Dear David Brown,

I am so somewhat surprised that you link the question of dark matter with string theory so strongly. MOND was proposed as a way to account for the flat rotation curves of stars in galaxies, and is not committed to any particular account of the nature or origin of the dark matter. And cosmological observations of gravitational lensing effects have become much more exact and sophisticated since 1983. The Bullet Cluster has been cited as fairly direct evidence for dark matter. Do you have results that show how to account for these observations without dark matter, and just with a modification of the gravitational dynamics?

Regards,

Tim Maudlin

    Sorry: I meant that the dark matter explanation of the rotation, as opposed to MOND, is not committed to any particular account of the dark matter, and in particular not to string theory.

    Dear Tim Maudlin,

    In your essay "How Mathematics Meets the World" there is the statement, "The puzzle is why the language of mathematics should be such an effective tool for describing the physical world." My guess is that the solution to the puzzle is: Nature is finite and digital with string vibrations confined to 3 copies of the Leech lattice. Why is string theory likely to be 'the only game in town'? Google "mystery magic matrix witten". What is the empirical evidence for MOND? Google "kroupa pawlowski milgrom new paradigm". Does the Bullet Cluster show that dark matter particles exist? See:

    Milgrom's perspective on the Bullet Cluster, The MOND Pages

    What is the empirical evidence for the Fernández-Rañada-Milgrom effect? See:

    Does the Rañada-Milgrom Effect Explain the Flyby Anomaly?

    My thinking is that the empirical evidence favors MOND, the mathematical evidence favors string theory (or M-theory), and the Fernández-Rañada-Milgrom effect is likely to be the string theoretical interpretation of MOND. I claim that an easy scaling argument demonstrates that the alleged effect is approximately equivalent to MOND. If in the standard form of Einstein's field equations the -1/2 is replaced by -1/2 + dark-matter-compensation-constant, gravitational lensing works approximately as well merely because the dark-matter-compensation-constant is very small in comparison to 1/2.

    4 days later

    Dear Sir,

    We have discussed relativity critically in our essay. Since GR is also an inverse square theory, if MOND is correct, GR would also need modification. But for this modified versions to work, some sort of unseen or "dark" presence is a must, which looks a lot like dark matter. It won't be described by particles in the way that dark matter is described - it may be described in a more wavelike form or a more field-like form. In other words, MOND can do away with dark matter but cannot describe the universe simply as the product of a tweaked Einsteinian gravity acting on the mass we can see. It modifies gravity, but through the backdoor it introduces extra fields, which mean that the distinction between dark matter and modified gravity isn't very clear. In a paper "No Evidence for a Dark Matter Disk within 4 kpc From the Galactic Plane" (http://arxiv.org/abs/1011.1289) the authors note that their findings directly contradict the predictions of MOND.

    The energy "uncertainty" introduced in quantum theory combines with the mass-energy equivalence of special relativity to allow the creation of particle/anti-particle pairs by quantum fluctuations when the theories are merged. As a result there is no self-consistent theory which generalizes the simple, one-particle Schrödinger equation into a relativistic quantum wave equation. QED began not with a single relativistic particle, but with a relativistic classical field theory, such as Maxwell's theory of electromagnetism. This classical field theory was then "quantized" in the usual way and the resulting quantum field theory is claimed to be a combination of quantum mechanics and relativity. However, this theory is inherently a many-body theory with the quanta of the normal modes of the classical field having all the properties of physical particles. The resulting many-particle theory can be relatively easily handled if the particles are heavy on the energy scale of interest or if the underlying field theory is essentially linear. Such is the case for atomic physics where the electron-volt energy scale for atomic binding is about a million times smaller than the energy required to create an electron positron pair and where the Maxwell theory of the photon field is essentially linear.

    However, the situation is completely reversed for the theory of the quarks and gluons. While the natural energy scale of these particles, the proton, meson, etc. is on the order of hundreds of millions of electron volts, the quark masses are about one hundred times smaller. Likewise, the gluons are said to be quanta of a Yang-Mills field which obeys highly non-linear field equations. As a result, strong interaction physics has no known analytical approach and numerical methods are said to be the only possibility for making predictions from first principles and developing a fundamental understanding of the theory. In QCD, the non-linearities in the theory have dramatic physical effects. One coherent, non-linear effect of the gluons is to "confine" both the quarks and gluons so that none of these particles can be found directly as excitations of the vacuum. Likewise, a continuous "chiral symmetry", normally exhibited by a theory of light quarks, is broken by the condensation of chirally oriented quark/anti-quark pairs in the vacuum. The resulting physics of QCD is thus entirely different from what one would expect from the underlying theory, with the interaction effects having a dominant influence.

    There is an urgent need to rewrite physics.

    Regards,

    basudeba

      Dear Miss. Sujatha Jagannathan:

      In your essay "Trick or Truth: The Mysterious Connection Between Physics and Mathematics", you state: "The puranic view asserts that the universe is created, destroyed, and re-created in an eternally repetitive series of cycles." My theory assumes that the preceding idea is basically correct but my theory is based upon Wolfram's atheistic, materialistic theory as expounded in "A New Kind of Science" (see NKS Forum, Applied NKS). However, according to the Space Probe B science team, my theory has already been ruled out. (If the 4 ultra-precise gyroscopes malfunctioned in the manner suggested by the Space Probe B science team, then I agree that my theory is wrong.) In any case, I think that Milgrom is the Kepler of contemporary cosmology (on the basis of empirical evidence accumulated by Milgrom, McGaugh, Kroupa, Pawlowski, and others). What MOND really means is unclear even to Milgrom.

      -- D. Brown

      Dear Basudeba Mishra,

      In your essay "Reasonable Effectiveness of Mathematics", you state "The validity of a physical statement is judged by its correspondence to reality." Judging whether a physical theory corresponds to empirical reality depends upon the fairness of the empirical tests. I claim that the string theorists fail to realize that the empirical game is rigged against MOND (by vested interests in dark matter particles). According to Milgrom, "The MOND Paradigm", 2008, page 7 (http://arxiv.org/abs/0801.3133) "Disc galaxies are predicted to exhibit a disc mass discrepancy, as well as the spheroidal one that is found for any mass. In other words, when MOND is interpreted as DM we should deduce a disc component of DM as well as a spheroidal one ..." The publication "No evidence for a dark matter disk within 4 kpc of the galactic plane" by C. Moni Bidin, G. Carraro, A. Méndez, and W. F. van AltenaI puts forward a model based upon 6 assumptions (pages 5 & 6): "I Steady state. The thick disk is in equilibrium with the Galactic potential, as expected for anold stellar population. Therefore, all temporal derivatives are set to zero. II Locally flat rotation curve. The rotation curve is assumed flat at the solar Galactocentricdistance. III No net radial or vertical stellar flux. The mean radial and vertical velocity components are zero, while the rotational component shows a non-null lag ... IV Exponential radial dispersion profiles. ... V Vertical constancy of scale lengths. ..." The assumption of a locally flat rotation curve needs to be explained by DM, MOND, or some other (as yet) unverified theory because Newton-Einstein gravitational theory does not predict a locally flat rotation curve. To interpret MOND as dark matter particles that obey the equivalence principle either does not work or requires some drastic new hypothesis, so that "a disc component of DM" does not really mean in MOND what "a disc component of DM" means in cold dark matter theory. There is a pressing need for a relativistically precise version of MOND (WHICH MATCHES THE EMPIRICAL EVIDENCE). I conjecture that anyone who wants to fully understand MOND needs to explain the space roar and the photon underproduction crisis.

      -- D. Brown

      David Brown,

      Nice work on your essay. Short and sweet but you obviously put a lot of thought into it. Most of these essays are very thought provoking but some are hard to read. I went a different route and wrote what I consider a more entertaining twist - sort of a blend of Knights of the Round Table and Lord of the Rings (See Doctors of the Ring - The Power of Merlin the Mathematician to Transform Chaos into Consciousness). It is based on a model that I am trying to get published, which I posted at http://vixra.org/abs/1402.0045 called the space-time-motion model. I invite you to read it and let me know what you think (email to stjohntheodore@gmail.com). Of course, I also invite you to read and rate my essay if you get the chance.

      Respectfully,

      Ted St. John

        Ted St. John,

        In your essay "Doctors of the Ring - the Power of Merlin the Mathematician to Transform Chaos into Consciousness", you state: "... some admit that they don't really understand what time actually is. ... The problem with trying to answer the question why is there only one dimension of time is: How can we be so certain that there is only one dimension of time if we don't even know what it is? True, it only takes one number to describe time, but not because it is a one-dimensional entity; it's because everyone agreed upon a single time standard in order to describe motion." Fernández-Rañada and Tiemblo-Ramos suggested that atomic time might be different from astronomical time -- I say that atomic time is guaranteed to be different from astronomical time because the work of Milgrom, McGaugh, Kroupa, and Pawlowski shows that some revision is needed in the current paradigm of cosmology. The physicists have agreed upon a single time standard based upon empirical findings, quantum field theory, and general theory relativity -- their time standard well works amazingly well for the most part. However, Milgrom's MOND, the space roar, and the photon underproduction crisis demonstrate that something is wrong somewhere in physicists' current understanding of the foundations of physics. -- D.B.

        17 days later

        Dear Mary Ann Slaby,

        In your essay "What is the Mysterious Connection Between Physics and Mathematics?", you wrote: "The mysterious connection between physics and mathematics resides in the calculus developed by Newton and Leibniz." Riemannian geometry generalizes calculus, and presumably the non-commutative geometry of string theory is the generalization of Riemannian geometry that works for quantum gravitational theory. I have a scheme for unifying MOND with string theory, but according to the Gravity Probe B science team my plan has already been empirically refuted. However, my guess is that the 4 ultra-precise gyroscopes worked correctly and confirmed the Fernández-Rañada-Milgrom effect. My basic idea is as follows: (1) Assume string vibrations are confined to 3 copies of the Leech lattice. (2) Assume that nature is finite and digital; the maximum physical wavelength is the Planck length times the Fredkin-Wolfram constant. For some ideas underlying (2) google "use of mathematics by richard hamming" and "nks chapter 9". In the Standard Model of particle physics there are 36 quarks with 18 matter/antimatter pairs and with 3 quark colors so that one might say there are 6 basic quarks. My guess is that the 6 basic quarks each have 4 dimensions of uncertainty so that there are 24 dimension of quantum uncertainty, 1 dimension of matter time, and 1 dimension of antimatter time, giving 26 dimensions for bosonic string theory. String vibrations might have 3 energy-density levels (low, medium, and high) so that string vibrations occur in 3 copies of the Leech lattice. The 3 copies of the Leech lattice allow 64 particle-path dimensions, with 3 dimensions of linear momentum, 3 dimensions of angular momentum, 1 dimension of matter time, and 1 dimension of antimatter time. Wolfram's automaton uses Fredkin-Wolfram information below the Planck scale to create approximations of energy, spacetime, and string theory. All measurement occurs on the boundary of the multiverse, which is 72-dimensional. The boundary of the multiverse is divided up into pairs of matter/antimatter universes, each having 71 dimensions. The explanation for dark matter and dark energy is that gravitons have a nonzero probability of escaping from a measurable universe into the interior of the multiverse. When a graviton escapes from the universe, dark matter string vibrations have to somehow compensate for the dark energy string vibrations. When the average temperature of the universe becomes sufficiently cold, the entire universe undergoes an instantaneous collapse. All the universes in the multiverse expand and collapse in a process that takes about 81.6 ± 1.7 billion years from initial big bang to collapse. According to Wolfram, there are 4 or 5 simple rules for Wolfram's automaton that can generate adequate approximations to quantum field theory and general relativity theory. If my scheme is to work, then the Koide formula and Lestone's heuristic string theory probably need to be valid physics.

        6 days later

        Dear David Brown,

        I claim I am doing 'independent' research in theoretical physics. My few papers are available at vixra. When I learned from your reply to Philip Gibbs that you love 'crackpot' ideas, I thought it will be good to go through your essay. You have put forth some relevant questions.

        I consider Dark matter a myth. What I propose is finite gravity with a speed dependent G. The present G is actually the G of Earth for its present speed.; it can be theoretically deduced from 'G' of electrons. The universe as a whole has a certain G which increases with expansion; the present G of the universe is 1.4194x10-3. Using this G, the present Earth- Moon distance can be accurately predicted. What do you think? A crackpot idea! Visit my site finitenesstheory.com for more details.

        Kindly go through my essay A physicalist interpretation of the relation between Physics and Mathematics.

        Dear Jose P. Koshy,

        In your essay you wrote, "The Standard Model of particles is a set of interpretations based on QM. Similarly, the ΛCDM model of the universe is a set of interpretations based on GR. These models are still incomplete, and require further refining." According to Kroupa, the ΛCDM concordance cosmological model has been ruled out. A theory of "finite gravity with speed dependent G" contradicts what I call the Fernández-Rañada-Milgrom effect, i.e., the -1/2 in the standard form of Einstein's field equations should be replaced by -1/2 + dark-matter-compensation-compensation, where this constant is approximately sqrt((60±10)/4) * 10^-5 . Note that Milgrom's acceleration law does not suggest "speed dependent G" but some modification of Newtonian gravitation which is acceleration dependent. On the empirical evidence, I could be wrong about everything except the Milgrom Denial Hypothesis. No matter what the future holds, I predict that a few ideas now deemed 'crackpot' will triumph -- however, these ideas will be very few in number and it is very unclear what the ideas will be.

        11 days later

        Dear Mr. Brown,

        I thought that your engrossing essay was exceptionally well written and I do hope that it fares well in the competition.

        I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.

        All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.

        Joe Fisher

          Dear Joe Fisher,

          In your essay "WHY THE REAL UNIVERSE IS NOT MATHEMATICAL", you wrote, "... it must be re-emphasized here that all appearances are deceptive. The real Universe is not apparent and this is why it is not mathematical." If mathematics is that part of human thinking that is precise, then I personally believe that mathematical thinking is a particular type of electromagnetic field and therefore is at least a component of the real universe. On page 2 of the "Meaning of Relativity", 5th edition, Einstein wrote, "The only justification for our concepts and system of concepts is that they serve to represent the complex of our experiences; beyond this they have no legitimacy." The gravitational theories of Newton and Einstein are correct over broad ranges of experimental tests -- beyond empirical testing, the true nature of reality is perhaps fundamentally a question of subjective opinion or philosophy.

          6 days later

          Dear David,

          As there is inconsistency between QM and cosmology, MOND is imperative; in that Gauge anomaly is causal for this inconsistency that invalidates Gauge theory. While this Gauge anomaly is a Vector gauge anomaly then that Gravitational anomaly invalidates General relativity. This is causal for the Gravity anomaly of Planets that is more pronounced with the observations of Galaxy clusters and their Superclusters.

          Thus, further developments on MOND emerges with the theory of Tensor-vector-scalar gravity and its extension, Bi-scalar tensor vector gravity theory; while MOG is developed on Scalar-tensor-vector gravity theory.

          All these incompleteness indicates that, redefining the Causality of gravitation is much imperative with string theory. Thus we may recommend for the modifications in string theory, in that a string-segment itself is to be considered as an eigen-rotational matter with energy, that is an alternative to the fermionic field.

          Thus, Gravitation between micro objects is a tensor derivative of a string-matter or collective tensor derivatives of few string-matters between invariable scalar structures of micro objects; whereas the Gravitation between macro objects is the resultant collective tensor derivatives of the string-matter bundles exists between that invariable scalar structures of macro objects, in time.

          With best wishes, Jayakar

            Dear Jakayar Johnson Joseph,

            In your essay "Before the Primordial Geometric origin: The Mysterious Connection between Physics and Mathematics" you wrote, "Though it may be obvious that our Universe is Mathematical, because of Initial singularity, the only possibility to explore the initial conditions of the Universe is with Gödel's incompleteness theorems that have inherent limitations." It might be possible to detect gravitational waves generated in the very early stages of the Big Bang. In my personal opinion, Gödel's first and second incompleteness theorems suggest that the mathematical concept of infinity is somewhat unsatisfactory -- to know what we really mean by "infinity" we might have to add infinitely many new axioms to Peano Arithmetic. One of my ideas is to replace the -1/2 in the standard form of Einstein's field equations by -1/2 + dark-matter-compensation-constant, where this constant is approximately sqrt((60±10)/4) * 10^-5 -- however, if the Gravity Probe B science team is correct, this idea has already been ruled out. If some "eigen-rotational string matter continuum paradigm" accurately describes empirical reality, there needs to be some MOND-compatible prediction, perhaps along the lines of TeVeS or some similar theory.

            8 days later

            David,

            You say that string theorists fail to recognize that Milgrom is the "Kepler of contemporary cosmology," and yet I interpret Witten's reply to you, as favorable to that idea. He gives credit to the observational cosmologists, and credit to the mathematical cosmologists.

            Just as Kepler's laws cannot be derived from first principles -- they are themselves first principles -- frameworks that explain frameworks, in a metamathematical and metaphysical way, are inductive hypotheses, and prior to the method of deduction from theory that characterizes rational science.

            Like Witten (and Newton), I like to begin with a mathematically complete idea and make my conclusions from that structure, by theorem-proving. That doesn't obviate any hypotheses from observation that might crop up from serious researchers -- yet why should one trust any inductive conclusion? As that sage Yogi Berra put it, "If you don't know where you're going, you might end up somewhere else."

            I got interested in Milgrom's research a few years ago after reading John Moffat's *Re-inventing Gravity.* I liked the book and the ideas in it -- in the end, though, I come back to my "center" in the fundamentals of field theory, and in agreement with Witten that "general relativity cosmology forces itself on us."

            My current essay is part of my attempt to reconcile field theory with cosmological initial conditions, which brings quantum field theory (and therefore string theory) back to center stage.

            Nice job of raising important questions -- my highest mark to you.

            Best,

            Tom

            Dear Thomas Howard Ray,

            In your essay "Science of the Possible, or the Probable?" (page 4), you wrote, "What quantum theorists know and seldom talk about, is that Bell's Inequality-- the formal mathematical statement of Bell's theorem-- is only locally real. The issue of nonlocality arises in the proof of the theorem, and that proof is only by way of double negation." In my opinion there is a problem about assigning mathematically and physically precise meanings to "locally real" and "nonlocality". Quantum field theory can provide infinitely many mathematical frameworks for particles that are unlikely to exist in terms of empirical reality. String theory (or M-theory) might be an order of magnitude worse than quantum field theory in terms of ambiguity. Wolfram has conjectured that there exist 4 or 5 simple rules that generate satisfactory approximations to quantum field theory and general relativity theory. I have attempted to make testable hypothesis based on Wolfram's conjecture. If the Gravity Probe B science team is correct, then my attempt has failed. In any case, I think that the string theorists need to explain the space roar, the photon underproduction crisis, and the empirical verifications of MOND found by Milgrom, McGaugh, Kroupa, and Pawlowski. One of my basic ideas concerning science is: Experimental physics trumps theoretical physics trumps mathematics trumps philosophy. To my way of thinking, philosophy is imprisoned by words, and mathematics is imprisoned by logically precise imaginings freed from empirical restraints. If we want to break out of our prisons of ignorance and false belief, then we need to do controlled empirical experiments. What is really meant by the word "infinity"? Gödel's first and second incompleteness theorems might suggest that the concept of a complete infinity suffers from inherent problems of axiomatization. If the foundations of physics have a satisfactory axiomatization, then such an axiomatization might imply that nature is finite and digital.

              David,

              I find the claim -- "axiomatization of physics (Hilbert's 6th problem) implies that nature is fundamentally both finite and digital" -- to be self-contradictory.

              Finite sets are continuous in principle, physically and mathematically. One can derive parts from the whole; the converse is not true, because the sum of the continuous whole is greater than that of its discrete parts. Take the simple arithmetic theorem -- that a point may simultaneously map to any set of points, provided that it is far enough away. That point at infinity has to exist, physically (and locally, i.e., in every measured time interval), or else Minkowski space-time and special relativity are falsified.

              The basic logical completeness of a generalized field theory (even including number fields) persuades me that nature is recursive. In my essay discussion forum -- in a recent attachment -- I demonstrated a continuous digital recursive function corresponding to the simplest prime number sequence.

              Tom