Dear Crowell,

Now let us call the most natural automaton simply "heredity" (or indeed any cycle, Carnot or whatever). Then the idea of entropy or 2nd law of thermodynamics is that each stage of evolution within an automaton path does in fact depreciate possibility of return to the initial state; so there must be a halt or "fatalism"

My question is: doesn't your undecidableness amount to what we already know as uncertainty? Such that above a cut-off (Heisenberg Cut?) there is higher probability of return to initial state (what we know as determinism) but below the cut (being what we know as the quantum scale) there is no probability of return to initial state i.e. the system is not well-behaved.

Now I put it to you that once you assume that a well-behavedness (or conversely "uncertainty") is simply put an automaton then it qualifies as the ALGORITHM or computer proper. This computer/algorithm is what I call simply THE OBSERVER (perhaps Wheeler's anticipation).

It is a response to your position that: "...a quantum field is propagating on spacetime,but where spacetime is the quantum field. This heuristically appears self-referential, and the physical ansatz is this nonlocality is an undecidable proposition of the above modal theory of causality."

By quantum theory, this state is rather at once a Godel "incompleteness" (the uncertainty) and yet a Peano (or Planck) "constant" (i.e. the conservation law).

My "observer" is in other words then the SUPERPOSITION proper.See What a Wavefunction is

So Wheeler's proposition does work! Pls see my essay and prove me wrong on this particular approach.

    I hesitate to call the Heisenberg uncertainty principle some derivative of Godel's theorem. However, my ansatz that this incompleteness rests with the associativity of fields is really just another form of the quantum uncertainty. There are limited ways of knowing what propositions about a mathematical system are undecidable, so my assumption here is not a form derivation of any sort. So my idea here is more of a physical assumption than a formal proof or derivation.

    The role of an observer is in some ways similar to a self-reference in mathematics. Godel's trick is to let a mathematical system contain predicates that act on their own Godel numbers as the subject. An observer is ultimately made of quantum particles and the act of a measurement has the appearance of being a sort of physical form of self-reference. Of course my paper is not about the measurement problem or the role of observers, but ultimately the universe is as it is so that observers can exist. This is a sort of strong form of the anthropic principle.

    As for fatalism, it is of course the case that the universe will end up as a pure de Sitter vacuum in a sort of heat death. This will be reached in around 10^{110} years. It will probably quantum decay from there over a far longer period of time into a Minkowki vacuum. That might sound like fatalism, just as saying that we are all going to die sounds fatalist. However, in the mean time a lot of different things can happen. In the sense of Plato's final cause the outcome might be in a sense fated, but what happens before then is not.

    Cheers LC

    Lawrence,

    There are two kinds of scientists, the kind which can perfectly build further on the theories one learned at school, and the kind which tries to find alternative interpretation of observations. However invaluable an education is, its disadvantage is that, since you've learned many theories describing phenomena, it is very hard to dream up a different approach which perhaps might solve some of the many fundamental contradictions and enigmas of present physics. Though it is very understandable that man came up with the big bang idea, I'm afraid that it actually is even a worse 'theory' than creationism which at least honestly, boldly states that the universe has been created by some outside intervention. As far as I am aware of, the universe either has been created by some outside interference (which is the position of both creationism and big bang cosmology), a possibility I reject or it creates itself. If so, then fundamental particles must be as much the cause, the source of forces as their effect, the product of their interactions, meaning that a force cannot be either attractive or repulsive, always, which is the mistaken belief string theory is based upon. String theory, like big bang cosmology don't solve anything but are part of the problem.

    Cheers AB

    6 days later

    Dear Lawrence

    Your quote from comment to Platan essay:

    "What do you think of algebraic curves over [0, 1, ∞] and the Langlands program?"

    By coincidence i used long time ago similar trick with pseudoscalar mesons.See my essay. I signify as 1 mass of proton and then observed what position would take place other pseudoscalar mesons.That i got phenomenon 18 degrees.

    Do you see some explanation?

    Yuri

      The number 18 is important in Jewish mysticism. I am not sure that has any bearing on what you are saying though.

      Is your number something similar to a Cabibbo angle or Weinberg angle?

      I'll take a look at your paper later today.

      Cheers LC

      It is not common with a Cabibbo angle or Weinberg angle

      Just put the values of mass on y=tanx plot, then exploring angles.

      Dear Laurence,

      (I copy the reply to your post on my page)

      Your post is very stimulating. I need time to look at this possibility of relating black-hole physics and entanglement, and non-associativity. On the other hand, I don't consider that entanglement is a primary category in non-local/contextual questions. It may be that conformal arguments adapted to Grothendieck's approach may approach the subject you are talking about. I should say that I am not familiar enough with black-hole physics to have a motivated opinion I intend to read and understand this Maldacena-Susskind paper before discussing more with you on this topic. Meanwhile, may be you can have a look at recent papers by Frédéric Holweck and co-authors (we are now working together) about entanglement and algebraic geometry.

      Thanks and best wishes,

      Michel

        Dear Lawrence, apologies if this does not apply to you. I have read and

        rated your essay and about 50 others. If you have not read, or did not

        rate "link:fqxi.org/community/forum/topic/1756] my essay The

        Cloud of Unknowing[/link] please consider doing so. With best wishes.

        Vladimir

        • [deleted]

        • Post #105

        The program of finding physics with [0, 1, ∞] can be found with the SL(2,C) group and the linear fractional transformation (LFT)

        f(z) = (az b)/(cz d),

        which has a correspondence with matrices of SL(2,C). The Mobius transformation or LFT is an automorphism group on the Argand plane, and this is equivalent to PSL(2,C). This projective linear group is then the automorphism group of C. If we let the constants a, b, c, d be points in C then the LFT

        f(z) = [(z - z_1)/(z - z_2)][z_3 - z_2)/(z_3 - z_1)]

        is for the identity f(z) = z a case where z_1 = 0, z_3 = 1, and z_2 = ∞. A matrix representation may be found by dividing through by z_i and taking the limit z_i --- > ∞.

        From this comparatively simple example we may move up to SL(2,H) and SL(2,O). In the case of SL(2,O) ~ SO(9,1), there is an embedding of SO(9) ~ B_4. This in turn is defined with the short exact sequence

        F_4: 1 --- > B_4 ---> F_{52/36} ---> OP^2 --- > 1

        where the strange symbol in the middle means that the 52 dimensions of F_4 - the 36 dimensions of B_4 ~ SO(9) defines the OP^2 projective Fano plane or OP^2 ~ F_4/B_4.

        The B_4 group is the SUSY group that Susskind employs with the holographic principle.

        The group F_4 is a centralizer in the E_8, which means it commutes with the automorphism of E_8, which is G_2. We then have a somewhat Rococo form of the same construction. A projective form of SL(2,O), PSL(2,O), defines matrices ~ aut(O) ~ G_2 which map three points to [0, 1, ∞] with the action of the 7 elements in the Moufang plane. I think I can find this matrix in the near future.

        Unfortunately I am moving shortly, so that is complicating plans to do much analysis. If I do this in the immediate future it will have to be in the next week.

        Cheers LC

        I read your essay sometime bzck. I have a list of these papers and which I have scored. I would probably have to reread or at least refresh myself about your paper. As I recall it is a bit of a metatheory.

        Cheers LC

        Lawrence

        Could you please explain where is your theory connected with Golden ratio?

        See part Symmetries... PSL(2,Z)etc

        http://en.wikipedia.org/wiki/Golden_ratio

        Yuri

          Lawrence,

          I loved your explanation of modal logic in causality. Very succinct! You brought back pleasant memories of doing symbolic logic in university.

          The notion that "causality is necessary incomplete" can also be appreciated from a quantum information point of view using a complex valued system. When an EPR state is prepared, all entropies are conditional on the observer, who is a subsystem in an "EPR-triplet". However, in making a measurement, the observer throws away her entanglement information so that the subsystem of the EPR pair is no longer conditional. (See my essay "A Complex Conjugate Bit and It".)

          A quantum correlated system thus becomes a classically correlated system. Using Venn diagrams, it becomes apparent that this process can be interpreted as a change in associativity.

          Best wishes,

          Richard

            Yuri,

            The polytope for the E8 grop, the Grosette polytope with 240 roots can be decomposed into the icosian of 120. The icosian or 120-cell has two quaternions with length (1/2)(1 +/- sqrt{5}) where the plus one has length 1.618..., which is the golden mean. In fact these quaternions define something called the golden field in a Galois ring. This is related to the Fibonacci sequence.

            Cheers LC

            Richard,

            Thanks for the kinds words. I agree that quantum measurements and even quantum teleportation involve the destruction of entanglement. Maybe better put the entanglement is transferred to a reservoir of states in an unpredictable manner. The entropy of the system is then indeed conditional, and a measurement loses this.

            I propose that the incompleteness has to do with associativity in QFT. My argument then involves the situation of fields near an event horizon. There is a profound difference between the classical case and the quantum case. I am not clear how this plays with standard quantum measurements. Zeh, as I recall, talks of a quantum horizon. Maybe there is some parallel situation there which makes associators play a role.

            I will try to read your essay soon. I am rather slowly getting around to as many as I can.

            Cheers LC

            Dear Lawrence

            Could you please find out explanation of symmetric angles picture between mass of proton and pseudoscalar mesons? This is simple parametrization proceeding.

            My essay

            http://fqxi.org/community/forum/topic/1818

              It could be due to some aspect of the eigenvalues for gluons in a supergroup. The icosian has quaternions (roots) that have magnitude given by φ. The icosian is in a sense half of the roots space of the E8 group. The masses of hadrons is determined by the quark masses, which is induced by the Higgs field, and by the confinement properties of the QCD gauge field, called gluons. The differences in these fields in the Y-B plane is given by certain roots, and those roots in some cases have the magnitude of the φ = (1 sqrt{5})/2

              That is about the best I can conjecture at this point. There might in some way be some semblance of reason for this.

              LC

              Hi Lawrence,

              I read your essay some time ago but only now got around to rating it -- was delayed in moving from ITB/Bandung to Thailand. In any case I very much liked the use of associators/non-associativity in your essay. Two FSU colleagues of mine (Merab Gogberashvili and Vladimir Dzhunshaliev) have worked on trying to include non-associativity into QFT. Merab in particular had some mantra about the connection of different algebras to physical quantities to the effect--> real numbers are connected with mass; complex numbers with charges; non-commutative numbers with spin; non-associative numbers with the quantum wave-function (actually I do not recall exactly what the last connection was but it was something to do with the quantum nature of matter). In any case you might find Merab's work of interest. Sorry it took so long to finally read your essay.

              Also I noticed your address (or one of them) is in Hungary. In this regard you might be interested in a conference Elias is arranging in Prague, Sept. 1 --5. It is a fairly large and broad conference but some of the workshops would seem related to your line of work. In any case the conference site is http://www.icmsquare.net/

              I hope this is not considered "advertising". Anyway if this post is not accepted we'll know :-).

              Best,

              Doug

                Doug,

                I have read several papers by Vladimir Dzhunshaliev on octonion field theory, and Merab Gogberashvili is a familiar name as well. Trying to understand how nonassociative mathematics of operators fits into physics is really the hard part. I think that quantum mechanics is purely complex, or C. Of course classical mechanics is R. Gauge theory can be written according to quaternions H. A lot of gauge theory is done though in standard vector form without quaternions. It is interesting though that Maxwell formulated electromagnetism, the first gauge field theory, in quaternions. Field operators in a second quantization act on a Fock space basis to give quantum amplitudes. So we have a relationship that might be heuristically written as π:H --- > C. The question is then whether there is some sort of higher level structure π:O --- > H.

                Spacetime I think offers a clue. A black hole horizon has some quantum uncertainty on a scale near the string or Planck length. There will then be an associative uncertainty with three quantum fields, where one of those fields is identified near the horizon. The standard approach to QFT is to assign a harmonic oscillator at every point in space, impose equal time commutators on that spatial surface with the Wightman criterion for commutation, and work from there. Yet that spatial surface on a small scale will have some noncommutative structure and this will lead to a host of uncertainties in assigning QFT operators. If there are event horizons this should lead to an associative uncertainty.

                The above "maps" between C, H and O, where a similar map π:C --- > R would be the relationship between quantum mechanics and classical mechanics, are really just forms of the Hopf fibration. The relationship between quantum and classical mechanics is of course a difficult subject in its own right. With each of these "ladders" on the Hopf fibration there is some increased uncertainty. Quantum mechanics saved physics from the UV divergence that classical mechanics predicted with the hydrogen atom. Similarly this may protect physics from divergences with black holes, such as the singularity and maybe with the current big problem of firewalls.

                Thanks for the good word. I had a computer crash (virus attack etc) that erased my voting code. I also had it written down on a paper that also went missing. I have not been able to vote on papers for about a week. The FQXi people have so far not serviced my request that it be retransmitted. I have also been a bit slow in reading papers this contest cycle. I see that you have a paper in the list. I seem to remember that last year your paper was riding fairly high, where mine in contrast tanked.

                Cheers LC

                Dear Lawrence,

                The title of your essay intrigued me because I think that Wheeler wanted us to recognise the same thing.

                I read your essay with much interest (I didn't need to understand the math, because the text was clear) and the conclusion that biology and EVEN consciousness will have to play a role is one that I took as essential inmy own contribution.

                After reading the essay it is always informative to read your reactions on the posts, which are very informative. Especially one reaction ( of may 20 02.42 GMT was in full correspondence with my own perception :

                "Any scheme for causality is going to be incomplete, it will not be able to encode ALL physical states. As a result it means that there exists a DEEPER FOUNDATION to the Universe" This incompleteness I am trying to describe in the infinite number of tones of grey between the digital entities zero and one.

                I really hope that can spare some time to read/comment and rate my essay : "THE QUEST FOR THE PRIMAL SEQUENCE" , I am sure you will find some thoughts we share together for a future approach of reality.

                respectfully

                Wilhelmus