Dear Torsten!

Excellent essay, and especially liked the conclusion: Time, among all concepts in the world of physics, puts up the greatest resistance to being dethroned from ideal continuum to the world of the discrete, of information, of bits. ... Of all obstacles to a thoroughly penetrating account of existence, none looms up more dismayingly than 'time.' Explain time? Not without explaining existence. Explain existence? Not without explaining time. To uncover the deep and hidden connection between time and existence ... is a task for the future. » Let's try together, physics and lyrics - the Universe is one ... Best regards, Vladimir

    Dear Torsten,

    I've had a quick look at your essay - nice approach. I'll read over more thoroughly before rating. I noticed the torus arises, which I've seen recently here http://www.labmanager.com/?articles.view/articleNo/35988/title/New--Simple-Theory-may-Explain-Dark-Matter/ related to dark matter via anapoles. Could this further your model?

    A unified field theory I'm working on has the Pi squared component, so perhaps our two models overlap.

    Anyway, best of luck with the contest. Hopefully you'll get chance to read, comment and rate my essay too.

    Best wishes

    Antony

      What you are arguing is that considering the CS Lagrangian, or counting degrees of freedom therein, and the Einstiein-Hilbert action and its DOFs in effect double counts. They are ultimately the same.

      The group of course in Lorentz setting is SO(2,1), which is the anyon system. I think in a graded system this leads naturally to supersymmetry or supergravity.

      As for scores, I thought about giving you an 8, which as I said is sort of the gold standard any more. I have some questions about what appears to be naked singularity implications. I don't think naked timelike singularities can exist in a classical setting. Check out Strominger et al and the relationship between solutions to the Einstein field equation and the Navier-Stokes equation. Naked singularities would correspond to a singular breakdown in the set of solutions to the NS equation. Of course naked singularities lead to other nettlesome matters of time loops and the rest.

      I am though trying to wrap my head around the prospect that for quantum black holes with an uncertain horizon that an observer has an uncertainty as to whether states measured are exterior or interior to the BH. Maybe for Kerr-Newman type solutions the timelike singularity inside the inner horizon then plays some sort of role in this case.

      I hope to write a more complete discussion on the knot polynomial, cobordism and the CS Lagrangian in the near future.

      Cheers LC

      Dear Vladimir,

      thanks for your interest. Wheeler expresses very well my own opinion.

      Time is the key to undrestand a lot.

      Best

      Torsten

      Dear Antony,

      I thought your essay was about Fibonacci numbers? I remembered on the phrase that "the whole world is contained in the number Pi but we miss only coding".

      All the b est for contest too.

      Torsten

      Hello Torsten,

      Yes my essay focuses on dimensionality around Black Holes following the Fibonacci sequence. This actually is a consequence of geometry utilised in my theory.

      I'd very much appreciate any comments you have on my essay. I agree that the whole world is contained in the number Pi, after all it is infinite, but has a real meaning to the Universe, so is by no means arbitrary.

      I've now read and rated your essay - I think you deserve to do very well - great work!

      Kind regards

      Antony

      Lawrence,

      maybe Im wrong but I considered naked singularities of another type then Strominger. My naked singularity is a saddle point which is characterized that there is a point where the geodesics meet. At this point there is no unique map betwenn the geodesics pointing to the singularity and geodesics pointing away. In particzular there is no sigular curvature.

      Otherwise I'm eager to hear your opninion to the knots.

      Torsten

      These type of singularities occur when the averaged weak energy condition (AWEC) T_{00} >= 0 is violated. A wormhole has this type of singularity associated with a Cauchy horizon. These types of singularities are less "damaging" in some ways. The geodesics that reach it are measure ε, comprising the select geodesics that define the inward separatices. However, the frequency of a photon on that path diverges and there is a UV divergence.

      A case of this is the extremal black hole. The two horizons r_{±} = m ± sqrt{m^2 - Q^2} merge at the extremal case. In the nonextremal case the inner horizon r_- is effectively the singularity, for inward geodesics have a UV divergence there. In the extremal case the singularity is "naked" in a sense, but it does not transmit information to the outside world. It is also a measure ε attractor for geodesic flows. In the case the BPS charge Q > m the black hole becomes spacelike and the AWEC is violated and it transmits information to the outside world. I don't think either the extremal or spacelike black hole conditions exist classically. Trying to spin a black hole up so that J = m is a GR version to trying to accelerate a mass to the speed of light.

      So this result with naked singularities has some big question marks. It could reflect some aspects of quantum mechanics. A near extremal quantum black hole has some quantum amplitude for being extremal or spacelike, just as a particle can instantly tunnel across a barrier. The result may then have some quantum physical interpretation.

      Cheers LC

      Dear Torsten,

      This is a tantalizing essay particularly after my reading of your last year writing. I like much the idea of using the diffeomorphism invariance as a way of classifying the 4-manifolds and their physical relevance.

      I have a few questions after my preliminary reading

      1)Are you aware of the attempt to see the visible universe as the Poincaré dodécahedral space (a 3-manifold) as reported for instance in http://arxiv.org/abs/math/0502566 ?

      2)I am puzzled by your sentence that 'given two fundamental groups we cannot decide whether these groups are isomorphic or not', where does it come from, you cite a paper by Markov in 1958! Is this related to the type of logic undecidability described by Lawrence B. Cromwell in this contest

      http://www.fqxi.org/community/forum/topic/1625 ?

      Michel

        Dear Sir,

        We never said that existence of space-time is due to information, but it is the interpretation of what you have written. In other words, it is the implication of your statement, which we have questioned by asking: "how can space-time 'contain information', which makes the existence of information dependent on space-time?" To this we had replied: "The only logical interpretation is, both exist independently, but inseparably linked as observable and result of observation - matter and its property." Do you disagree to this?

        Kindly read our essay published on May 31, 2013 before contradicting us or attributing wrong statements to us.

        Regards,

        basudeba

        Dear Michel,

        thanks for your interest. I will read you essay soon.

        Now to your questions:

        1) Yes I knew this model and had an email exchange with Luminet about it. In the last year, we (Jerzy and me) published a paper where we we showe that a Poincare sphere alone cannot describe the evolution but a sum of two can.

        2) Markov showed this result by reducing the problem to the word problem in group theory. Beginning with 4-manifolds, one can realize every finitely presented group as the fundamental group of a 4-manifold or higher. The word problem is the statement that there is no algorithm to decide wether two finitely presented groups are isomorphic. Lawrence argues with Gödel but the word problem is more connected with Turing/Church.

        Good luck for the contest!

        Best wishes

        Torsten

        Torsten,

        Fascinating essay. I've always questioned the role of topology as a valid description of nature, (actually I challenge ALL assumptions!) but you've now given me a far more rounded view of the subject. As primarily an astrophysicist I've always been struck by the ubiquitous toroidal forms of energy and collections of matter in the QV. (I explore it's quantum implication in terms of orbital angular momentum in my essay).

        I particularly find resonance with; "the measurement of a point without a detailed specfication of the whole measurement process is meaningless in GR." Indeed I describe and axiomise a detection and measurement process. also;

        "For two data sets of the spacetime, there is no algorithm to compare the two sets. The result of an experiment is undecidable." In astronomy the lack of a relativistic algorithm for inertial system (spatial frame) transitions, i.e. barycentric to ECI frame is analogous.

        and; "matter and interaction (as gauge theories) can be described as special submanifolds of the space where these submanifolds are determined by the smoothness structure of the spacetime."

        But what scale are you prescribing smoothness as opposed to 'granualarity', or quantization of energy? is 'granule' smoothness a valid topological concept?

        I hope you'll read and comment on mine. I'd hoped more suitable for the average Sci-Am reader, but I fear I may have crammed too much of the the ontological construction in again - so it takes careful reading!

        Very well done for yours. I found no reason not to give it a top score. Congratulations on now leading by the way! But you have some good competition.

        best wishes

        Peter

          Hi Torsten,

          How did you find the experiment? Did you have time to take a look?

          I am ready for a severe criticism.

          Best regards

          Hi Jacek,

          yes I read your paper about the experiment. But I don't understand why the two photons have the same spin. I understood the thought experiment (it is not far away from ym own ideas) but how is the experiment and the thought experiment related? I do not see the motivation.

          I know the standard theory (going back to Fresnel) but why is your experiment so important?

          Torsten

          Ok Torsten. The most likely my description is not clear enough and this is my fault so I treat it as an occasion to improve. I will try to clarify the real experiment and his relation to the thought one.

          In both experiments the point is that the photon is not a point particle (like in Standard Model) that is reflected from another point particle (one of many creating the mirror) but instead it travels around a "particle" (anyone being a part of the mirror) and comes back along a geodesic. The way it goes is a geodesic (acc. to my concept) because the mirror's particle deforms the spacetime much enough (or simply it is that deformation itself). If our photon goes along the geodesic (straight line!) it does not change its spin.

          Acc. to Standard Model the photon does not go around along a geodesic but it is simply reflected and as a cause of that reflection the spin is changed.

          So it is a realization of the thought experiment.

          I have proposed to use a photon and not e.g. an electron because the experiment is much easier to carry out by means of a polarization. The mirror is obviously not the same as a single particle deforming a spacetime (like in the thought experiment) but it is practical and relatively easy to use. The potential problem could be a photoelectric effect, Compton scattering or pair production.

          The outcome of the experiment can be contradictory to Standard Model. And we could forget the duality, wave function collapse and so on... That is a motivation.

          I am ready to clarify more if needed.

          Dear Torsten

          I have a feeling you want to conclude that : all of every jobs same are ....IS A TASK FOR THE FUTURE.

          http://fqxi.org/community/forum/topic/1802

            5 days later

            Dear Peter,

            thanks for your comment, I'm also sorry for the delay inanswering.

            I also like your point of view. It is not totally different to my approach. It contains a lot of geometric ideas, in particular the representation of the quantum state as helical wave. I also have helical states (but in the foliation).

            I rated your essay also very high but a longer time ago.

            Now to your question about granularity: There is an isomorphism between piecewise-linear and smooth 4-manifolds. Therefore the granularity is not important for the results. Of course there is a limit (lower bound) for the number of used cells to describe the 4-manifold but nothing more.

            Best wishes

            Torsten

            Dear Hoang,

            maybe I do not understand your sentence.

            I think the problem of time is an important problem for the future.

            Did you have this in mind?

            Best

            Torsten

            Dear Jacek,

            Now I understood your motivation. But unfortunately this experiment is already done with the standard result.

            You used the outcome of the experiment when you try to make a photo of an object behind a window. You need a polarisation filter for the photons which are reflected by the window. But by standard theory, these phtonos have a fixed polarization in agreement with the standard theory.

            Maybe I miss some point.

            Best

            Torsten

            Torsten,

            Really a wonderful entry, which I think very naturally connects the work you've been doing to the concept of discrete information. If I understand things correctly, you diverge from Wheeler's original idea of a "Bit" by using the handle decomposition of spacetime as a *set* of discrete data, rather than the binary YES/NO which Wheeler envisioned. I wonder if you consider this to be fundamental - can we not reduce this set down further to a set of binary questions? Can this be done in a unique way?

            Two additional sections I was particularly interested in. Emphasizing that there is not a unique algorithm to differentiate between two fundamental groups is an interesting choice - it suggests there is quite a bit more to talk about. In Wheeler's view I suppose this would mean that the fundamental group is not part of the fundamental apparatus?

            You also bring up a result which I was not familiar with, and that is the connection between sphere bundles and the gravitational interaction. It seems that maybe the geometric models you have been working with might provide a path to a proof of this?

            In any case, really great entry for the contest; clear, thought-provoking, and novel. I wish you the best of luck!

            Chris Duston