Hi Lawrence,

here are some ideas ...

Hello thinkers,

Very interesting these extrapolations. But I am insisting about the finite groups. Furthere more a photon in my line of reasoning possesses the serie of uniqueness.So a serie begining from the main central sphere.After the serie is a fractalization with specific spherical volumes. the serie is between 1 and x. So a photon is so complex in fact because its quantum number is very important.See also that this numbers the same than our cosmological number of spheres(without the quantum spheres of course).So it is very relevant about the broken symmetry indeed due to informations correlated with volumes and the rotations spinal and orbitals.The tori of stability take all their meaning. See that the system is a fusioned system.The desnity is relevant correlated with mass, and the polarity m/hv due to evolution. So the exchanges is probably a fusioned system and not a binar system in its pure generality.

See also that the informations are very relant when we consider the VOLUMES OF SPHERES !!!The informations can be bosonic or fermionic.Personnaly I beleive that the volumes of fermions are more stable due to the encoding of evolution.The bosonic encoding is more subtle due to its quantum number and its fractal cited above. The sortings and synchros appear with a universal proportionality.

Regards

    1st timer submission, not yet submitted, while reviewing selected works for possible End Notes.

    Good history and very interesting paper but got lost in the heavy math, wish I was abreast of all covered...but love your ideas "G implying 1/mass and QFT as unit less coupling, have different times" (if I interpret correctly)

    First I see E/f = h and Power = E/t. Dividing one gets, t/f, so IF t = 1/f it implies either t squared of 1/f squared. Square roots generate plus and minus, a past and future with no present?

    Second, mass and energy, respectively, as the inscribed sphere, tangent to the face of a regular tetrahedron where sphere and tetrahedron have equal surface-to-volume ratios at ANY size, e.g. equivalent "activity" as free energy.

    Comment? (may use in end notes)

      The gravitational constant in naturalized units is "area," so it is sqrt{G} that is ~ length or reciprocal of mass.

      Verlinde has a proposal that the work done by gravity W = ∫F•dr is equal to entropy S = nkT. There has been some controversy over this. However if we look at an increment of work done through some increment of time δt, I will not worry about the relativistic issues with this definition of time for now, then the increment of work is

      δW = F•(dr/dt)δt = Pδt.

      Power has in natural units reciprocal length squared L^{-2}, or ~ 1/G. Consequently, this increment in work can be written as δW = δt/G ~ n/G. We interpret G as the fundamental Planck unit of area, and n = # of Planck units of area generated by this work. This would then correspond (roughly) to the Bekenstein bound or entropy S = kA/4L_p^2. This is why I think his entropy force of gravity pertains to moving the holographic screen.

      Cheers LC

      Thanks guys for the response. I think the situation we face with quantum gravity may mirror something in the past. The solution might in part be under our noses.

      LC

      Dear Lawrence Crowell,

      You begin your essay with a well written summary of physics history, beginning with "the motion of particle executes little variations to find the proper path", then undergoing a "radical shift [from] variation of the least action in classical physics [to] the path integral in the quantum mechanics of fields." Like some others in this essay contest, I am more inclined to attempt to derive quantum theory from classical fields than vice versa, so I particularly liked your explanation that "constructing a propagator for a field on that very same field" leads to problems.

      In analyzing the limits of space-time, you point out that we are limited by the fact that beyond a certain point, our probe creates black holes that hide the information from us. [That's one reason I treat non-relativistic quantum mechanics and weak field gravity, where we know, at least potentially, whereof we speak.] Thus you point out, "space-time itself is a barrier to the complete specification of an observable." You then say "information conservation demands...". If you'd care to comment on the grounds on which you base a belief in "information conservation" I would be interested. I know it is often assumed nowadays, but I'm not sure on what it is based. I assume you do not begin with quantum error correcting code to achieve this.

      While I don't buy either quantum gravity or supergravity, nevertheless your observations about "the breakdown in the ability to measure everything about the universe" are quite interesting, as is your conjecture that this implies time, unitarity, locality, and causality to be emergent. You seem to agree with Philip Gibbs, so I suspect these are the waters the "math beyond physics" school swim in today. In my previous essays and in my dissertation, "The Automatic Theory of Physics", I presented logic and mathematics as emergent, so I tend to question any ultimate conclusions based on math that go beyond physical barriers to observation. Frank de Meglia may have as much claim to this territory as anyone.

      Nevertheless, having chosen to play the game of 'math beyond physics', you do a bangup job of it, ending up with one electron, one quark, one photon in a universe based on underlying quantum error correction codes.

      Best of luck in the contest,

      Edwin Eugene Klingman

        Thanks for the thumbs up. I seem to be falling downwards in the community rankings, though my paper has only been up about 36 hours. I am not sure what is going on there, for I know the physics I present is better than a whole lot of the papers ranking higher.

        Cheers LC

        It is not difficult to quantize weak gravity. This is usually written as a bimetric theory g_{ab} = η_{ab} h_{ab}, where η_{ab} is a flat spacetime (Minkowski) metric and h_{ab} is a perturbation on to of flat spacetime. We may write a theory of the sort g_{ab} = (e^{ω})_a^c η_{cb}, where the bimetric theory is to O(ω) in a series expansion

        g_{ab} =~ (δ_a^c ω_a^c) η_{cb}.

        Gravitons enter in if you write the perturbing metric term as h_{ab} = φ_aφ_b, or ω_a^c = φ_aφ^c. The Ricci curvature in this weak field approximation is

        R_{ab} - (1/2)Tg_{ab} = □h^t_{ab},

        with h^t_{ab} the traceless part of the metric, and □ the d'Alembertian operator. Which in a sourceless region this computes plane waves. The two polarization directions of the graviton may then be interpreted as a form of diphoton, or two photons in an entanglement or a "bunching" as in Hanbury Brown-Twiss quantum optical physics.

        If we now think of extending this to a strong field limit there are the square of connection terms Γ^a_{bc} in the Ricci curvature, or cryptically written as R ~ ∂Γ ΓΓ where there is the appearance of the nonlinear quadratic term in the connection. This nonlinear term indicates the group structure is nonabelian, so the photon interpretation breaks down. The graviton in this case is a form of di-gluon, or gluons in a state entanglement or chain that has no net QCD color charge. This connects with the AdS_n ~ CFT_{n-1} correspondence, where for n = 4 the conformal field theory is quark-gluon QCD physics. Further D-branes have QCD correspondences and this takes one into the general theory I lay out. One does need to look at the references to learn more of the specifics. The quantum phase transition to entanglement states is given in the paper I write in ref 11 L. B. Crowell

        The simple fact is that as physics develops it will invoke new mathematics. I don't think I am overly mathematical in this essay, and I leave most of those details in the references. A theoretical physicist I think is wise to have a decent toolbox of mathematical knowledge and thinking. Physics invokes ideas of symmetries, remember Noether: symmetry corresponds to conservation law, and invariant quantities can also have connections with topology and number theory. I think the more one is familiar with advanced mathematics the more capable one is of thinking deeply about these matters.

        It is true that my work is commensurate with P. Gibbs'. If field theoretic locality and spacetime are emergent structures then so is causality. This emergence is connected with a quantum phase transition, or a quantum critical point (tricritical point of Landau), and something occurring on a scale much larger than the string length.

        Cheers LC

        hello to both of you ,

        Mr Corda,

        Happy to see you again.

        Regards

        "Physics invokes ideas of symmetries, remember Noether: symmetry corresponds to conservation law, and invariant quantities can also have connections with topology and number theory."

        "Invokes" is an excellent choice of word. My impression is that many physicists today would go farther and claim that symmetry is the basis from which the universe 'emerges' -- a very questionable assumption.

        I also agree that "the more one is familiar with advanced mathematics the more capable one is of thinking deeply about these matters." But that doesn't address the issue that "mathematics hangs on logic." And to assume that when space and time are abolished (coming "close to what we might call nothingness") somehow logic and math still exist, is to assume a lot. I believe it is a wrong assumption.

        Edwin Eugene Klingman

        Large symmetries are clearly important. The more general a symmetry group is, say with a larger Lie group, the transformations of that group can maintain a more general vacuum as a vacuum. In other words, symmetry preserves the ground state (vacuum), and broken symmetry does not, or maintains a more restricted ground state. There may of course be other elements to the foundations of physics than simply using ever larger Lie groups, such as removing certain postulates like locality of field data.

        A lot of this about mathematics and logic relies upon the philosophy of mathematics, which I have read about and find somewhat interesting. However, I am not that steeped in the subject, nor does it concern me that deeply. Some mathematical subjects have no reference to geometry, such as most of number theory. Of course we humans have to exist with all our causal structure in spacetime to study it. However, a mathematical realist would say that number theoretic proofs are true whether we know them or not.

        Cheers LC

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        • Post #26

        Dear Lawrence Crowell,

        While you now correctly spelled annus, I see you wrong again: "The introduction of the Monad, as Leibniz conceived it, is a direct result of his disagreement with Descartes and Spinoza." (http://www2.sunysuffolk.edu/schievp/file22m.html)

        You wrote on p. 3: "This would not quantum mechanics in any natural or realistic

        way." I do not understand this sentence.

        According to the title of your essay, unitarity is a foundation that is not a foundation. I wonder why you did not anticipate readers like Yuri and me who do not feel forced to immediately understand such play with words just because you mentioned the nebulous word "emerging". Having searched for "unitarity" in the text of your essay, I did not get the due explanation but only two hits.

        The abstract promised replacement of unitarity by modularity, a word that is not at all mentioned in the text.

        We merely learn: unitarity "might be emerging". In "abandonment of locality and unity" you did perhaps also mean unitarity, not unity; because the next sentence speaks of the loss of unitarity.

        I do not just criticize some imperfections but I am also ready to factually question it if you are willing to deal with my admittedly quite different view.

        Sincerely,

        Eckard

        Eckard

          "...a mathematical realist would say that number theoretic proofs are true whether we know them or not."

          That is exactly the type of religious 'belief in a Platonic realm of math' that I referred to on Phil Gibbs thread. Besides, the question is not "whether we know them or not", but whether, in a space-less and time-less state that comes "close to what we might call nothingness", it makes any sense to claim that logic and math "exist".

          An 'appeal to authority'-based statement, unproved, and almost certainly unprovable, is exactly the type of assumption that this essay contest was designed to challenge.

          Edwin Eugene Klingman

          The matter over Leibniz is not in my essay. I appear to be wrong with respect to Spinoza in my blog post.

          The sentence is missing the word be, which is unfortunate. it should read, "This would not be quantum mechanics in any natural or realistic

          way."

          I discuss modularity towards the end. I was planning on breaking this out further, and in fact did so more. However, I exceeded the word/page limits for the essay. So this got rather scant mention at the end.

          The word unity is supposed to be unitarity.

          The emergence of unitarity is complicated. The existence of singularities means that quantum wave functions are not analytic functions. They are meremorphic, which define modular function or forms. I wrote a bit more on this in a post above on Aug. 13, 2012 @ 14:44 GMT. This is a deep subject, which gets into Borel groups, Leech lattices and so forth. The length restriction on this essay prevents me from breaking this out. Besides most of this that I have worked out is on notebook paper and not published. Yet analytic functions or unitarity occurs in the special case the singularity is removed or has minimal nonlocal connection to a region outside the event horizon in the case of a black hole. This occurs for large black holes.

          I am not sure what the main objection is you want to raise. I am not likely to respond much if your objection is about the foundations of mathematics or set theory.

          Cheers LC

            I am not particularly interested in getting further into math foundations issues.. My point is there are plenty of mathematical topics which are independent of geometry. The question of mathematical realism, which is related to Platonism, is something I am not interested in debating much. There are various schools of math foundations, intutionism, constructivism and so forth, and I am not particularly a partisan to one over the other. The mathematics I work with is not terribly dependent on set theory subtleties, and most mathematics used in physics is not directly dependent on these matters.

            This extends to Blumschein as well. If I recall he has some big alt-math idea that "upends" the foundations of mathematics. I am not terribly interested in going there.

            Cheers LC

            Thank you. My approach is perhaps simply too naive, but suggests work for confirming Dr. Tykodi's approach and a preliminary definition of consciousness, aka panpsychism..

            • [deleted]

            • Post #32

            "An 'appeal to authority'-based statement, unproved, and almost certainly unprovable, is exactly the type of assumption that this essay contest was designed to challenge." Because I did not design this contest I would like to be more cautious and replace the speculative word "designed" by "tempting".

            Blumschein, that's me, does also not see the solution to what some physicist dare to call a crisis to be found in intuitionism or constructivism. Nonetheless he got aware that Hilbert behaved rude toward Brouwer. Hilbert's successor Hermann Weyl rejected considerable parts of Hilbert's set theory and called Hilbert a piper to whom all followed like rats.

            Blumschein just tries to upend back what was upended. He agrees on that set theory (ST) is unnecessary - except for providing the elusive feeling of rigorous foundations.

            In his last essay he pointed to some ST-related imperfections in mathematics. This time he tries to investigate how Cantor's naive ST not just resembles but even contributed to similar confusion between model and reality in physics.

            He sees unitarity and the usual notion of time abstract notions that must not be believed to fit one-to-one with reality. He sees causality (in the sense of contextual dependence on what already happened) an indisputable property of reality.

            I think that unitarity is a special case of modular transformations when there is no singularity, or if in the case of a black hole the singularity is hidden by a very classical event horizon that causes decoherence of nonlocal fields across it. If the event horizon is quantized, say with a very small black hole, then this breaks down. Further, the meaning of spacetime and light cones becomes lost. They are so to speak blurred out by quantum fluctuations.

            If the definition of spacetime breaks down on a very small scale then the definition of time is lost. If there is no effective definition of time there is then no unitary time development of quantum states or observable by an operator, such as the Hamiltonian. This is a loss of unitarity.

            The Wheeler-DeWitt equation tells us this to begin with. The Hamiltonian in classical gravity is zero, or NH = 0, for N the lapse function. This is a standard result of ADM general relativity. The reason for this is Gauss' law, where there is no boundary sphere around the universe by which one can integrate out the mass-energy contained within. This argument can be posed according to the nature of coordinate time in general relativity, where this is a frame dependent quantity and physics should not depend upon it. So the Schrodinger equation

            i∂ψ/∂t = Hψ = 0

            is seen to be zero on both the left and right hand side in a consistent manner. This is the Wheeler-DeWitt equation Hψ = 0, which is the quantum form of the Hamiltonian constrant NH = 0. There is in this case no Hamltonian which acts as a Hermitian operator that define a unitary time development operator. Unitarity is gone.

            What takes the place of unitary transformations are modular transformations, in particular the Eisestein series and Jocobi functions. The Jacobi functions are realizations of the E_8 and Leech lattice Λ_{24} based sporadic groups --- in particular the Mathieu group of quantum error correction.

            In that case my essay does propose the removal of or change in established physical postulates.

            I am less concerned with mathematical foundations. The connection to matters such as Zermelo-Fraenkel (ZF) set theory is at best very subtle, and really could be nonexistent. ZF set theory has some strange features, such as the duplication of spheres with the Axiom of Choice. There are alternatives such as Polish sets. This goes double for philosophical issues over how or whether mathematics exists independent of physical reality or the mind of a mathematician. These questions simply go far beyond the scope of what I am concerned with.

            Cheers LC