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..

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  • 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

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    • Post #35

    Dear Doctor Crowell,

    Because I am an uneducated non-physicist, I was unable to fully understand many of the exquisite rational arguments you touched upon in your exceptional brilliantly written essay. I was immensely gratified by your posted contention that "One of the things I think comes from this is the universe contains only one of each particle" seems to agree with my understanding of the singular universe as posited in my essay Sequence Consequence. Could technological advancement be confusing all of us as to the true nature of the universe? Natural sunlight barely penetrates 10 fathoms into the ocean. Yet fabricated electrical flashlights are used thousands of fathoms deep. I do not understand how fabricated electrical light can overcome density while much more powerful sunlight cannot.

      You think really that you can make what you want with my spheres and spherization Theory or What ??? :)

      well a duplication of spheres with an axiom of choice , it is interesting.

      and a toe also no? second :)

      third :) soon at New York my friends and we shall discuss about my spheres in live.

      They turn so they are...

      ps eureka form belgium, the real toe.The real gut, the real spherization ! with humility of course.

      not guys !!!but Steve or Mr Dufourny.

      It is a kind of respect above the strategies !

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      • Post #40

      Light is attenuated in water by particles that absorb or scatter light. The extinction of light over a distance is the same for sunlight striking the water surface and for photons leaving a flashlight underwater.

      I'll take a look at your essay. Good luck.

      Cheers LC

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      • Post #41

      Lawrence,

      Meromorphic (not meremorphic) means analytic with exception of singularities. For instance Joy Christian made the singularity of Riemannian sphere at infinity an issue in physics. Used to write C U {infty}, mathematicians are treating only the "north-pole" of it as a singular point while they do not take care for the "south-pole", i.e., for the zero. For EEs like me it is common practice to operate with poles and zeros almost as naturally as with north and south.

      If we assume that the singularity alias actual infinity is just a mathematical fiction, then this might also hold for zero and the ideal (Peirce) continuity; and those who ascribe physical correlates to singularities are simply victims of their inability to realize that even the most advances mathematical tools are just tools that must not be misused in an intuitive pre-mathematical manner. Weren't you unable to refute Ernst Fischer's essay?

      Eckard

      Fischer's essay is a case of how one gets out of something what one puts in. He uses equation of state for static matter to show that there is no singularity. This is of course to be expected. The matter is composed of particles on nongeodesic paths in spacetime, which if these are meant to modelgeodesic flow corresponds to a violation of the equivalence principle. Otherwise this is just a model of a star or some bulk material object which has no singularity by construction. I am a bit amused that his essay is in the top slot.

      Check out Gibbs' blog entries, he spells very colorfully. I wont misspell meramorphic again, or is it merumorphic or ... :)

      Cheers LC

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      • Post #43

      Hi Lawrence,

      I get the feeling I understood more of this essay than last years. So it is, I think, more accessible. (I made two separate attempts.) The history was interesting. I understood a chunk of problems you pointed and the reasons for then considering each in turn, though not the mathematical explanations themselves. My own failing I know. It is probably straightforward to those with the necessary familiarity with mathematics.

      As I rarely understand much of what you write I think we have both done rather well with this essay. I wish I was able to give more positive feedback. I hope you get lots of informed readers who will be able to properly understand and talk to you about the essays content, which is probably far more fascinating than I can appreciate. Good luck in the competition.

        Hi Lawrence:

        I enjoyed reading your paper, especially the discussion related to the widely known "Foundations that are not Foundations."

        The fundamental question is how to determine what is the most fundamental reality or physical process that governs the Foundation of the universe. I demonstrate in my posted paper -" From Absurd to Elegant Universe" that current crisis in physics and cosmology as evidenced by the well-known paradoxes and singularities are artifacts of the missing Foundation of the fundamental physics of the spontaneous decay and birth of particles. Hence, many of the so-called foundational assumptions or phenomena are shown to be artifacts rather than foundation of the universe or a universal theory. When this missing foundational physics is counted in, it not only successfully predicts the observed accelerated expansion of the universe and galactic star velocities but also resolves paradoxes and singularities of the Cosmic Conundrum today. It also provides understanding of the inner working foundations of quantum mechanics.

        I would greatly appreciate it if you could please review my paper and provide your comments.

        Thanking you in advance,

        Best Regards

        Avtar Singh

          There is a growing understanding of a correspondence between quantum chromodynamics (QCD) and gravitation. The AdS/CFT correlation is one of them. More recently developments such as the BCFW recursion relationship indicate that calculation techniques for QCD and quantum gravity are related to each other. Gravitons are I think entanglements of gluons, or what we might call gluon chains. Certain complex self interacting states of gluons can form effective mass states. Remember that gravity interacts with mass-energy, so gluons can be self-interacting --- similar to gluons. In classical gravity there are some solution types that are intermediate to the near field solution, a black hole, and the far field solution as gravity waves. A black hole can be thought of as a condensate of particles or gravitons in a state that is completely self-confined.

          Quark-gluon plasmas produced by RHIC and the lead heavy ion collisions at the LHC can produce very transient states corresponding to black holes, or with tiny quantum amplitudes corresponding to black holes. These amplitudes are not large enough to generate a full bonifide black hole, as seen in previous fears of the LHC producing an Earth devouring black hole, but they should be sufficient to test these theories.

          holographic graviton

          Cheers LC

          Hi Avtar,

          I loaded up your paper, which time permitting I will try to read today. Singularities in one sense do reflect a failure of an existing theoretical structure. In a more general theory they becomes something else, or are removed.

          There is a growing understanding of a correspondence between quantum chromodynamics (QCD) and gravitation. The AdS/CFT correlation is one of them. More recently developments such as the BCFW recursion relationship indicate that calculation techniques for QCD and quantum gravity are related to each other. Gravitons are I think entanglements of gluons, or what we might call gluon chains. Certain complex self interacting states of gluons can form effective mass states. Remember that gravity interacts with mass-energy, so gluons can be self-interacting --- similar to gluons. In classical gravity there are some solution types that are intermediate to the near field solution, a black hole, and the far field solution as gravity waves. A black hole can be thought of as a condensate of particles or gravitons in a state that is completely self-confined.

          Quark-gluon plasmas produced by RHIC and the lead heavy ion collisions at the LHC can produce very transient states corresponding to black holes, or with tiny quantum amplitudes corresponding to black holes. These amplitudes are not large enough to generate a full bonifide black hole, as seen in previous fears of the LHC producing an Earth devouring black hole, but they should be sufficient to test these theories.

          holographic graviton

          Cheers LC

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          • Post #47

          Lawrence,

          Concerning singularity, I decided to add new arguments here.

          Your objection against Ernst Fischer were already rejected by himself.

          Anyway, I appreciate your insight that pre-mathematical assumptions are decisive.

          Eckard

          Fischer never really countered my argument. He indeed said there was no motion, geodesic or otherwise (which is not quite right). He used a static equation of state to show that a collapsing body (not static) does not produce a singularity. It is trivially true, but this is not the case of a collapsing body so there can't be a singuarity.

          There is motion, even for a body at rest, for it is moving forwards in time. For a gravitating body in a static configuration matter is on a nongeodesic motion forwards in time.

          When I get the time I will read your essay.

          Cheers LC

          I am going to catalyze you in live.

          :) you know that I am not a fan of paradoxs.

          The meiosis of a sphere, interesting.or a mitosis.interesting :)

          immeasurable measures ??? Not really rational that.

          You know Lawrence, I find your knowledges very relevant, but you know the aim is not to enumerate the concepts but to apply them with a pure rational and dterministic road. In fact , when there are too much pseudo convergences, so it implies an ocean of confusions.Implying an impossibility to have a true general theory.

          In fact you know indeed your physics and maths.But is it sufficient for the generality. I am surprised to see how you interpret the boundaries ? You know Lawrence ,forget your chains ....and open your universal heart.

          The mind of a mathematicians is the same than for physics. They must be always rational and dterminsitic.

          ps you can make better :)

          ps2 the unitarity, the singularity,it is these central spheres, Lawrence.

          ps3 I have an idea for the serie,the fractal from the main cnetral sphere, in logic the serie is universal at all scales for the uniqueness. I ask me if the primes can help, I beleive that yes for the periodic oscillation.between 1 and x. The number of planets become relevant for our universal sphere.and we take the number 1 for the central sphere. The volumes are under this logic. The primes can help for the correct serie. It is essential to have finite groups and boundaries you know Lawrence for our quantization and our axiomatizations.If not the thermodynamics are not ok.like the proportions of our universal mecanic.

          It is evident you know.

          Regards and good luck, your essay is very well.

          Steve,

          I am not entirely sure what you are trying to say. Though I am sure you have some sense that it is deep and profound.

          Cheers LC