Why might the Koide formula be essential for understanding the foundations of physics?

http://en.wikipedia.org/wiki/Koide_formula

According to the conventional wisdom, dark matter certainly has positive gravitational mass-energy and positive inertial mass-energy and obeys the equivalence principle -- presumably because Einstein's field equations are true. However, note that I have suggested 3 corrections to Einstein's field equations: one for MOND, one for the Koide formula, and one for Lestone's heuristic string theory. Consider this idea: mass-energy can be converted into space-time. Write square-root(mass) = Koide-constant * area. What might this mean? Mass-energy of big bang = (Koide-Constant)^2 * (volume of spacetime at time of maximum expansion of the universe) * (81.6 ± 1.7 billion years) *c, where c is the speed of light in vacuo. Can astrophysicists explain the space roar? Does the space roar suggest the validity of the Koide formula (as NOT merely a coincidence)?

Does Milgrom's MOND suggest a modification to Einstein's field equations?

My idea is that dark matter has positive gravitational energy and zero inertial mass energy -- this means replace the -1/2 in the standard form of Einstein's field equations by -1/2 + dark-matter-compensation-constant.

How many astrophysicists have looked at the following?

http://vixra.org/abs/1410.0186 "Where Are the Dark Matter Particles?"

Is Milgrom the Kepler of contemporary cosmology?

David

Great essay. Certainly one of the best here. Well set out, written and argued, though it helps that I agree most of your arguments and (though more limited!) conclusions. A few specifics.

1. I like & agree your 4 trumps, (though I suspect we'll find one Trump may be enough!)

2. Thanks for the Crick quote. I'll get the book. I certainly agree in my own essay; All approaches at a higher level are suspect until confirmed at the molecular level indeed I suggest the next step or even two below molecular level.

3. I also than answer YES, that; consciousness reduces to molecular psychology reduces to molecular biology reduces to chemistry reduces to physics if not quite to present doctrines of physics!

I'm not a mathematician, so it's a pleasant surprise to find so much agreement. However from the observational cosmology view I seem to have identified apparently slightly more logically complete options than I understand (maybe only a little) Milgromian cosmology gives. Consistent derivations of dark matter, energy, gravity and cosmic redshift (without needing accelerating expansion) emerge (I've published papers if you're interested).

I'd like to go into that further but best stick to the essays for now. I'd love a mathematicians view or even promise of input into my own logic.

Best of luck in the contest.

Peter

    Peter Jackson: Your essay's abstract begins with "Artificial intelligence can already learn..." and ends with "No conclusion is possible as to whether or not a cosmic architect created our own or any universe." I doubt the existence of miracles, immortal souls, and/or supernatural entities -- but do we really have convincing evidence that miracles do not occur in the Andromeda Galaxy? Can we really be sure that human consciousness is not merely a simulation in a higher being's computer game? As to AI learning, where might it end?

    https://en.wikipedia.org/wiki/Technological_singularity

    From the following list of physicists, I would vote for Steven Weinberg as the best role model for aspiring theoretical physicists.

    http://www.science20.com/hammock_physicist/who_todays_einstein_exercise_ranking_scientists-75928

    -- D. Brown

    I want to elaborate on some of my conjectures. Consider 7 conjectures:

    (1) Time exists because 2^46 divides the order of the monster group, i.e., time exists because of the symmetries associated with the embedding of the Sylow 2-subgroup of the monster group.

    (2) Space exists because 3^20 divides he order of the monster group, i.e., space exists because of the symmetries associated with the embedding of the Sylow 3-subgroup of the monster group.

    (3) There are 3 generations of fermions because 13^3 divides the order of the monster group.

    (4) Time and antimatter-time exist because 11^2 divides the order of the monster group, thus allowing Witten's 11-dimenstional model to govern the interactions of bosons, leptons, and quarks; these interactions can be mathematically described by the interactions of the monster group and the 6 pariah groups.

    (5) There are 6 basic quarks because there are 6 pariah groups.

    (6) If G is a finite group, then define Lie-group(G) to be the Lie group associated with the minimal Lie group representation of G. There exists a system of information transfer associated with Lie-group(monster group), and Lie-group(5-Sylow subgroup of the monster group) and the Lie-group (...) associated with the 6 pariah groups and their associated 5-Sylow subgroups.

    (7) The reason that 7^6 divides the order of the monster group is that each of the 6 basic quarks has a 3-dimensional linear momentum, a 3-dimensional angular momentum, and quantum spin.

    Is Milgrom the Kepler of contemporary cosmology? Google "witten milgrom" and "kroupa milgrom" for more information.

      Hello,

      It is relevant considering the ranking of groups.Have you already thought about the padics numbers and the groups and the morphisms.I beleive that an extension of quaternions could be relevant inj superimposing the vectors, scalrs in converging with the spherical volumes.If the quantum BHs and BHs are correlated with this matter not baryonic implying gravitation with the cold so we have a road to better understand the scales and correlated laws.The works of Clifford or Hopf also could help.I beleive strongly that the spherical volumes are essential.The points are well but we can imrpove the détails with the 3 motions of these spherical volumes.The sortings and synchros appear when we consider also the senses of rotations and angles.The good reccurent method can be found.The aim being to understand better this infinite gravitational potential energy and this kinetic énergies distributed if In can say in a simplistic point of vue.I beleive that the groups can be found,me I am a nursery manI have not the skillings for simulations,but if somebody can try several methods by simulations, it could be very relevant.They turn so they are after all these sphères.Regards

      Steve Dufourny: "... an extension of quaternions could be relevant ..." It seems plausible that both quaternions and octonions could be relevant -- if there are 6 basic quarks because there are 6 pariah groups ... (not yet well-formulated).

      https://books.google.com/books?id=irt7nOFaR3sC "Quaternionic Quantum Mechanics and Quantum Fields" by Stephen L. Adler, 1995

      Sepunaru, Daniel. "On Hypercomplex Extensions of Quantum Theory." arXiv preprint arXiv:1501.05853 (2015).

      In my previous post there is the typo "... 3^20 divides he order ..."

      I would like to try to explain some of the backstory of my essay. In Tahiti, Paul Gauguin painted his famous masterpiece (oil on canvas) now known as "D'où Venons Nous/Que Sommes Nous/Où Allons Nous" (Where Do We Come From? What Are We? Where Are We Going?). Gauguin's 3 questions are indeed important. There might be a kind of fatal paradox in science -- to fully answer many scientific questions, superhuman intelligence might be required. Thus, the ongoing progress of science and technology might entail the downfall of the human species -- what Ray Kurzweil, a supreme optimist, calls the "Singularity". Is Darwinian evolution brutal, extravagant, wasteful, relentless, and inevitable? Will superhuman beings treat human beings with benevolence and solicitude? What is the fundamental Darwinian trend of consciousness? What is consciousness? Specifically, what might be a mathematical model or computer simulation of visual consciousness in primates? Would a full answer to the preceding question require superhuman intelligence?

      https://www.youtube.com/watch?v=mXGZ3euhq4g History of Neuroscience: Francis Crick, YouTube, 2012

      Is the science of human consciousness necessary for understanding who we are? Where are we going? Where is our universe going? Where did the big bang come from? My guess is that the empirically valid answers to the 2 preceding questions require 3 distinct modifications to Einstein's field equations. (Google "einstein's field equations 3 criticisms" for more information on my guesses.

      "The development of science, from ancient times to the present, has been a series of nearly unbroken steps where one concept after another has moved out of the shadows of doubt and uncertainty and into the light of accepted scientific fact. The atomic hypothesis, whether matter is made up of atoms, is only one of many atomic hypotheses. So far every such question, discrete versus continuous, about a property of our world either remains undecided or it has been decided as discrete (atoms, electricity, light, angular momentum, etc.). It is hard to imagine the proof that some property will never admit to a finite description, no matter how fine grained. On the other hand, what is interesting is that so many concepts once thought of as continuous are now accepted as discrete. Finite Nature assumes that that historical process will continue to a logical conclusion where, at the bottom, everything will turn out to be atomic or discrete, including space and time." -- Edward Fredkin

      http://www.ai.mit.edu/projects/im/ftp/poc/fredkin/Finite-Nature

      Stephen Wolfram conjectured that there exists 4 or 5 simple rules that yield empirically valid approximations to quantum field theory and general relativity theory.

      Now (19th of February) I would like to elaborate on my conjectures on how the monster group and the 6 pariah groups might enable the empirical confirmation of Wolfram's conjecture.

      What is a register in a digital computer?

      According to Wikipedia, "In computer architecture, a processor register is a quickly accessible location available to a computer's central processing unit (CPU). Registers usually consist of a small amount of fast storage, although some registers have specific hardware functions, and may be read-only or write-only. Registers are typically addressed by mechanisms other than main memory, but may in some cases be memory mapped."

      http://en.wikipedia.org/wiki/Processor_register

      For Wolfram's automaton, imagine a geometric-register in which a huge, but finite, number of points might somehow approximate a higher-dimensional geometric structure. For each prime number p that divides the order of the monster group or one of the orders of the 6 pariah groups, there might exist a p-Sylow subgroup geometric-register that contains a higher-dimensional geometric structure that has Euclidean dimension equal to the order of that particular p-Sylow subgroup. There might be a network of Fredkin-Wolfram information in which Fredkin-time, Fredkin-distance, and Fredkin-digit-transition are precursors of time, distance, and energy in quantum field theory and in general relativity theory.

      A huge number of updates by Wolfram's updating parameter might create one Planck time interval with an approximate array of quantum information in a huge, but finite number, of alternate universes. All of the alternate universes would occur on the boundary of the multiverse. Directly measured particles would occur in a particular alternate universe. Indirectly measured particles would be virtual particles that occur in the interior of the multiverse. During one Planck time interval, Wolfram's automaton might read the Fredkin-Wolfram information on the boundary of the multiverse, store information in the Fredkin-Wolfram net and in the geometric-registers associated with the monster group and the 6 pariah groups, and, after a huge number of stages of computing and storing, then output the approximations of quantum information to all of the alternate universes. Thus, Wolfram's automaton would read, store, compute, update, and output in an endless cycle of computing below the Planck scale. Why should anyone believe such a scenario?

      http://vixra.org/abs/1407.0088 "MOND and the Photon Underproduction Crisis"

      http://vixra.org/abs/1407.0113 "Lambda-VDM Model: a Testable Modification of Lambda-CDM"

      Thanks for sharing.It is relevant all this for the fractalisation of our scales.

      All the best.

      Do the predictive successes of Milgrom's MOdified Newtonian Dynamics (MOND) constitute physical evidence that a multiverse exists?

      In the standard form of Einstein's field equations, replace the -1/2 by

      -1/2 + dark-matter-compensation-constant.

      Replace F = G * m1 * m2 / r^2 by F = ((1 - 2 * D-M-C-C)^-1) * G * m1 * m2 / r^2 , where

      D-M-C-C = dark-matter-compensation-constant = sqrt((60±10)/4) * 10^-5 (approximately). Let m1 be the mass of a galaxy and let m2 represent the mass of a star in the galaxy.

      F = ((1 - 2 * D-M-C-C)^-1) * G * m1 * m2 / r^2 =

      m2 * (gravitational-acceleration-of-m2-with-respect-to-m1).

      F = G * m1 * m2 / r^2 =

      m2 * ( (gravitational-acceleration-of-m2-with-respect-to-m1) * (1 - 2 * D-M-C-C) ). If we break up the zones of gravitational-acceleration into sub-zones of approximately constant gravitational-acceleration then we approximately recover the MONDian law of acceleration.

      http://iopscience.iop.org/article/10.1086/421338/meta McGaugh, Stacy S. "The mass discrepancy-acceleration relation: disk mass and the dark matter distribution." The Astrophysical Journal 609, no. 2 (2004): 652.

      Dear David Brown

      I have some observations....

      You said in your foundations of Physics section of your essay, "Experimental Physics trumps"

      You may probably know.......the MOND or Milgrom Cosmology faces big problem of Dark matter. Dark matter was not found experimentally.

      Dynamic Universe Model predicted "No Dark Matter" 10 years back, Now that is came true experimentally

      See the papers on...

      http://vaksdynamicuniversemodel.blogspot.in/p/10-feb-201-6-all-my-published-papers.html

      Best

      =snp.gupta

      Is Lestone's theory of virtual cross sections essential for the development of Milgromian cosmology?

      John P. Lestone of Los Alamos National Laboratory wrote,

      "Introduction to my idea

      Before Hawking's work (and others) black-holes were believed to be point objects with only mass, spin, and charge. This is why Einstein (1930s) and others have previously considered the possibility that fundamental particles (like leptons) are quantum micro black holes. Black holes are now believed to have a temperature, entropy, and thus many internal degrees of freedom. Individual black holes are objects amenable to statistical mechanics.

      My heretical statement

      If black holes (once thought to be point objects) are amenable to statistical mechanics, then why not fundamental particles like leptons? (1988)

      Introduction to my idea continued

      I consider the possibility of a very strange "unknown" imaginary class of particles, with several unique (bizarre) properties including

      (1) My particles have a very high temperature(s).

      (2) Despite having a very high temperature, my imaginary particles can not change their rest mass upon the emission of electromagnetic energy. Using known physics my imaginary particles (if isolated) can not emit any "real" photons".

      (3) However, I consider the possibility that my imaginary particles can emit and absorb unphysical L=0 "virtual" photons via the time-energy uncertainty principle.

      (4) The emission and absorption is controlled by statistical arguments involving their classical temperature and possibility other effective temperatures.

      ,,," http://permalink.lanl.gov/object/tr?what=info:lanl-repo/lareport/LA-UR-16-22121 J. P. Lestone, "Possible path for the calculation of the fine structure constant", Los Alamos Report LA-UR-16-22121, April 2016, Los Alamos National Laboratory

      How might Lestone's bizarre virtual particles with virtual non-zero cross sections be incorporated into a new theory of the foundations of physics that makes empirically valid predictions concerning Milgrom's MOND, the space roar, and the photon underproduction crisis? Assume that string vibrations are confined to 3 copies of the Leech lattice -- such drastic restriction might eliminate the string landscape and enable string theorists to make several new and empirically valid predictions. If nature is finite and digital, the most important mathematical structures involved might the monster group, the 6 pariah groups, the Leech lattice, and the Clebsch diagonal cubic surface. Below the Planck scale, there might be some kind of Fredkin-Wolfram physics in which Fredkin-Wolfram information and symmetries within Wolfram's automaton might allow particle physics with virtual particles to be understood of Fredkin time, Fredkin distance, and Fredkin digit transition. The Fredkin-Wolfram physics would not allow direct measurement but might "explain" quantum micro black holes (with some Lestone-modification to general relativity theory) in terms of "non-measurable" Fredkin heat and Fredkin energy. All of the alternate universes would be cold in terms of Fredkin heat and would occur on the boundary of the multiverse. All of the virtual mass-energy would occur in the interior of the multiverse and would be hot in terms of Fredkin heat. The network Fredkin speed would be big-C, a non-measurable speed that would seem to be incredibly faster than c (the speed of light in a vacuum). Because of dense and incredibly fast networking with the interior of the multiverse, one might think of the multiverse as being flattened out with an incredibly "Fredkin hot" quantum foam in which string vibrations transfer Fredkin-Wolfram information. Massive bosons might consist of 1 vibrating string confined to a 1-sphere. Leptons might consist of 3 vibrating strings confined to a 2-sphere. Quarks might consist of 9 vibrating strings confined to a 3-sphere. Is the preceding merely "techno-babble" that does make sense in terms of physics? Is Milgrom the Kepler of contemporary cosmology? Is it necessary to make 2 modifications to Einstein's field equations to account for the space roar and Milgrom's MOND? Does Lestone's theory of virtual cross sections suggest a Lestone-modification to Einstein's field equations?

      I conjecture that paradigm-breaking photons caused by inverse Compton scattering from relativist jets explain the GZK paradox.

      http://en/wikipedia.org/wiki/Greisen-Zatsepin-Kuzmin_limit

      Consider Einstein's field equations: R(mu,nu) + (-1/2) * g(mu,nu) * R = - κ * T(mu,nu) - Λ * g(mu,nu) -- what might be wrong? Consider the possible correction R(mu,nu) + (-1/2) * g(mu,nu) * R =

      - κ * (T(mu,nu) / equivalence-principle-failure-factor) - Λ * g(mu,nu), where

      equivalence-principle-failure-factor = (1 - (T(mu,nu)/T(max))^2)^(1/2)

      -- if T(max) = +∞ then Einstein's field equations are recovered. I conjecture that the preceding correction might provide a basis for understanding 2 things: (1) how photons can acquire incredibly large kinetic energy from relativistic jets and (2) Lestone's theory of virtual cross sections.

      https://arxiv.org/abs/physics/0703151 "Physics based calculation of the fine structure constant" by John P. Lestone, 2009

      http://permalink.lanl.gov/object/tr?what=info:lanl-repo/lareport/LA-UR-16-27659 Los Alamos Report LA-UR-16-27659 "Semi-classical Electrodynamics: A Short Note" by John Paul Lestone, issued 2016-10-05

      http://permalink.lanl.gov/object/tr?what=info:lanl-repo/lareport/LA-UR-16-22121 J. P. Lestone, "Possible path for the calculation of the fine structure constant", Los Alamos Report LA-UR-16-22121, April 2016, Los Alamos National Laboratory

      http://www.worldscientific.com/doi/abs/10.1142/S0217732308027199?journalCode=mpla Lestone, J. P. "Black-Body Photon Clustering by Semiclassical Means." Modern Physics Letters A 23, no. 15 (2008): 1067-1077.

      According to Wikipedia, "Several remarkable properties of j have to do with its q-expansion (Fourier series expansion), written as a Laurent series in terms of q = exp(2πiτ), which begins:

      j(τ) = 1/q + 744 + 196884 * q + ..."

      http://en.wikipedia.org/wiki/j-invariant

      Note that 6! = 1 * 2 * 3 * 4 * 5 * 6 = 720 and 744 - 720 = 24. Does 744 - 720 = 24 have some profound meaning in the foundations of physics?

      Is spacetime 4-dimensional? Is spacetime 26-dimensional? Measurements of spacetime using clocks and surveying instruments demonstrate that spacetime is 4-dimensional. I say that, from one point of view, spacetime is 26-dimensional. 26 dimensions = 1 dimension of matter time + 1 dimension of antimatter time + 24 dimensions of (±, ±, ± )-space. What is (±, ±, ±)-space? For the measurement of space, employ 6 particle beams consisting of 3 electron beams and 3 positron beams. For each dimension of space, employ all 3-tuples of beams selected from the 6 beams. By definition, (±, ±, ±)-space consists of 3 dimensions of ordinary space, each of which is measured in 8 different ways by using all of the possible 3-tuples of the 6 beams. The 24 dimensions of (±, ±, ±)-space reduce to the 3 dimensions of ordinary space because quantum field theory is empirically valid -- however, (±, ±, ±)-space might be useful for representational redundancy (because of the role that the Leech lattice plays in the foundations of physics.)

      Note that the order of the monster group is

      2^46 * 3^20 * 5^9 * 7^6 * 11^2 * 13^3 * 17 * 19 * 23 * 29 * 31 * 41 * 47 * 59 * 71 --

      observe that 2^46 * 3^20 * 5^9 / 720^9 = 9216 = 2 * 72 * 64 -- does the preceding numerology suggest that the number of permutations of 6 basic quarks with 3 quark colors (for both matter and antimatter) might involve matter-time, antimatter-time, a 72-ball, and 64 fundamental particles in free space? (Add the axion, the graviton, and the inflation to the 61 fundamental particles of the Standard Model.)

      In my essay for this fqxi contest, I noticed an error in my quotation from Charles Jennings in "Nature Neuroscience" (2000)

      " ... it is impressive that so much agreement has been reached on how Where to proceed ..."

        Replace the error by "... it is impressive that so much agreement has been reached on how to proceed ..."

        Also, I have mentioned in comments in this comments section several mathematical structures, i.e., monster group, pariah groups, Leech lattice, and Clebsch diagonal cubic surface, in connection with my speculations on Milgromian cosmology.

        If my speculations on Milgromian cosmology are not examples of self-delusion, then my guess is that the hypergeometric series highlighted by Hosono in equation (1.1) of the following publication

        https://arxiv.org/pdf/hep-th/0404043v4.pdf "Central charges, symplectic forms, and hypergeometric series in local mirror symmetric" by Shinobu Hosono, 2005

        might also play an essential role in Milgromian cosmology and the foundations of physics.

        5 days later

        I have conjectured 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. I have 2 main guesses: (1) String theory with the infinite nature hypothesis implies supersymmetry and no MOND. (2) String theory with the finite nature hypothesis implies MOND and no supersymmetry. Can string theory explain dark matter, dark energy, inflation, the space roar, and the photon underproduction crisis? It seems to me that string theory provides a means of unifying mathematics, theoretical physics, and theoretical computer science.

        Consider the following hierarchy:

        infinitary mathematics (Zermelo-Fraenkel set theory, Mochizuki's IUT with alternate universes of quantum logics)

        /

        finitary mathematics (monster group) -- string theory -- theoretical physics (quantum field theory, general relativity theory)

        /

        quantum computing, computer science, nanotechnology, chemistry, condensed matter physics

        /

        computer software, AI, robotics, engineering -- molecular psychology -- theoretical biology, molecular biology, biotechnology

        /

        social sciences, humanities

        My guess is that Lestone's theory of virtual cross sections can be justified in terms of the string landscape and in terms of string theory with the finite nature hypothesis (but in substantially different ways).

        J. P. Lestone has introduced a highly speculative approach to estimating the fine structure constant in terms of his theory of virtual cross sections. Lestone wrote,

        "Introduction to my idea

        Before Hawking's work (and others) black-holes were believed to be point objects with only mass, spin, and charge. This is why Einstein (1930s) and others have previously considered the possibility that fundamental particles (like leptons) are quantum micro black holes. Black holes are now believed to have a temperature, entropy, and thus many internal degrees of freedom. Individual black holes are objects amenable to statistical mechanics.

        My heretical statement

        If black holes (once thought to be point objects) are amenable to statistical mechanics, then why not fundamental particles like leptons? (1988)

        Introduction to my idea continued

        I consider the possibility of a very strange "unknown" imaginary class of particles, with several unique (bizarre) properties including

        (1) My particles have a very high temperature(s).

        (2) Despite having a very high temperature, my imaginary particles can not change their rest mass upon the emission of electromagnetic energy. Using known physics my imaginary particles (if isolated) can not emit any "real" photons".

        (3) However, I consider the possibility that my imaginary particles can emit and absorb unphysical L=0 "virtual" photons via the time-energy uncertainty principle.

        (4) The emission and absorption is controlled by statistical arguments involving their classical temperature and possibly other effective temperatures.

        ..." http://permalink.lanl.gov/object/tr?what=info:lanl-repo/lareport/LA-UR-16-22121 J. P. Lestone, "Possible path for the calculation of the fine structure constant", Los Alamos Report LA-UR-16-22121, April 2016, Los Alamos National Laboratory

        MY GUESS is that there might be a plausible way of justifying (1)-(4) in terms of string theory with the string landscape. Assume a string landscape in which all the alternate universes have Standard Model free parameters that are very close to each other. If there is (in the string landscape) an extremely hot interstitium which is 10-dimensional and super-hot with respect to all the cooler alternate universes, and ALSO most of the virtual energy close to each alternate universe is slightly super-hot but cool enough that it is ALMOST conventional in terms of 4-dimensional spacetime, then it seems to me that (1)-(4) might be justifiable.

        Also, in string theory with the finite nature hypothesis, several of Ramanujan's formulas might be crucially important. In particular, I want to mention the Theorems on pages 10 & 12 and equation (11.4) on page 17 of B. C. Berndt's "An overview of Ramanujan's notebooks".

        http://www.math.uiuc.edu/~berndt/articles/aachen.pdf

        Criticisms from some physicists suggest that they misunderstand my analysis of the Koide formula. For me, the point is NOT that the Koide formula predicts some particular range of values for lepton masses -- the WHOLE POINT is that square-root(mass) has some kind of profound meaning in terms of physics. Conventional wisdom says that there exists a Planck time and a Planck length. Does there exist a Wolfram time and a Wolfram length? In other words, it is true that the wavelengths of photons and gravitons can be arbitrary long or is it true that there exists a maximum wavelength in the physical universe? How do physicists know the answer to the previous question? If there is a maximum length in the physical universe, then should there be a modification of Einstein's field equations (even after quantum averaging)?

        According to Einstein's field equations and string theory with the infinite nature hypothesis, our universe expands forever. What is the explanation for the space roar? Does the Koide formula suggest that there might be a modification of Einstein's field equations? Consider Einstein's field equations: R(mu,nu) + (-1/2) * g(mu,nu) * R = - κ * T(mu,nu) - Λ * g(mu,nu) -- what might be wrong? Consider the possible correction R(mu,nu) + (-1/2) * g(mu,nu) * R * (1 - (R(min) / R)^2)^(1/2) = - κ * T(mu,nu) - Λ * g(mu,nu), if R(min) = 0 then Einstein's field equations are recovered.

        EINSTEIN'S "THE MEANING OF RELATIVITY", 5TH EDITION, PAGES 83 AND 84

        [edit note: for page 83, all except last paragraph of page 83 deleted]

        If there is an analogue of Poisson's equation in the general theory of relativity, then this equation must be a tensor equation for the tensor g(mu,nu) of the gravitational potential; the energy tensor of matter must appear on the right-hand side of this equation. On the left-hand side of the equation there must be a differential tensor in the g(mu,nu). It is completely determined by the following three conditions:

        1. It may contain no differential coefficients of the g(mu,nu) higher than the second.

        2. It must be linear in these second differential coefficients.

        3. Its divergence must vanish identically.

        The first two of these conditions are naturally taken from Poisson's equation. Since it may be proved mathematically that all such differential tensors can be formed algebraically (i.e. without differentiation) from Riemann's tensor, our tensor must have the form

        R(mu,nu) + a g(mu,nu) R

        in which R(mu,nu) and R are defined by (88) and (89) [edit note: see page 77]. Further, it may be proved that the third condition requires a to have the value - 1/2 . For the law of the gravitational field we therefore get the equation

        (96) R(mu,nu) - (1/2) g(mu,nu) R = - κ * T(mu,nu) .

        Equation (95) [edit note: see deleted part of page 83] is a consequence of this equation. κ denotes a constant, which is connected with the Newtonian gravitational constant.

        CRITICISM OF EINSTEIN'S ASSUMPTION for R

        How do physicists know that there is not some law of nature that forces R ≥ R(min), always and everywhere? The Koide formula suggests that square-root(mass-energy) might somehow be construed as area. If so, the entire universe might undergo an instantaneous (i.e. one Planck time interval) collapse. If the universe collapses when the average temperature of the universe gets too cold, then Einstein was wrong. Therefore, there might be some modification involving R that changes the underlying physics basis for eternal cosmological expansion. Can physicists cite empirical evidence that proves that the preceding speculation is wrong? Theorists might cite theoretical reasons why the proposed modification is wrong, but CAN THEY CITE EMPIRICAL EVIDENCE WHICH CLEARLY DISCONFIRMS THE PROPOSED MODIFICATION?

        http://www.math.columbia.edu/~woit/wordpress/?p=9129 "Can the Laws of Physics be Unified?"

        https://www.quora.com/What-was-Lubos-Motls-greatest-contribution-to-physics

        https://www.quora.com/Is-there-any-hope-of-reformulating-String-Theory-without-supersymmetry

        https://www.quora.com/Does-string-theory-require-supersymmetry-Why

        It seems to me that I have not done a good job of explaining my viewpoint to string theorists and to critics of string theory.

        First of all, who do I think are the 2 best critics of string theory: Answer: Burton Richter & Sheldon Glashow. What is my thinking on the "String Wars"? Google "witten magic mystery and matrix". Consider 5 questions:

        1. Is string theory the "only game in town" for unifying quantum field theory and general relativity? I say yes. 2. Does string theory predict general relativity theory? I say yes. 3. Does string theory predict quantum field theory? I say yes. 4. Does string theory predict nonabelian gauge symmetry? I say yes. Does string theory predict supersymmetry? I say that string theory with the infinite nature hypothesis predicts supersymmetry but string theory with the finite nature hypothesis predicts no supersymmetry, i.e. no superpartners at all. What do I say is wrong with the thinking of string theorists? String theorists seem to think that nature is smooth, differential, geometric, and higher dimensional in terms of spatial dimensions. I suggest that their thinking is a kind of half-truth. I suggest that there are precisely 64 basic particles. In terms of the interior of the multiverse, these 64 different particles by means of their independent motions create 64 dimensions of virtual spacetime. Each matter particle has 3 dimensions of linear momentum, 3 dimensions of angular momentum, and 1 dimension of quantum spin in the matter-quantum-spin-dimension. Each antimatter particle has 3 dimensions of linear momentum, 3 dimensions of angular momentum, and 1 dimension of antimatter-quantum-spin-dimension. Altogether, the motions of the particles create a 72-ball of virtual particle motion. This 72-ball somehow allows the monster group and the 6 pariah groups to guide string vibrations on 3 copies of the Leech lattice. This set-up somehow creates a mathematical bridge between the Fredkin-Wolfram network and and an approximation to string theory with the infinite nature hypothesis. In order for string theory with the finite nature hypothesis to work it is necessary for string theory with the infinite nature to "almost work". The most important insight is that string theory the infinite nature hypothesis implies supersymmetry and no MOND, while string theory with the finite nature hypothesis implies MOND and no supersymmetry. I say that Milgrom is the Kepler of contemporary cosmology and that the empirical successes of MOND imply that at least 1 of Newton's 3 laws of motion are wrong. Consider (± 1st law, ± 2nd law, ± 3rd law), where + means true and - means false. Milgrom thinks that the basic problem is with the 2nd law, but I think that the basic problem is with the 3rd law. By introducing a nonzero dark-matter-compensation constant, the result is the mathematically simplest modification of Einstein's field equations. An easy scaling argument then allows the approximate recovery of MOND in the Newtonian approximation. I suggest that Newton and Einstein wrongly assumed that gravitational energy is conserved. I suggest that some gravitons can escape from the boundary of the multiverse (where all direct measurement occurs) into the interior of the multiverse (which has immense "Fredkin heat"). By making 3 different modifications to Einstein's field equations it might be possible to provide physical justifications for Milgrom's MOND, the Koide formula, and Lestone's heuristic string theory. These 3 modifications might provide a new starting point for quantum gravity. Am I completely wrong? Maybe so.

        David,

        Modified Newtonian dynamics (MOND( could offer a viable explanation. Physicists are found of inventing something new rather than modifying the old -- makes one think of obsolescence. My essay does get into a speculation about DM created by the multitudinous forces of normal matter and motion. I'll have to follow the discussion of MOND more.

        Check mine out and see what you think.

        Jim

        Is Bell's theorem true? Joseph Polchinski wrote, "The second superstring revolution began in 1995. Over a period four years, we discovered dualities of quantum field theories, dualities of string theories, duality between quantum field theories and string theories (that is, AdS/CFT), D-branes, Matrix theory, and quantitative understanding of black hole entropy."

        https://arxiv.org/abs/1601.06145 "Why trust a theory? Some further remarks (part 1)" by J. Polchinski

        Consider 4 hypotheses. Hypothesis 1. By using clever D-brane adjustments, string theorists can provide mathematical models of any plausible or implausible physics -- even including miracles and cartoon physics. Hypothesis 2. The Copenhagen Interpretation is philosophically wrong but empirically irrefutable because it does not rule out the string landscape. 3. Bell's theorem is philosophically wrong but empirically irrefutable because it does not rule out the string landscape. 4. String theory with the infinite nature hypothesis can explain Milgrom's MOND but in a mathematically awkward way, such as by MOND-chameleon particles or something else. Is Milgrom the Kepler of contemporary cosmology? The empirical successes of MOND imply that at least 1 of Newton's 3 laws of motion is wrong. Consider (± 1st law, ± 2nd law, ± 3 law), where + means true and - means false. My guess is that the 4 most plausible possibilities are: (1) a Verlinde-type in which gravity is emergent and all of the 3 laws fail at the origin of the emergence; (2) a Bekenstein-type theory in which the 2d law fails but the 3rd law is true; (3) a string landscape theory in which all of the 3 laws are true but MOND-compatible, dark matter particles exist; (4) dark-matter-compensation-constant modification of Einstein's field equations. Am I correct on Milgrom's MOND, the Koide formula, and Lestone's theory of virtual cross sections?

        Is there some way that Lestone's theory of virtual cross sections might be justified in terms of the string landscape? In the string landscape, let us assume that there is a 10-dimensional ultra-hot interstitium among alternate universes and that, within the string landscape, alternate universes exchange virtual energy if and only if they have "almost exactly" the same virtual vacua. Furthermore let us assume that our own universe is very close to the multiverse average in terms of its free parameters in the Standard Model. Then it might be possible to hide Lestone's imaginary particles with virtual cross sections in the multiverse interstitium of the string landscape. The ultra-hot interstitium might consist entirely of virtual energy in which there are "bubbles" consisting of 2-spheres with 3 vibrating strings confined to the surface of each 2-sphere. The alternate universes might have "point-paricle" leptons that exchange virtual photons with nearby "bubbles" in the interstitium. Approximate curling up of 9 spatial dimensions might allow Lestone's speculative intuitions to have an approximate model in 4-dimensional spacetime. Could the preceding scenario work?

        Lestone has introduced a highly speculative approach to estimating the fine structure constant in terms of theory. Lestone wrote,

        "Introduction to my idea

        Before Hawking's work (and others) black-holes were believed to be point objects with only mass, spin, and charge. This is why Einstein (1930s) and others have previously considered the possibility that fundamental particles (like leptons) are quantum micro black holes. Black holes are now believed to have a temperature, entropy, and thus many internal degrees of freedom. Individual black holes are objects amenable to statistical mechanics.

        My heretical statement

        If black holes (once thought to be point objects) are amenable to statistical mechanics, then why not fundamental particles like leptons? (1988)

        Introduction to my idea continued

        I consider the possibility of a very strange "unknown" imaginary class of particles, with several unique (bizarre) properties including

        (1) My particles have a very high temperature(s).

        (2) Despite having a very high temperature, my imaginary particles can not change their rest mass upon the emission of electromagnetic energy. Using known physics my imaginary particles (if isolated) can not emit any "real" photons".

        (3) However, I consider the possibility that my imaginary particles can emit and absorb unphysical L=0 "virtual" photons via the time-energy uncertainty principle.

        (4) The emission and absorption is controlled by statistical arguments involving their classical temperature and possibly other effective temperatures.

        ..." http://permalink.lanl.gov/object/tr?what=info:lanl-repo/lareport/LA-UR-16-22121 J. P. Lestone, "Possible path for the calculation of the fine structure constant", Los Alamos Report LA-UR-16-22121, April 2016, Los Alamos National Laboratory

        MY GUESS is that there might be a plausible way of justifying (1)-(4) in terms of string theory with the string landscape. Assume a string landscape in which all the alternate universes have Standard Model free parameters that are very close to each other. If there is (in the string landscape) an extremely hot interstitium which is 10-dimensional and super-hot with respect to all the cooler alternate universes, and ALSO most of the virtual energy close to each alternate universe is slightly super-hot but cool enough that it is ALMOST conventional in terms of 4-dimensional spacetime, then it seems to me that (1)-(4) might be justifiable.

        https://arxiv.org/pdf/0908.0333.pdf "String Theory" by David Tong, 2012

        http://www-hep.physics.uiowa.edu/~vincent/courses/29276/Vecchia.pdf "The Birth of String Theory" by P. di Vecchia, Lect. Notes Phys., 737, 59-118 (2008)

        http://www.sns.ias.edu/witten

        "... a proper theoretical framework for the extra term in the uncertainty relation has not yet emerged ..." p. 29 in reference to equation (9) of "Reflections on the Fate of Spacetime" by Edward Witten

        http://www.sns.ias.edu/ckfinder/userfiles/files/Reflections(3).pdf

        http://www.superstringtheory.com/people/witten.html

        http://www.math.columbia.edu/~woit/wordpress/?p=9129 "Can the Laws of Physics be Unified?"

        https://www.quora.com/What-was-Lubos-Motls-greatest-contribution-to-physics

        https://www.quora.com/Is-there-any-hope-of-reformulating-String-Theory-without-supersymmetry

        https://www.quora.com/Does-string-theory-require-supersymmetry-Why

        In string theory with the infinite nature hypothesis, the idea is to say that the equivalence principle is 100% true but the Heisenberg uncertainty principle needs to be modified to include both hbar and alpha-prime. In string theory with the finite nature hypothesis, the idea is to say that the Heisenberg uncertainty principle is 100% true but the equivalence principle is completely false for both dark energy and dark matter, i.e., dark energy has negative gravitational mass-energy and zero inertial mass-energy, while dark matter has positive gravitational mass-energy and zero inertial mass-energy. According to Fredkin, nature contains neither infinities nor infinitesimals. If t is the time parameter and Fredkin is correct, then our universe does not expand forever because t cannot be arbitrarily large -- thus a Koide-type modification to Einstein's field equations is needed. If Fredkin is correct then energy-density cannot be arbitrarily large and there needs to be a corresponding modification to Einstein's field equations in order to limit the energy-density.