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

        Tom,

        Einstein and Leonardo da Vinci apparently believed that nature is infinite. According to Leonard da Vinci, "La natura è piena d'infinite ragioni, che non furon mai in isperienzia." (Nature is full of infinite reasons, which people have never realized.)

        "Finite Nature is the hypothesis that ultimately every quantity of physics, including space and time, will turn out to be discrete and digital; that the amount of information in any small volume of space-time will be finite and equal to one of a small number of possibilities." -- Edward Fredkin, "A New Cosmogony"

        Can quantum information be explained in terms of Fredkin-Wolfram information below the Planck scale? Perhaps not. However, even if nature is infinite, the amount of actual data accumulated by scientists will probably always be finite. Google "witten milgrom" for more information on how the Copenhagen theory of measurement might be replaced by a Fredkin-Wolfram theory of measurement.

        "Einstein and Leonardo da Vinci apparently believed that nature is infinite."

        Not Einstein. General relativity describes a universe "finite and unbounded."

        Tom,

        Assume the universe has an approximately constant curvature on average. General relativity describes a universe homeomorphic to the 3-sphere if and only the curvature is positive. In the Friedmann model, the curvature is either zero or negative. However, you seem to be correct that Einstein believed the universe is finite and unbounded. I copied the following from the Skeptics Stack Exchange:

        TAKE THE 2-MINUTE TOUR ﾃ-- Skeptics Stack Exchange is a question and answer site for scientific skepticism. It's 100% free, no registration required.

        Did Einstein say "Two things are infinite: the universe and human stupidity; and I'm not sure about the the universe."

        ... DOTS ADDED

        The following quotation is commonly attributed to Albert Einstein:

        "Two things are infinite: the universe and human stupidity; and I'm not sure about the the universe."

        However, I've been unable to find a reliable source confirming the quote. Can anyone confirm or reject the genuiness of this citation?

        quotes albert-einstein

        shareimprove this question

        edited Oct 20 '13 at 23:59

        user5582

        asked Oct 20 '13 at 22:17

        Dominik

        203125

        2

        This item at Quote Investigator may be a useful source. - Compro01 Oct 20 '13 at 22:29

        @Compro01: I think there is enough there to make that an answer. - Oddthinking笙ｦ Oct 20 '13 at 23:44

        As an aside, I'm not sure Einstein believed in an infinite universe as such. Prior to Hubble's results (circa 1929), he seems to have leaned towards a static universe, which would lead then to Olbers' paradox (which was well known) if it was infinite and eternal at the same time. Later on, he seems to have been convinced by the evidence that it is expanding. I'm not sure how an infinite universe can expand, but perhaps that's just me :) A good summary of some of these topics can be found here. - Daniel B Oct 22 '13 at 5:56

        Yeah Daniel I agree Einstein held to finite universe till the day he died. It was the common view among Physicist at the time. - Neil Meyer Oct 28 '13 at 10:16

        ... DOTS ADDED

        Unable to determine veracity of quote. It pretty much depends on whether or not you believe a single man's claim about a personal conversation with Einstein.

        According to Quote Investigator, the origin of the quotation being attributed to Einstein is the book Gestalt Therapy Verbatim by Frederick S. Perls.

        As Albert Einstein once said to me: "Two things are infinite: the universe and human stupidity." But what is much more widespread than the actual stupidity is the playing stupid, turning off your ear, not listening, not seeing.

        Further context on the quote is given in another Perls book, In and Out the Garbage Pail.

        I spent one afternoon with Albert Einstein: unpretentiousness, warmth, some false political predictions. I soon lost my self-consciousness, a rare treat for me at that time. I still love to quote a statement of his: "Two things are infinite, the universe and human stupidity, and I am not yet completely sure about the universe."

        He also used the quote in a previous book Ego, Hunger, and Aggression: a Revision of Freud's Theory and Method, though did not cite it to Einstein, but rather to "a great astronomer"

        Wikiquote lists the quote as "disputed" and also notes similar quotations from various people dating back to 1880.

        David,

        I will add this, though. As Ed Fredkin says, " ... the amount of information in any small volume of space-time will be finite and equal to one of a small number of possibilities."

        I agree. My research tells me that the mathematics of Einstein's finite and unbounded model -- meaning finite in time, bounded at the singularity of creation, and unbounded in space -- does not change when converted to a model finite in space and unbounded in time.

        So "Can quantum information be explained in terms of Fredkin-Wolfram information below the Planck scale?"

        Why not? The Planck limit is empirical. Quantum information is self-limiting at multiple scales and not necessarily restricted by the Planck limit.