Michel,

I don't have as much time this morning to expand on this, so I will just make this rather brief for now. I will try to expand on this later today or tomorrow.

The three-qubit entanglement corresponds to a BPS black hole. The four qubit entanglement is the case of an extremal black hole. I think there is an underlying relationship between functions of the form (ψ|ψ) = F(ψψψ), an elliptic curve with the cubic form corresponding to the 3-qubit, and the "bounding" Jacobian curve that defines a quartic for G(ψψψψ). This I think is some sort of cohomology.

The G2 I think defines a frame bundle on the E8 which defines the F4 condition for 18 rays in the spacetime version of Kochen-Specker.

As I said I should have more time later to discuss this in greater depth.

Cheers LC

5 days later

Torsten,

I finally got a little bit of time to write more on what I had mused about a couple of weeks ago. This all seems to center in a way around a type of cobordism with respect to these replacements of handles or Casson handles. The replacement of a circle with a knot suggests a type of theory that involves Hopf links. The trefoil for instance is by the Jones polynomial such that a left - right trefoil equals a Hopf link.

The manifold constructed from the knot K is

M_k = ((M^3\D^2xS^1)xS^1)∪_T^3 ((S^3\(D^2xK))xS^1).

On the left the R^1 in M^4 = M^3xR is replaced by S^1, and we can think of the S^1 as a periodic cycle with a real number line as a covering. Think of a wheel rolling on the real number line, or a spiral covering of a circle. In this setting the crux of the matter involves replacing a circle S^1 with a knot K. Physically this avoids topologies with circular time or closed timelike loops such as the Godel universe. The S^1 to the right of each expression is the embedding "time cycle" and the three manifolds of interest are (M^3\D^2xS^1) and S^3\(D^2xK). In a thin sandwich, a narrow section of spacetime separated by two spatial surfaces, we may think of the bottom spatial surface or bread slice as (M^3\D^2xS^1) and the second one as S^3\(D^2xK). We might further be so bold as to say the bottom surface is a left handed trefoil and there is a superposition of two surfaces, one with a right handed trefoil and the other with two S^1s in a link. There is then a type of cobordism between the bottom slice of bread and the top, which in this case might be a map from (M^3\D^2xS^1) ∪_T^3 S^3\(D^2xLT), for LT = left refoil to (M^3\D^2xS^1★S^1)∪_T^3 S^3\(D^2xRT). There the star means linking.

This is a theory of topology change in spacetime, or of some underlying topological change in topology which still maintains an "overall smooth" structure. This is then a type of topological quantum field theory (TQFT). A TQFT just means a theory that is a quantum field theory up to homotopy. This is a way of looking at fields (eg the knots as Wilson loops of fields) according to the underlying space they exist on. This approach amounts to cutting up the space into pieces, examining the fields there and then looking at the entire ensemble (pieces up back). This then has an underlying locality to it this way. However, the connection between knot polynomials and quantum groups indicates there is also something nonlocal as well.

This conjecture means that TQFT assigns data to all possible geometric element to a space, from a 0-dim point to the full manifold in an n-dim cobordism. For a space of n-dimensions there is a functor F

F:bord_n^f --- > A

For A an algebra. The algebra is the generator of the group G = quantum group. Physically the algebra corresponds to the connection coefficients A which form the Wilson loops ∮A•dx = ∫∫∇•Ada (to express this according to basic physics). This is a sort of Grothendieck topos or category system, which relates a knot group with a cobordism. I conjecture that a complete understanding of this system is a TQFT.

I will write in greater detail later on this, for I have sketched out some of this. Physically (or philosophically if you will) the description of spacetime this way is I think equivalent to a description of TQFT in general. In fact one result of the AdS/CFT correspondence is that a 4-spacetime as the boundary of an AdS_5 is equivalent to 10-dim supergravity. The exotic structure of 4-dim manifolds may then be a manifestation of 10-dim supergravity.

I copied this on my essay blog site, so if you respond to this there I get an email alert.

Cheers LC

    Lawrence,

    thanks for the reply. Yes, I know TQFT like the Chern-Simons theory with Wilson lines leading to the knot polynomial.

    The Seiberg-Witten invariant for this exotic 4-manifold is the Alexcander polynomial, i.e. a knot polynomial but with a complicated TQFT. The Alexander polynomial is rather a classical then a quantum invariant.

    I will think about your ideas more carefully.

    Torsten

    Torsten,

    I have more of this sketched out. I wanted to write further today, but I got busy reviewing a paper. As for a classical invariant, check out Agung Budiyono's paper. It is the sort of idea of quantum mechanics that sends most quantum physicists screaming in horror. This is a stochastic approach to QM which along with the Bohm QM is weak, but these ideas I think can have their place.

    Cheers LC

    Dear

    Thank you for presenting your nice essay. I saw the abstract and will post my comments soon.

    So you can produce material from your thinking. . . .

    I am requesting you to go through my essay also. And I take this opportunity to say, to come to reality and base your arguments on experimental results.

    I failed mainly because I worked against the main stream. The main stream community people want magic from science instead of realty especially in the subject of cosmology. We all know well that cosmology is a subject where speculations rule.

    Hope to get your comments even directly to my mail ID also. . . .

    Best

    =snp

    snp.gupta@gmail.com

    http://vaksdynamicuniversemodel.blogspot.com/

    Pdf download:

    http://fqxi.org/community/forum/topic/essay-download/1607/__details/Gupta_Vak_FQXi_TABLE_REF_Fi.pdf

    Part of abstract:

    - -Material objects are more fundamental- - is being proposed in this paper; It is well known that there is no mental experiment, which produced material. . . Similarly creation of matter from empty space as required in Steady State theory or in Bigbang is another such problem in the Cosmological counterpart. . . . In this paper we will see about CMB, how it is generated from stars and Galaxies around us. And here we show that NO Microwave background radiation was detected till now after excluding radiation from Stars and Galaxies. . . .

    Some complements from FQXi community. . . . .

    A

    Anton Lorenz Vrba wrote on May. 4, 2013 @ 13:43 GMT

    ....... I do love your last two sentences - that is why I am coming back.

    Author Satyavarapu Naga Parameswara Gupta replied on May. 6, 2013 @ 09:24 GMT

    . . . . We should use our minds to down to earth realistic thinking. There is no point in wasting our brains in total imagination which are never realities. It is something like showing, mixing of cartoon characters with normal people in movies or people entering into Game-space in virtual reality games or Firing antimatter into a black hole!!!. It is sheer a madness of such concepts going on in many fields like science, mathematics, computer IT etc. . . .

    B.

    Francis V wrote on May. 11, 2013 @ 02:05 GMT

    Well-presented argument about the absence of any explosion for a relic frequency to occur and the detail on collection of temperature data......

    C

    Robert Bennett wrote on May. 14, 2013 @ 18:26 GMT

    "Material objects are more fundamental"..... in other words "IT from Bit" is true.

    Author Satyavarapu Naga Parameswara Gupta replied on May. 14, 2013 @ 22:53 GMT

    1. It is well known that there is no mental experiment, which produced material.

    2. John Wheeler did not produce material from information.

    3. Information describes material properties. But a mere description of material properties does not produce material.

    4. There are Gods, Wizards, and Magicians, allegedly produced material from nowhere. But will that be a scientific experiment?

    D

    Hoang cao Hai wrote on Jun. 16, 2013 @ 16:22 GMT

    It from bit - where are bit come from?

    Author Satyavarapu Naga Parameswara Gupta replied on Jun. 17, 2013 @ 06:10 GMT

    ....And your question is like asking, -- which is first? Egg or Hen?-- in other words Matter is first or Information is first? Is that so? In reality there is no way that Matter comes from information.

    Matter is another form of Energy. Matter cannot be created from nothing. Any type of vacuum cannot produce matter. Matter is another form of energy. Energy is having many forms: Mechanical, Electrical, Heat, Magnetic and so on..

    E

    Antony Ryan wrote on Jun. 23, 2013 @ 22:08 GMT

    .....Either way your abstract argument based empirical evidence is strong given that "a mere description of material properties does not produce material". While of course materials do give information.

    I think you deserve a place in the final based on this alone. Concise - simple - but undeniable.

      My mention of consciousness at the end, in connection with top-down physical or causal theories, was a bit conjectural. In a way I put that in there because I know a lot of people want to hear about consciousness and physics. Call it a bit of self-promotion.

      To be honest I don't know what role consciousness has with physcs or the universe. A lot of people think it is a quantum process. I don't know about that honestly. I think it could be argued that consciousness is the ultimate classical or macroscopic non-quantum system. Consciousness at least generates an epiphenonenon of wave function collapse.

      Cheers LC

      Dear S.Gupta,

      I will take a look at your paper soon. I have fallen behind in reading these papers because I have had to review or referee a paper for a journal. Thanks for the interest in my paper.

      Cheers LC

      This mathematics is involved with kissing numbers. The big sourcebook on this is Conway and SLoane, "Sphere Packing, Lattices and Codes." These spheres in the 4-dim case are connected to Planck units of volume. The packing system is the 24-cell or equivalently the F4 group.

      These systems are error correction codes. In the case of sporadic groups the quantum error correction is meromorphic which preserves quantum information. In the simple case there is no pole this recovers unitarity. In the study of this it is important to keep the connection to Jacobi theta functions. This also connects up with the Ramanujan Mock theta function and the partition function for the integers. This partition function is related to the density of states of a bosonic string as well as the thermal partition function of a black hole.

      There are deep relationships involved with this. My essay here is an attempt to lay down some physical arguments for this.

      Cheers LC

      Dear Lawrence,

      Congratulations on a well written essay dense with impressive references to many relevant issues raised by the fqxi contest question. The technical aspects of your discussion went over my head (and probably for many others here), particularly in the section about logic and in the applicability of the Incompleteness Theorem to the issues at hand.

      That said I could confidently say that I agree with several of your points: 1- The need for a 'philosophy' to approach questions of Reality in physics. 2- The undecidability of It/Bit 3- That a density matrix allows the expression of quantum states as qubits (which was my conclusion). In my Theory (see below) GR is reduced to a density gradient. 4- That "in theoretical physics there may exist assumptions that act as excess baggage that prevent workers from addressing fundamental problems" which was a major argument in my paper, although your saying it sounded much less presumptuous than when I did. Not only in this contest, but in my last year's "Fix Physics!" essay - since most of my ideas are qualitative. 5- The relevance of causality sets which in my Beautiful Universe Theory also found here are simply the Hamiltonians of qubit-like (spherical degree of freedom at every point) transfer of angular momentum locally, causally and linearly in a Universal lattice.

      On a personal note I visited Purdue around 1965 to visit my brother-in-law who did his PhD in physics there. One is wont to believe in a Flat Universe in that locale!

      With best wishes for your success

      Vladimir

        Hi Vladimir,

        Indiana is not just a case of a flat universe, but a flat Earth. It is in many ways socially backwards, and there were Ku Klux Klan rallies in the 1980s when I was there. That is rather embarrassing.

        The elimination of excess baggage is important. In my elementary demonstration with modal logic it means that certain physical axioms or postulates can be "turned off" in certain domains. It is similar to Godel's theorem, where certain propositions about a mathematical system are not provable and they can be toggled on or off to create different systems. Euclid's fifth axiom is of that nature and its on and off state define euclidean flat geometry and Riemannian geometry respectively. Your FQXi essay reads a bit like a narrative on this sort of thing.

        Cheers LC

        Darrell,

        Your essay does read as some narrative on a similar idea. You take the perspective of an alien. It will be extremely interesting if we should ever get radio contact from ETI to see how different they perceive the universe. The question is whether their mathematics and physics are in some ways mapped into ours, or if there is some isomorphism betewen their math and physics and ours.

        Cheers LC

        Hi Lawrence,

        I agree that ""It From Bit" is not decidable", or rather, that it is a question which belongs to what to me is an outdated paradigm.

        I have yet to read an essay which treats the question where all information comes from, how information becomes information. What I mean is this: If there would be only a single charged particle among uncharged particles in the universe, then it wouldn't be able to express its charge in interactions. As it in that case it cannot be charged itself, charge, or any property, for that matter, must be something which is shared by particles, something which only exists, is expressed and preserved within their interactions. If particles, particle properties (its) are both cause and effect of their interactions, of the exchange of bits, if particles only exist to each other if, to the extent and for as long as they interact, exchange information, then you cannot have one without the other nor can one be more fundamental than the other.

        If the information as embodied in particle properties and the associated rules of behavior a.k.a. laws of physics must be the product of a trial-and-error evolution, then information only can survive, become actual information when tested in practice, in interactions between its carriers, between actual, physical, material particles, whatever we may mean with 'material'.

        What strikes me in all the essays I've read (also of previous contests) is that everybody, without exception, thinks about the universe as an object which has particular properties as a whole and evolves in time, as something we may imagine to look at from the outside and can make statements about, as if it is a mechanism which, once winded up at the bang, after the bang only can unwind in a preordained fashion, as if there is a collection of platonic truths which exist outside the universe, as if there is an absolute, objectively observable reality at the origin of our observations we cannot perceive due to imperfect instruments and to the uncertainty principle.

        My point is that if a particle cannot exist, have properties if there's nothing outside of it to interact with, then the same must hold for the universe. The fallacy of Big Bang Cosmology (BBC) is that we can only speak about the properties and state of the universe if there's something outside of it, something it can interact with, and, like the charged particle its charge, something it owes its properties to: if it has been created by some outside intervention. For this reason BBC is an even worse 'theory' than creationism which at least honestly states that, yes, there is Someone outside of it Who created the universe. If a universe which creates itself out of nothing, without any outside intervention has to obey the conservation law which says that what comes out of nothing must add to nothing, then everything inside of it, including space and time somehow must cancel, add to nil, meaning that it has no physical reality as a whole, as 'seen' from the outside, but only exists as seen from within. If in that case it doesn't make sense to speak about the properties it has or the state it is in as a whole, then it also makes no sense to make such statements from within. In other words, we need a completely different approach, an entirely different paradigm if we ever are to comprehend the universe rationally, as opposed to causally, something I'm trying to do in blog, a study which, I'm afraid, is a bit of a mess.

        As I argued in a previous essay, this means that we can no longer conceive of the speed of light as the (finite) velocity light moves at, but that c just refers to a property of spacetime, which is something else entirely. (Though you agreed with my statement that we ought to "replace causality with reason ...to understand our world", I hope that you realize, accept that if causality goes out the window, then so does the interpretation of c as the (finite) velocity of light.) In regarding the universe as an object we can imagine to look at from without, a Big Bang Universe (BBU) lives in a time realm not of its own making: as it is the same cosmic time everywhere, here it takes a photon time to travel so here c does refer to the velocity light moves at. In contrast, a Self-Creating Universe (SCU) does not live in a time realm not of its own making: as it contains and produces all time within, here clocks are observed to run slower as they are more distant even if they are at rest relative to the observer. As in a SCU it is not the same time everywhere, here a space distance is a time distance so in this universe a photon bridges any spacetime distance in no time at all, in contrast to a BBU where the photon covers a space distance in (a finite) time. The difference is as subtle as it is crucial to comprehend our universe. Evidently, in a universe where the communication between particles over any spacetime distance is instantaneous, things like the double-slit experiment, the EPR paradox become obvious. The problem is that nobody seems to be able to escape the essentially religious narrative of BBC and start to try to understand the universe from within. Frankly, I'm appalled that everybody takes the word of the heroes of physics as a God's word instead of trying to see whether a different interpretation of observations might solve some of the most glaring contradictions of physics.

        Regards, Anton