Dear Jochen,

thanks for your interest. I'm glad to see that you are interested in my work. The essay is more like a program which was partly realized.

Weizsäcker's view had a large impact on my work. I disagree that our space is a simple manifold like the 3-sphere. But Weizsäcker concentrated more on the time-like logic and the derivation of quantum mechanics. Anyone speaks about Wheeler but Weizsäcker was the first and he went further.

I'm looking forward to read your further comments.

Best

Torsten

Dear Torsten,

Excellent essay! In my opinion, your program, as described in the essay, is very much in the spirit of Wheeler's dream "it from bit", and of Weizsacker's ideas. I have a lot of questions, but I think I will get answers to many of them from your papers. I hope to make more time to go carefully through all of them in a couple of months or so.

Good luck!

Cristi Stoica

P.S. I just saw you commented on my essay right now! Not, this is what I call entanglement!

    Dear Cristi,

    thanks for your words. Of course you can ask the questions now. The cited papers are not easy reading.

    Good look fr your essay too!

    the entangled Torsten

    Hi Torsten,

    This is very nice to see you here. Excellent essay! In my 2011 FQXi essay I have used your publication (Torsten Asselmeyer-Maluga, Helge Rosé. On the geometrization of matter by exotic smoothness. arXiv:1006.2230v1) in references. That is very rare that academic entrant, as you, accepts physics as a manifestation of geometry. Even though barely all of physicists accept General Relativity they also accept a sudden jump from the big distance scale (GR) to the small one (QM) and the geometrization disappears. What about the distance scale invariance of the laws of physics? No one matters. It is explicitly showed in the ratings of essays.

    In my essay in Table 1 I have defined that the conformally flat spacetime is the Bit and the matter is the It emerging from the spacetime but the reverse way is also possible. The matter and space have the same root (ancestor, predecessor). As you see we generally agree. Differences are in technical details.

    In my opinion we need to find the one, universal, distance scale invariant metric, reducing to Einstein GR metric within Solar System distance scale and having ability to generate predictions. The first prediction of my (and also yours) concept is my spin experiment outcome. Then depending on the outcome we shall create the proper metric. The progress I have made since 2011 is that experiment.

    Best regards

      Hi,

      Thanks for the message on my page. I will have time to read some essays this weekend, and yours is at the top of the list.

      I wrote further on my blog page on exotic manifolds and its possible role in quantum gravity. You are right, as I remember, that there is a Godel-type result with result with respect to exotic R4s.

      Cheers LC

        Hi Torsten,

        OK, I've had a little time to read now, so I can perhaps try to add my two cents. First of all, I think your realization that diffeomorphism invariance implies that a continuous manifold in GR doesn't contain more information than some triangulation is something that deserves being shouted from the rooftops---I've always thought that continua are something of an ontological burden, and should be avoided if possible. (The argument, or rather side remark, I make on this in my essay is essentially due to Achim Kempf---maybe you're familiar with his approach.)

        I also was struck by the relationship you uncover between measurement and undecidability---this is another one of those ideas that keeps cropping up in unexpected places, and something I keep coming back to without, however, coming up with much of anything concrete (I've said a few things about this on the thread of Lawrence Crowell's essay). Perhaps the paper by Paterek et al., where they propose that outcomes of quantum experiments are random iff the proposition they encode is undecidable (from some set of axioms encoded in the preparation procedure), is of interest, but maybe it's a blind lead. Brukner has done some further work in this direction, and together with Zeilinger, has also professed views drawn very much from Weizsäcker.

        Regarding Weizsäcker, yes, I think many of his cosmological arguments look somewhat quaint from a modern perspective, especially all the 'large numbers'-stuff, so I wouldn't want to commit myself to a 3-sphere cosmos as well. But I believe the argument for the 3-dimensionality of space being related to the 3-dimensionality of the qubit state space is not without merit; recently, it's been put into a modern information-theoretic form by Müller and Masanes. Of course, I suppose that to you, the advantage of 4-d spacetime is that it gives you a lot of smoothness structures to play with! (Incidentally, with your argumentation regarding 'the spacetime is the Bit', I'm not sure you're that far from the Weizsäckerian picture, in particular when you're talking about Stern-Gerlach measurements.)

        Coming from the quantum side of things, I must confess that any attempt to 'geometrize the quantum' instead of quantizing geometry finds me a bit hesitant, but your argument regarding 'wild' embeddings as deformation-quantized versions of tame ones is nevertheless intriguing, I'll have to think about it for a bit. Maybe there's a sort of dual perspective thing here: you can start with the quantum, and get a 3(+1) dimensional spacetime out, or you start with the spacetime, and out pops the quantum (via a suitable embedding). That's probably a bit fanciful, but that way, everybody gets what they want...

        Anyway, I've got to go now, it was a joy reading your essay, and I hope you do well in the contest!

        Cheers,

        Jochen

        Dear Jacek,

        thanks for your interest.Shame over me, I do not know that you use the geometrization paper in your essay. Also I will read you rcurrent essay, it seems our work is closer related than expected. In particular I'M interested in your experiment.

        So, more later

        Torsten

        Copoied from my page:

        Hi Torsten,

        I remember reading an article back in the 1990s about how the classification of exotic R^4s was not enumerable, which had connections to Godel's theorem.

        The exotic R4 structure has its origin in the Casson handles as pointed out by Freeman. A thickened disk D^2 --- > D^2xR^2 can produce various structures, which by the self duality of four dimensions leads to these strange conclusions. In scanning your paper I see you invoke Casson handles. The number of such structures by h-cobordism turns out to be infinite, which as I say above, I remember this to be nonenumerable. This result was proven by one of the big mavens in this area, Atiyah, Freeman, Taubes, ... ?

        The one element of this is that the e8 Cartan matrix as the eigenvalued system for an E8 manifold, an exotic R4. It has been a while since I have studied these matters, but as I remember this tells us how to tie 3-manifolds in 7 dimensions in the Hopf fibration S^3 --- > S^7 --- > S^4. The dual to this structure are 4-manifolds. The 7 manifold this knotting is performed is in the heterotic S^7 --- > S^{15} ---- > S^8, and the e8 Cartan matrix gives the eigenvalues for the 7-space.

        The interesting thing about the E8 is that the 8-dimensional space is equivalent to the group in a lattice construction; the root-weight space is ~ the space itself. The E8 manifolds of Freeman are I think embedded in the set of possible 8-spaces. This suggests a duality between the smooth manifold in 4-dim and a discrete or noncommutative manifold in a quantum sense.

        Physically this seems evident from data obtained so far. Measurements of the dispersion of light from extremely distant sources invalidate a discrete structure to spacetime. This tells us that a measurement of spacetime structure by measurement of photons that traverse a large distance give no signature of grainy structure. Yet a lattice perspective of spacetime with the Grosset polytope and the 120-polytope of quaternions in 4-dim would suggest a noncommutative geometry. However, if the lattice is equivalent to the space, then this smooth structure is dual to a grainy picture of spacetime. This structure should emerge in an extremely high energy experiment that probes small regions, rather than testing across vast distances.

        Cheers LC

        Mr.聽Asselmeyer-Maluga,

        In your article you write "smooth spacetime contains only a discrete amount of information", are you refering for instance to quantum theory? In that case the gravitational wave is to be observed yet. If you mean every information, then please explain further.

          • [deleted]

          Hi Torsten,

          Your essay was excellent reading. I'm unfortunately not fluent in topology but have tried to explore similar ideas with a discrete background independent foundation. It's more like å gut feeling than anything else but I suspect that space-time is structure built with the bits, aka at least one level of complexity above raw bits. Is it room for that in your opinion?

          I try to explore these Ideas in my completely non mathematical essay. And think that it should be possible to deduce why we have a velocity limit, and from there why there's no space-time beyond the event horizon in black holes (which is not covered in the essay) Thinking about bits as the foundation can give rise to ideas on how entanglement works, alternative interpretation of what happens in the double-slit experiment. Even how physical laws arises.

          If you would take time to read it - and shoot it down if you like - I would be very happy because we have some similar ideas. (I would really like to get some feedback on some of the ideas there - trails of before the interesting ideas there. Probably because it's badly written)

          Anyways - excellent essay and best regards

          Kjetil

            I think I explained this phrase in the text below. But here is an extract: if spacetime is a continuous 4-manifold that one may think that it contains also a continuous amount of information. But as I discuss in the essay, it is not true. The reason is the demand of diffeomorphism invariance which reduces the amount of information to a countable set (which is in most cases finite).

            Of course this result has also an impact on quantum theory but I discuss this theory later.

            Best

            Torsten

            Lawrence,

            interesting ideas. I thought to wait with an answer until you read my essay.

            Freedman used the Cantor set to parametrize all Casson handles. I think you had thsi result in mind. The reference to Gödel's theorem is via the word problem, i.e. there is no algorithm to decide whether two finitely generated groups are isomorphic or not. The application of thsi result to 4-mnifolds is the following fact: every finitely generated group is the fundamental group of some 4-manifold.

            Yes your are right the E8 manifold is related to the exotic R^4. The appearance of the E8 (equal to the Cartan matrix of the E8 Lie group) is rather mystical. I know it came from the classifaction of quadratic forms but is there a deeper reason? I have to think about your ideas.

            Best

            Torsten

            Hi Kjetil,

            I agree that the direction of your essay is very similar to my essay. The universe contains a discrete amount of information but (as I discussed) it does not mean that the space or the spacetime is discrete (like space quanta).

            The idea that "We must also introduce an element of chance, or our system would be terrible static." is interesting. Dynamics and probability are connected that is in the spirit of Weizsäcker (but unfortunately he wrote nearly everything in german). I also agree that "The relation

            between space and matter is also interesting and one of the defining features of space.". I think this relation is much closer than we think.

            So, again many of your main ideas are close to my.

            Best

            Torsten

            I read the first few pages of your essay with some care. It is interesting that you discuss the issue of quantum measurement. This touches on the issue of contextuality in QM. The Kochen-Specker theorem proves there is not context in QM for any quantum measurement. The observer is free to choose the orientation of their SG apparatus, which means choosing a basis in the Hilbert space of the system. Since any basis is freely given by any unitary transformation there is no QM prescription for a basis of choice. General relativity has a similar concept with covariance, and gauge theory is also similar. The measurement problem boils down to how it is that a quantum system is reduced to a certain eigenvalue, and in addition how it is that the basis for that eigenvalue is "chosen." In a Bohr or Copenhagen context this seems to suggest there are operating rules of nature outside of the QM, call it "classicality," that perform this role. In an MWI context there is still some auxiliary postulate or physical axiom involved with how it is the world eigen-branches into the many worlds.

            This is not necessarily an act of consciousness. First off the splitting is perfectly random, and randomness may well have its fundamental meaning within quantum mechanics. The outcomes of measurements just updates a Bayesian prior on the nature of the world, and the information obtained is a measure of the Chaitan-Kolmogoroff entropy.

            A measurement involves the use of energy. The Stern-Gerlach experiment imposes a divergent magnetic field in order to split the spin of electrons according to a certain z-orientation or basis. Energy is a funny thing, because its conjugate variable is time. There is no time operator that acts on a basis |t> so that T|t> = t|t>. The problem of course is that there would exist a unitary operator U = e^{-iεT} that continuously evolves the energy ε and energy spectra could not be discrete nor can it be bounded below. In a related manner with Fourier transforms we do not have negative frequencies, or negative energy, and integrate Fourier sums of ωfrom [0,∞) which differs from the position and momentum variables that are integrated from (-∞, ∞). Also position and momentum have classical correspondence with Poisson brackets in classical mechanics, while energy and time do not. Quantum measurements seem to require both time and energy. Energy must be applied to define a basis, and the succession of measurements, say of p and then x is done in a tensed fashion, and of course gives a different result than a measurement of x and then p.

            I notice paper goes into the nature of time. The discussion appears similar to what you did last year. I will try to think about this, for time in general relativity is a really strange concept. The ADM approach to general relativity results only in the constraints NH = 0 and N_iH^i = 0. In a quantum setting with momentum metric variable π^{ij} = -iδ/δg_{ij} the Hamiltonian constraint results in the equation HΨ[g] = 0, which is related to the Schrodinger equation

            HΨ[g] = -i∂Ψ[g]/∂t

            But the time variation part is zero. In a general spacetime, say think of a spherical universe or an infinite open one with uniform distribution of mass-energy, there is no natural boundary from which one can integrate over a field to evaluate mass-energy inside; this would be a GR form of Gauss' law. I will have to ponder your ideas about time within this setting. If one is not able to define mass-energy, then correspondingly the definition of time is difficult as well.

            Cheers LC

            Hi Torsten,

            I really appreciate that you took your time to read and comment. And I must apologize that my question was too hung up in my own ideas, and I really have to go deeper into your line of thought. (Which probably means that I have to learn and understand topology - now I wonder how I can squeeze that in an already tight schedule... :) )

            A million thanks - on several levels

            Kjetil

            Hi Kjetil,

            no problem. I know that my essay is not easy-reading.

            I like your ideas, you ask the right questions.

            In case of any question, please write me.

            Best

            Torsten

            In my essay I followed Weizsäcker to consider QM and the quantum measurement togeter with the problem of time.

            The question is why one obtains [math]H\Psi=0[/math] (the Wheeler deWitt equation) for quantum gravity? The equation is stationary, no time. But a short look at the model uncovers: that is natural. I start with a global hyperbolic spacetime having always the form [math]\Sigma\times {\mathb R}[/math] and fulfilling strong causility. For every point at the Cauchy surfaces, I have a unique geodesics to future and to the past. I obtained the (borring) model of Parmenides block universe. In this universe there is no time in agreement with the Wheeler deWitt equation.

            A change of the foliation will also change the situation. And exotic smoothness gives a natural explaination for a change of the foliation

            But as I discuss in the essay, this special foliation (and exotic smoothness) gives also a model for a measurement. During the writing of the essay I obtained the interpretation.

            More later

            Torsten

            Torsten, I feel that I have learnt about an interesting new perspective from your essay. I did not really know what the fuss with smooth structures was about before. Now I understand it a little better.

            The idea that physics is derived from topology is an appealing one nut it depends on whether there is any non-trivial topological structure at small scales in space-time. I think physicists have gone to and fro with this idea. In the last few years I think that the boring flat topology has been winning out but with the new Susskind/Maldacena insight that entanglement is related to wormholes, we could see things swing back to non-trivial topologies. In that case the maths of smooth-structures should be a big topic of interest.

            My own approach is to start from an algebraic structure and try to derive geometry as emergent. In a sense it is the opposite of your approach, but the real meat is in the relationships between algebra and geometry and relationships go both ways.

              Dr. Asselmeyor-Maluga

              I am a self-taut (thinking makes me tense) realist. May I please make a comment about your essay? In my essay BITTERS, I contend that reality is unique, once.

              Writing about "bits" you stated "The sequence is an expression of the dynamics (of the timed motion of bits) and for a given position in the sequence we know the unique precursor and successor." (of)

              Respectfully, the only way we could suspect that the position of any precursor and successor bit placement was unique would be if the bit was unique. Each real bit is unique once and because each real bit is unique once, it cannot travel sequentially. It can only travel uniquely once. Only abstract bits can travel sequentially because they are not unique.

                Philip,

                thanks for your comment. The interesting point with exotic smoothness is that you don't need a complex topology. Also the boring flat R^4 carries exotic smoothness structures (uncountable infinite many). An exotic R^4 looks globally like a usual R^4 but at small scales it can be very complicated.

                I also used algebraic structures to understand topology/geometry. But I think it is very complicate to consider algebraic structures like groups by their own. Usually these objacts act on some other object, in most cases a space. You are right the relation goes both ways, see for instance Klein's Erlanger program. But maybe I have to read more about your work.