 3^4 * 14/ 5^11 = 6.59750 * 10^9 approx.
3477.48^(1/4) - 7 - 3/5 - (11/2) * 3^2 / 5^3 = 3.21039 * 10^-6 approx.