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Torsten Asselmeyer-Maluga: on 8/9/13 at 9:02am UTC, wrote Dear Jonathan, thanks a lot for your words. Yes, finally I got it (with...

Jonathan Dickau: on 8/8/13 at 23:40pm UTC, wrote Glad you could make it Torsten, Your essay certainly deserves to win...

Torsten Asselmeyer-Maluga: on 8/7/13 at 19:43pm UTC, wrote Dear Michael, thanks for your rating and I do the same for you. very...

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Torsten Asselmeyer-Maluga: on 8/7/13 at 7:20am UTC, wrote Hi Yuri, I rated your interesting essay with a high rang. Best Torsten

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FQXi FORUM

May 31, 2020

CATEGORY: It From Bit or Bit From It? Essay Contest (2013) [back]
TOPIC: Spacetime weave - Bit as the connection between Its or the informational content of spacetime by Torsten Asselmeyer-Maluga [refresh]

Author Torsten Asselmeyer-Maluga wrote on Jun. 4, 2013 @ 15:40 GMT

Essay Abstract

In this essay I will discuss the relation between information and spacetime. First I demonstrate that because of diffeomorphism invariance a smooth spacetime contains only a discrete amount of information. Then I directly identify the spacetime as carrier of the Bit, and derive the matter (as It) from the spacetime to get a direct identification of Bit and It. But the picture is stationary up to now. Adding the dynamics is identical to introducing a time coordinate. Next I show that there are two ways to introduce time, the global time leading to quantum objects or the local time leading to a branched structure for the future (tree of the Casson handle). This model would have a tremendous impact on the measurement process. I discuss a model for the measurement of a quantum object with an explicit state reduction (collapse of the wave function) caused by gravitational interaction. Finally I discuss some applications of the model to explain inflation and the Higgs potential.

Author Bio

I'm a post-doc worker at the German Aerospace Center. I received my PhD at Humboldt university. My research interests are wide-spreaded from evolutionary algorithms and quantum computing to quantum gravity. Since more than 15 years I try to uncover the role of exotic smoothness in general relativity and quantum gravity.

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Edwin Eugene Klingman wrote on Jun. 5, 2013 @ 01:04 GMT

Dear Torsten,

I enjoyed your essay, although topology is not my strong suit. You speak of changes of state caused by an interaction in which it implies bit. I agree with this view.

You then analyze experiments in terms of closed curves in a manifold and ask whether the fundamental groups are isomorphic. You say there is no algorithm for a decision: "for two data sets of the space-time, there is no algorithm to compare the two sets. The result of an experiment is undecidable." In your Stern-Gerlach example, you point out that the knowledge of a measurement requires a coordinate system, and, if I understand you correctly, imply that the "set of space-time points therefore containing all information about coordinates, [and] in principle also all measurement results" imply that space-time is the bit.

I'm not sure how you envision "data sets". A primitive experiment can be based on counters generating numbers, and these numbers constitute the data. The question is what to do with the numbers, and how to 'model' reality with the set of numbers. I discuss the relevant algorithm for handling such data sets in my essay. I believe it might be relevant to your approach. I hope you find it interesting.

Although in reality the counter outputs tend to be correlated with the position of the counters in space-time, I believe this fact can be fully suppressed without changing the nature of the results. It's an interesting problem. I believe space-time can be abstracted away in favor of pure sets of numbers, although the result will be abstract 'features' that may only be meaningful when related to space-time.

Also interesting is that my model of the electron also leads to a torus, although I do not develop this in my essay. Perhaps all roads do lead to Rome.

There's another way in which our models seem to agree. You say "the choice of a global time produces a quantum state [...] but the choice of a local time structure gives a complicated partition of the space." I find the same result in my theory.

I like your alternative to the many worlds or branching space-time interpretation... although I suspect I am missing some of the fine points of your weave of saddle points.

I too focus on the fact that gravity couples to every kind of energy. You note this implies gravitation is energy exchange. I agree although I would perhaps see it as energy transformation. And the "formation" part of energy transformation is inherently coupled to the "formation" part of 'in'-formation, as I explain in my essay.

I will reread your essay for a better understanding.

Edwin Eugene Klingman

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Author Torsten Asselmeyer-Maluga replied on Jun. 5, 2013 @ 07:53 GMT

Dear Eugene,

I'm glad to see your essay which I have to read. I agree that the numbers (as results from experiments) should come together to give a view of our reality. This point of view is strongly related to interpretations and logic, i.e. more in the direction of topos theory. Jerzy (my coauthor) is an expert, I have to discuss it with him.

More after reading your essay

Torsten

Jochen Szangolies wrote on Jun. 5, 2013 @ 05:24 GMT

Dear Torsten,

very glad to see you enter this essay, I've been following your 'exotic smoothness'-approach for some time now (though I can't claim to ever have really sat down and worked through all the mathematical details). I'm also happy to see you dedicate your essay to Weizsäcker---I've already had a bit of a discussion with Phil Gibbs regarding his contributions, especially regarding its and bits (i.e. urs), and how they're somewhat sadly neglected these days. Looking forward to reading your essay, I'm sure I'll be back with further comments.

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Author Torsten Asselmeyer-Maluga replied on Jun. 5, 2013 @ 07:57 GMT

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

Jochen Szangolies replied on Jun. 5, 2013 @ 16:23 GMT

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

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Author Torsten Asselmeyer-Maluga replied on Jun. 13, 2013 @ 08:13 GMT

Jochen,

I'm deeply sorry for overlooking your answer in my essay thread.

In particular I have to read the refernces you gave. The whole subject is not easy reading, I know it. We (Carl and me) needed 7 years to write the book "Exotic smoothness and physics", in particular to present the topic as easy as possible.

The idea of the usage of wild embeddings as quantum states was born last year before the FQXi essay contest. I understand your problems with "geometrization of the quantum". It took me also a long time to accept it.

But let me clarify, my main interest is in the interplay between 3D and 4D. The introduction of smoothness structures is necessary if you consider the path integral in quantum gravity. You have to integrate over all exotic smoothness structures. It was folklore in the 90s that the man contribution came from the exotic part. But no one was able to proof it. For the exotic R^4 I'm not far away to proof it.

In my whole work I was driven by "naturalness". The next structure afetr the topology (before geometry) is the smoothness structure which is not unique in 4D. Therefore one must consider them.

I also enjoy reading your essay and I agree in most points. I'm also glad that you also like Weizsäcker (which is mostly forgotten in the physics community).

All the best for the contest

Torsten

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Cristinel Stoica wrote on Jun. 5, 2013 @ 08:15 GMT

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!

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Author Torsten Asselmeyer-Maluga replied on Jun. 5, 2013 @ 08:21 GMT

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

Jacek Safuta wrote on Jun. 5, 2013 @ 13:30 GMT

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

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Author Torsten Asselmeyer-Maluga replied on Jun. 5, 2013 @ 19:14 GMT

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

Jacek Safuta replied on Jun. 18, 2013 @ 09:44 GMT

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

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Author Torsten Asselmeyer-Maluga replied on Jun. 18, 2013 @ 13:29 GMT

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

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Jacek Safuta replied on Jun. 18, 2013 @ 15:15 GMT

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.

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Author Torsten Asselmeyer-Maluga replied on Jun. 24, 2013 @ 22:59 GMT

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

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Lawrence B Crowell wrote on Jun. 5, 2013 @ 15:47 GMT

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

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Lawrence B Crowell replied on Jun. 6, 2013 @ 01:39 GMT

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

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Author Torsten Asselmeyer-Maluga replied on Jun. 6, 2013 @ 12:03 GMT

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

Lawrence B Crowell replied on Jun. 6, 2013 @ 15:41 GMT

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

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Author Torsten Asselmeyer-Maluga replied on Jun. 7, 2013 @ 21:36 GMT

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

$H\Psi=0$

(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

$\Sigma\times {\mathb R}$

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

Lawrence B Crowell replied on Jun. 10, 2013 @ 15:52 GMT

Hi torsten,

I wrote a longer post on some of this. The Hamilton constraint or the Wheeler-DeWitt equation amounts to the problem that lapse functions or diffeomorphisms between spatial surfaces do not define time. I might be wrong, but I have thought this seems to be an aspect of the inability to define a coordinate atlas on 4-dim spaces that is diffeomorphic to all others. I expand on this in greater detail below.

Cheers LC

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Koorosh Shahdaei wrote on Jun. 6, 2013 @ 08:49 GMT

Mr. 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.

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Author Torsten Asselmeyer-Maluga replied on Jun. 6, 2013 @ 11:53 GMT

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

Anonymous wrote on Jun. 6, 2013 @ 09:01 GMT

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

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Author Torsten Asselmeyer-Maluga replied on Jun. 6, 2013 @ 12:14 GMT

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

Kjetil Hustveit replied on Jun. 6, 2013 @ 20:56 GMT

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

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Author Torsten Asselmeyer-Maluga replied on Jun. 7, 2013 @ 21:05 GMT

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

Philip Gibbs wrote on Jun. 8, 2013 @ 11:04 GMT

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.

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Author Torsten Asselmeyer-Maluga replied on Jun. 10, 2013 @ 08:26 GMT

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.

Joe Fisher wrote on Jun. 8, 2013 @ 17:13 GMT

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.

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Author Torsten Asselmeyer-Maluga replied on Jun. 10, 2013 @ 08:30 GMT

Mr. Fisher

Thanks for your helpful comment. Yes, you are right, for a sequence the bit must be real. In see the sequences more like sequences of measured results, i.e. I implicitly assume their existence. The ord 'bit' implies it, but I try to follow your approach and will read your essay soon.

Best

Torsten

Lawrence B Crowell wrote on Jun. 10, 2013 @ 15:28 GMT

I finally got to read your paper with a fair amount of care to detail. I have not scored it yet. I read a hard copy last night and was not on line.

The following comes to mind with this. Given the four manifold M^4 a subregion D^2xT^2 is removed and the complement or dual of D^2xKxS^1 in S^3xS^1 is surgically inserted. It is common to think of spacetime as M^4 = M^3xR. So the manifold...

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attachments: knotcorb.PNG

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Author Torsten Asselmeyer-Maluga replied on Jun. 11, 2013 @ 21:33 GMT

Lawrence,

these are great ideas. I also thought about knot cobordisms but not in connection with path integrals and knot polynomials. In the knot surgery above, one generates the infinite number (countable) of smoothness structures by the infinite number of knots.

I agree that the knot controls the amplitude for the transition.

Thanks for bringing to my attention. I have to further think about.

Best wishes

Torsten

Lawrence B Crowell replied on Jun. 12, 2013 @ 15:28 GMT

Unfortunately time is a bit narrow right now. I will try to expand on this in greater depth maybe this evening or tomorrow. Ed Witten sees a great foundation to the knot polynomial approach to path integrals. The occurrence of knot topology suggests a Chern-Simons type of theory, where there are underlying cocycle conditions for a L_{cs} = A/\dA + (1/3)A/\A/\A with a quantum interpretation.

Cheers LC

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Lawrence B Crowell replied on Jun. 13, 2013 @ 02:55 GMT

The role of the knot polynomial I think is involved with holography. The Lagrangian for spacetime

S = ∫sqrt(g)(R + L_m)dtd^3x + (1/8π)∮ρdS

Here the curvature ρ is evaluated on the null boundary of the spacetime. This is composed of the extrinsic curvature K_{μν} which is K = dP, for P a displacement on the surface, and in addition the CS term L_{cs}. This is a division of a cochain into a coboundary plus cocycle.

Physically the cocyle can be seen according to Lorentz transformations. Near the horizon as measured afar there is a Lorentz contraction of the radial direction. In the (M^3/KxS^1)xS^1 the contraction eliminates the spatial S^1 and this leaves the knot on the stretched horizon. This is a part of the quantum information on the horizon.

I have yet to assign scores. The problem is that some “trolls” have been assigning ones, and this has the effect of making a 5 in a sense the “new 10.” I would probably give your paper an 8 to 10, the 8 reflecting a bit of a problem I might have with something, but with the renormalized score I have been unsure what to do. I decided to give your paper a 7, which reflects a top or near top score with this unfortunate tendency for these “troll scores” that drop everyone’s score down.

Cheers LC

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Author Torsten Asselmeyer-Maluga replied on Jun. 13, 2013 @ 07:48 GMT

Lawrence,

at first thanks for the vote. I gave you an "8" long ago (for the same reasons you gave me an "7").

But now back to physics. Maybe there is an easier way to obtain the knot polynomials. Consider the Einstein-Hilbert-action for the knot cobordism. In particular near the boundary of the knot it looks like (Knot) x [0,1]. So you can made a ADM splitting to get the Einstein-Hilbert action of the 3dim boundary + boundary terms. But the 3D Einstein-Hilbert action is the Chern-Simons term (as shown by Witten) and from the boundary terms (afetr another splitting) you obtain the Wilson line. So one part of the path intergral over the knot cobordism is the knot polynomial, in particular the Kauffman polynomial (you have an SO(3) group for the Chern-Somons action).

I will be also interested in some of the problems I had with my essay.

Lawrence B Crowell replied on Jun. 13, 2013 @ 15:37 GMT

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

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Author Torsten Asselmeyer-Maluga replied on Jun. 13, 2013 @ 21:35 GMT

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

Lawrence B Crowell replied on Jun. 14, 2013 @ 03:44 GMT

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

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basudeba mishra wrote on Jun. 11, 2013 @ 02:50 GMT

Dear Sir,

How do you say that: “Information refers to an inherent property concerning the amount of uncertainty for a physical system.” Information can lead to decrease in uncertainty. But it cannot tell us about the degree or amount of uncertainty. Whether we can have “ALL” information about a system, is doubtful. You cannot apply Heisenberg’s principle to information.

Wheeler’s definition of “It” as “apparatus-elicited answers to yes-or-no questions, binary choices, bits” has to be read with “registering of equipment-evoked responses”. The binary unit, or bit, is a message representing one of two choices: 1 or 0 – on or off – yes or no. The ‘on’s are coded (written in programming language) with 1 and the ‘off’s with 0. By themselves 1 or 0 does not mean anything. Related to a context, 1 signals some concept representing information about materials objects exists in that context and 0 means it does not exist. Thus, except signaling the agreement or non-agreement with something predefined (i.e., a concept), binary has no other use. Thus, “It” stands for the information content or the concept about something, which is the “Bits”. Information is always about something, say, some material, but it not the material itself. There is no need to bring in several weird concepts to deny this simple truth.

The state is the direct expression of information, provided it is measured (perceived as such) by a conscious agent to collapse to a fixed state at a given time. Otherwise it may evolve in time independently on its own, but would be meaningless to the observer (superposition of all possible states). Hence “It implies the Bit” does not hold because “It” stands for the information content or concept of an object as distinct from the object proper - “Bits”. It may report the state of the quarks, leptons or bosons, but it is not the same as the quarks, leptons or bosons in that state. These two are distinctly different.

If “every ’it’ - every particle, every field of force, even the space-time continuum itself - derives its function, its meaning, its very existence entirely - even if in some contexts indirectly – from the apparatus-elicited answers to yes-or-no questions, binary choices, bits”, then the existence of space-time continuum itself should be derived from the “apparatus-elicited answers to yes-or-no questions, binary choices, bits”. In other words, the existence of space-time is due to information. Then how can space-time “contain information”, which makes the existence of information dependent on space-time? The only logical interpretation is, both exist independently, but inseparably linked as observable and result of observation – matter and its property. You also admit it in your conclusion No.1. In that case, the whole paragraph is redundant and amounts to name dropping only.

The rest of your essay follows a similar pattern. It would have been better to have presented a cogent analysis of real observables without aimlessly pulling in various directions and importing unrelated hypotheses to spread the cult of incomprehensibility.

Regards,

basudeba

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Author Torsten Asselmeyer-Maluga replied on Jun. 11, 2013 @ 22:08 GMT

Dear Sir,

thanks for the special instructions.

Information in this context refers to entropy. But what you wrote is not a contradiction to my intention.

I completely disagree with you to obtain spacetime from information. Information is conncetd with matter. We use the abstract concept of a state to express it. But it is our view of the world. We obtain information by measurements, I agree with you in this point. But this information is not connected to an observer. In particular the observer needs a coordinate system to expres the result.

In my essay, I discussed the relation between spacetime and matter. So if spacetime is matter then information as connected to matter should be also contained in spacetime. Nothing more, nothing less.

Torsten

basudeba mishra replied on Jun. 15, 2013 @ 10:44 GMT

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

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Vladimir Rogozhin wrote on Jun. 13, 2013 @ 10:45 GMT

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

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Author Torsten Asselmeyer-Maluga replied on Jun. 13, 2013 @ 19:32 GMT

Dear Vladimir,

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

Time is the key to undrestand a lot.

Best

Torsten

Antony Ryan wrote on Jun. 13, 2013 @ 13:19 GMT

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/tit
le/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

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Author Torsten Asselmeyer-Maluga replied on Jun. 13, 2013 @ 19:40 GMT

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

Antony Ryan wrote on Jun. 13, 2013 @ 19:53 GMT

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

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Michel Planat wrote on Jun. 14, 2013 @ 14:56 GMT

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

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Author Torsten Asselmeyer-Maluga replied on Jun. 15, 2013 @ 22:40 GMT

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

Peter Jackson wrote on Jun. 17, 2013 @ 16:19 GMT

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

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Author Torsten Asselmeyer-Maluga replied on Jun. 23, 2013 @ 14:58 GMT

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

Peter Jackson replied on Jul. 31, 2013 @ 13:30 GMT

Torsten,

Thanks for the elucidation. I need to get more up to date with sub manifolds as gauges, but find the 'simplest idea' to be a kinetic interaction with particles with structure, not the QM assumption breaching the Law of the Reducing Middle. Now applying points, and yours now done.

Best of luck

Peter

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Hoang cao Hai wrote on Jun. 18, 2013 @ 21:06 GMT

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

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Author Torsten Asselmeyer-Maluga replied on Jun. 24, 2013 @ 22:51 GMT

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

Christopher Duston wrote on Jun. 26, 2013 @ 15:20 GMT

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

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Anonymous replied on Jun. 26, 2013 @ 21:18 GMT

Chris,

thanks for the excellent question. In my opinion, every discrete information cane transformed into a sequence of yes/no question. But I think you are interested in the concrete example of a 4-manifold.

Has the handle (attached to the 4-ball) an index larger than 2?

Yes: it is a 3-handle

NO: Has it index 2? No: It is a 1-handle

Yes: Now I have to ask question about the attaching of the 2-handle, i.e. you have to ask about the knot. (For instance, use the braid representation of the knot and ask about the generators: Do you produce an overcrossing of the first two strands of the braid? etc.)

For the next handle start again with these questions.

The problem with the fundamental group is a little bit more puzzeling. You can do an experiment to determine the fundamental group. You can also describe this group by yes/no question but you cannot reproduce your experiment. So, the fundamental group is part of the apparatus but you cannot decide whether this group is isomorphic to the fundamental group of the second experiment.

Yes, I have a proof for the sphere bundle/graviton equivalence but it is not in good shape to present it. The main idea is the usage of a Cartan connection. Then one may ask what characterizes a (simple-connected) spin 4-manifold. Using Freedman: the Euler characteristics and the signature. Both invariants can be expressed as integrals over the Euler and Pontrjagin form, respectively.

Then using the sphere bundles and the Cartan connection one can change these invariants into the Einstein-Hilbert action (plus the cosmological constant) and into the other part of the Holst action (with Immirizi parameter).

As soon I will complete this construction you will get the paper.

Thanks for the wishes

Torsten

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Lawrence B Crowell wrote on Jun. 27, 2013 @ 00:35 GMT

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...

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Lawrence B Crowell replied on Jun. 28, 2013 @ 01:05 GMT

from my blog page:

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

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Author Torsten Asselmeyer-Maluga replied on Jun. 29, 2013 @ 22:05 GMT

Dear Lawrence,

I will be absent for the next three weeks with sporadic email check.

You can also write me to my email accout:

torsten.asselmeyer-maluga@dlr.de

I will answer you as soon as possible when I'm back.

All th best for you

Torsten

Hoang cao Hai wrote on Jun. 27, 2013 @ 04:25 GMT

Send to all of you

THE ADDITIONAL ARTICLES AND A SMALL TEST FOR MUTUAL BENEFIT

To change the atmosphere "abstract" of the competition and to demonstrate for the real preeminent possibility of the Absolute theory as well as to clarify the issues I mentioned in the essay and to avoid duplicate questions after receiving the opinion of you , I will add a reply to you :

1 . THE...

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Satyavarapu Naga Parameswara Gupta wrote on Jun. 28, 2013 @ 02:13 GMT

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...

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Author Torsten Asselmeyer-Maluga replied on Jun. 29, 2013 @ 21:50 GMT

Dear SNP,

interesting collection of experimental results. I agree that every theory must be based on experiments. Reeality is much more important.

All the best for you

Good luck for the contest

Torsten

Sreenath B N wrote on Jun. 29, 2013 @ 14:59 GMT

Dear Torsten,

I have down loaded your essay and soon post my comments on it. Meanwhile, please, go through my essay and post your comments.

Regards and good luck in the contest.

Sreenath BN.

http://fqxi.org/community/forum/topic/1827

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Author Torsten Asselmeyer-Maluga replied on Jun. 29, 2013 @ 21:01 GMT

Dear Sreenath,

interesting essay. In particular I like your multi-disciplinary view. I have only some comments:

- I think, that quantum mechanics do not imply that space and time is discrete. We don't know the curve of the electron but the space points can exist.

- Pure mathematics based on axioms but that is not as rigid as it sounds. In particular as shwon by Gödel, every axiom system (expressing or encoding information in a specific manner) is incomplete. It left open a lot of flessibility to change math.

Hopefully more later

I will be absent for the next three weeks

Good luck and all the best

Torsten

James Lee Hoover wrote on Jul. 3, 2013 @ 18:02 GMT

Torsten,

If given the time and the wits to evaluate over 120 more entries, I have a month to try. My seemingly whimsical title, “It’s good to be the king,” is serious about our subject.

Jim

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Sreenath B N wrote on Jul. 11, 2013 @ 09:39 GMT

Dear Torsten,

You have tried a novel geometric approach to solve the problem existing between space, time and matter by identifying space-time first with Bit, then with It (that is matter); hence you could write space-time = Bit = It = matter. But how far this could be true when you say that space-time is a ‘smooth’ four dimensional manifold and out of which you can construct a ‘discrete’ manifold in order to identify it with the Bit? In other words, how do you ‘quantize’ smooth space-time in to a Bit?

Secondly, how do you link the collapse of the wave function to the gravitational interaction? Is it sheer imagination?

Wish you best of luck in the essay contest.

Sreenath

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Author Torsten Asselmeyer-Maluga replied on Jul. 29, 2013 @ 14:32 GMT

Dear Sreenath,

sorry for the long gap in answering your question (I was on vacation with my family).

Spacetime can be a bit, because the information contained in the spacetime is discrete.It has nothing to do with the quantization of the spacetime itself. So, there is no fundamental length etc. But diffeomorpism invariance enforces us to consider only discrete information. I agree with that it is maybe a kind of quantization of the spacetime.

The link between gravitation and measurement is a conjecture (originally from Penrose). I considered a model for the measurement process. Finally I got a reduction of the wave function from a geometric process (adding a sphere bundle). Now I had to think about these geometric objects. In a previous paper I showed that torus bundles are related to gauge interactions. So, what is a sphere bundle? From the symmetry point of view, I found only one conclusion: it must be a graviton. Currently I work on a real derivation of this result.

Thanks

Torsten

Héctor Daniel Gianni wrote on Jul. 13, 2013 @ 19:28 GMT

DearTorsten Asselmeyer-Maluga:

I am an old physician that does not know nothing of mathematics and almost nothing of physics. Why I am writing you?, because I think I can hel in some ways in “space-time” with the experimental meaning of “time” I send you a summary so you can decide in reading or not my essay “The deep nature of reality”

I am convince you would be interested in reading it. ( most people don’t understand it, and is not just because of my bad English) “Hawking, A brief history of time” where he said , “Which is the nature of time?” yes he don’t know what time is, and also continue saying…………Some day this answer could seem to us “obvious”, as much than that the earth rotate around the sun…..” In fact the answer is “obvious”, but how he could say that, if he didn’t know what’s time? In fact he is predicting that is going to be an answer, and that this one will be “obvious”, I think that with this adjective, he is implying simple and easy to understand. Maybe he felt it and couldn’t explain it with words. We have anthropologic proves that man measure “time” since more than 30.000 years ago, much, much later came science, mathematics and physics that learn to measure “time” from primitive men, adopted the idea and the systems of measurement, but also acquired the incognita of the experimental “time” meaning. Out of common use physics is the science that needs and use more the measurement of what everybody calls “time” and the discipline came to believe it as their own. I always said that to understand the “time” experimental meaning there is not need to know mathematics or physics, as the “time” creators and users didn’t. Instead of my opinion I would give Einstein’s “Ideas and Opinions” pg. 354 “Space, time, and event, are free creations of human intelligence, tools of thought” he use to call them pre-scientific concepts from which mankind forgot its meanings, he never wrote a whole page about “time” he also use to evade the use of the word, in general relativity when he refer how gravitational force and speed affect “time”, he does not use the word “time” instead he would say, speed and gravitational force slows clock movement or “motion”, instead of saying that slows “time”. FQXi member Andreas Albrecht said that. When asked the question, "What is time?", Einstein gave a pragmatic response: "Time," he said, "is what clocks measure and nothing more." He knew that “time” was a man creation, but he didn’t know what man is measuring with the clock.

I insist, that for “measuring motion” we should always and only use a unique: “constant” or “uniform” “motion” to measure “no constant motions” “which integrates and form part of every change and transformation in every physical thing. Why? because is the only kind of “motion” whose characteristics allow it, to be divided in equal parts as Egyptians and Sumerians did it, giving born to “motion fractions”, which I call “motion units” as hours, minutes and seconds. “Motion” which is the real thing, was always hide behind time, and covert by its shadow, it was hide in front everybody eyes, during at least two millenniums at hand of almost everybody. Which is the difference in physics between using the so-called time or using “motion”?, time just has been used to measure the “duration” of different phenomena, why only for that? Because it was impossible for physicists to relate a mysterious time with the rest of the physical elements of known characteristics, without knowing what time is and which its physical characteristics were. On the other hand “motion” is not something mysterious, it is a quality or physical property of all things, and can be related with all of them, this is a huge difference especially for theoretical physics I believe. I as a physician with this find I was able to do quite a few things. I imagine a physicist with this can make marvelous things.

With my best whishes

Héctor

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Author Torsten Asselmeyer-Maluga replied on Jul. 29, 2013 @ 14:41 GMT

Dear Héctor

sorry for the long gap in answering your question (I was on vacation with my family).

I agree with you that time is connected with dynamics (something changed) and the time of the clock is man-made. But we have to understand how dynamics works and then we also understand:"what is time". As I argue, time is an order element to obtain a place in the sequence of measurement results.

I will read your essay soon.

Best wishes

Torsten

Hugh Matlock wrote on Jul. 16, 2013 @ 18:42 GMT

Hi Torsten,

Thanks for a very informative essay.

I agree with you on the important role that S3 can play in cosmology, and have developed a model using compactified Minkowski space S3xU1 for dynamics. In my Software Cosmos essay the overall picture is the simulation paradigm, and I show how using S3 can address several observational puzzles in cosmology.

Perhaps my model has some usefulness to your research; in any case I would love to hear what you think of it.

Hugh

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Author Torsten Asselmeyer-Maluga replied on Jul. 29, 2013 @ 15:06 GMT

Hi Hugh,

sorry for the long gap in answering your question (I was on vacation with my family).

I will read your essay soon.

Torsten

adel sadeq wrote on Jul. 21, 2013 @ 04:56 GMT

Hi Torsten,

The main reason for joining this contest was not to win, but to see if I can get any professional physicist with interest in foundational issues, to evaluate my idea. I appreciate any criticism no matter how harsh, although I do prefer constructive ones. I have rated you fairly high ( I follow up on your work regularly), but as I said I don’t care for rating mine, but that is your prerogative. I will also ask you some basic questions about your theory a bit later.

Many thanks

Adel

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Author Torsten Asselmeyer-Maluga replied on Jul. 29, 2013 @ 15:04 GMT

Dear Adel,

sorry for the long gap in answering your question (I was on vacation with my family).

see on your page fro me comment.

Torsten

Paul Borrill wrote on Jul. 23, 2013 @ 01:17 GMT

Nice Paper. Worth reading again.

I liked the introduction to Von Weizsacker. I wish I could read this reference in English.

Similar conclusion to Lawrence Crowell’s paper --> undecidable.

Interesting ideas. I’m not sure if I agree with them, but worth thinking about:

- because of diffeomorphism invariance, spacetime itself is the Bit.

- gravitation enforces the state reduction after a measurement.

I agree, time is the big issue. Wheeler identified this long ago, and the standard quantum formalism in Hilbert space contains hidden assumptions regarding a background for time.

Is this a task for the future? I think other papers in this contest (and previous ones going back to 2008) are likely to have already made major headway on this task.

Overall, the paper covers too much ground. Everything from information theory to Higgs. I suspect the author would have done better to focus and be clear on one or two concepts, instead of so many.

I still enjoyed it very much, and will read other works from this author.

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Author Torsten Asselmeyer-Maluga replied on Jul. 29, 2013 @ 15:11 GMT

Dear Paul,

thanks for your interest. I remembered that in the essay contest last year I was critized that there is no greater view and I'm to restrictive.

But I will take your critique more serious. Yes, the matter is very abstract but I hope to make clear that the subject is interesting and should be considered.

Best

Torsten

Than Tin wrote on Jul. 24, 2013 @ 23:27 GMT

Dr. Torsten

Richard Feynman in his Nobel Acceptance Speech (http://www.nobelprize.org/nobel_prizes/physics/laureates/19
65/feynman-lecture.html)

said: “It always seems odd to me that the fundamental laws of physics, when discovered, can appear in so many different forms that are not apparently identical at first, but with a little mathematical fiddling you can show the relationship. And example of this is the Schrodinger equation and the Heisenberg formulation of quantum mechanics. I don’t know why that is – it remains a mystery, but it was something I learned from experience. There is always another way to say the same thing that doesn’t look at all like the way you said it before. I don’t know what the reason for this is. I think it is somehow a representation of the simplicity of nature.”

I too believe in the simplicity of nature, and I am glad that Richard Feynman, a Nobel-winning famous physicist, also believe in the same thing I do, but I had come to my belief long before I knew about that particular statement.

The belief that “Nature is simple” is however being expressed differently in my essay “Analogical Engine” linked to http://fqxi.org/community/forum/topic/1865 .

Specifically though, I said “Planck constant is the Mother of All Dualities” and I put it schematically as: wave-particle ~ quantum-classical ~ gene-protein ~ analogy- reasoning ~ linear-nonlinear ~ connected-notconnected ~ computable-notcomputable ~ mind-body ~ Bit-It ~ variation-selection ~ freedom-determinism … and so on.

Taken two at a time, it can be read as “what quantum is to classical” is similar to (~) “what wave is to particle.” You can choose any two from among the multitudes that can be found in our discourses.

I could have put Schrodinger wave ontology-Heisenberg particle ontology duality in the list had it comes to my mind!

Since “Nature is Analogical”, we are free to probe nature in so many different ways. And you have touched some corners of it.

With regards,

Than Tin

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Author Torsten Asselmeyer-Maluga replied on Jul. 29, 2013 @ 15:15 GMT

Dear Than,

interesting idea. But did you really think, that Plancks constant (as the main constant of quantum mechanics) is the reason for all dualities? I agree that Bohr considered its complementary principle (which is roughly your first two dualities).

I like the cite of Feynman, but I think he has in mind: simple but complicated enough.

Best wishes

Torsten

PS: sorry for the long gap in answering your question (I was on vacation with my family).

Ram Gopal Vishwakarma wrote on Jul. 27, 2013 @ 23:10 GMT

Dear Torsten,

I was informed about your interesting idea of `the geometrization of matter’ by one of the participants. I have, in fact, also used this concept in my essay which may interest you. It has been shown there that the matter fields (as well as the gravitational fields) are represented by the metric field of the so-called `vacuum’ Einstein field equations and the energy-stress tensor is a redundant part of Einstein’s theory.

You claim that spacetime is the Bit. What about matter in the new perspective?

Best Regards.

___Ram

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Author Torsten Asselmeyer-Maluga replied on Jul. 29, 2013 @ 15:18 GMT

Dear Ram,

sorry for the long gap in answering your question (I was on vacation with my family).

According to my ideas, matter is also part of the spacetime (a part of the 3-space). So verything is unified: spacetime and matter, Bit and It.

Best

Torsten

Anonymous wrote on Jul. 30, 2013 @ 08:38 GMT

Hi Torsten,

( a copy from my thread)

Thank you for evaluating my essay, we have had some exchange in physicsforums about your theory before. You asked very good questions.

The answer to the higher modes is easy, yes it can be done (and I have actually done it). It is an automatic consequence of schrodinger equation result. As a matter of fact I get the 1/r law...

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adel sadeq replied on Jul. 30, 2013 @ 08:54 GMT

Torsten,

That post was mine. also let me ask you this as a mathematician. In my system theoretically I must throw infinite numbers of lines, and if you take a very small region it will contain dense almost infinite numbers of points. Does that constitute a a true continuum or it is still discrete no mutter how many points there are?

Thanks

Adel

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Author Torsten Asselmeyer-Maluga replied on Jul. 30, 2013 @ 14:37 GMT

Adel,

at first to your question: a line is continuous i.e. it has a continuous number of points. It doesnt't matter how long the line is.

You need an uncountable number of points to form a line nothing less.

More later

Torsten

adel sadeq replied on Jul. 31, 2013 @ 01:39 GMT

Torsten,

Thanks for your reply. Of course the line segment has uncountable points, that's elementary. But My question was (more clearly) that if I pick infinite random points on a that line uniformly, would I cover all the points on the line? My guess is that it will not since you have irrationals and maybe some other problems. Is that correct? I hate to make this a forum, I won't feel bad if you don't answer.

Thanks

Adel

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Akinbo Ojo wrote on Jul. 30, 2013 @ 17:12 GMT

Dear Torsten,

Seems I am reading some of the best essays last! Very nice entry.

Your arguments are quite sound from basic physical principles and GR viewpoint.

My own arguments are more from a philosophical perspective and not as quantitatively argued but I think there are still similarities in our picture. Like you I agree time will bring out the discreteness in continuous space picture, if that is what you mean by foliation. I also discuss a linkage between Time and Existence at a discrete level, although from a philosophical view not from that of a physicist.

I very much agree with your plan to derive matter from the space, i.e. the geometrization of matter. This should be one of the next goals of physics. I myself have started thinking along this line.

Following additional insights gained from interacting with FQXi community members on my essay, I posted on my blog the judgement in the case of Atomistic Enterprises Inc. vs. Plato & Ors delivered on Jul. 28, 2013 @ 11:39 GMT.

A deserving above the average score!

Best regards,

Akinbo

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Author Torsten Asselmeyer-Maluga replied on Jul. 31, 2013 @ 09:20 GMT

Dear Akinbo,

thanks for your words. Yes my intention is to uncover the geometric origin of matter. In particular, I try to obtain it from simple assumptions like the use of exotic smoothness structures.

Unfortunately, I had only time to skim over your essay. There are parallels to my view and I'm glad that you notice it. I have to read it more carefully because it is more philosphically.

Best wishes

Torsten

Michel Planat wrote on Jul. 31, 2013 @ 10:13 GMT

Dear Torsten,

I thought to have rated (highly) your paper at the time I red it. But my mark seems to have been lost, may be when the system was interrupted.

Did you have a chance to read my own essay? Any way I will give you the rate I had in mind and possibly more because I learned during this contest.

Best wishes,

Michel

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Author Torsten Asselmeyer-Maluga replied on Jul. 31, 2013 @ 12:54 GMT

Dear Michel,

yes, I read your essay but was on the vacation before I had the chance to write you. I like your geometric model very much (I rated your essay long ago with maximum score).

Now after a second reading I have some questions:

- You used the dessin d'enfants to visualize the contextuality. I understood the Mermin square but how did I see it in dessin d'enfant (Fig. 3b). Is it the number of half-edges (odd number) which produces the contradiction?

- Why is the transitive action so important? In case of a non-trivial orbit, you can check every point seperately.

One remark about the triple 0,1,infty: In the projective geometry, you always have the invariance w.r.t. the inversion operation. In the context of your model it means you have the operator and its inverse operator. Then 0 is related to infty and 1 is related to itself via inversion.

Thanks in advance for the answers.

Torsten

Michel Planat wrote on Jul. 31, 2013 @ 14:17 GMT

Dear Torsten,

Thanks for your careful reading.

1) It is not straight to see the contradiction in the dessin of Fig. 3b, I failed to see it in general (for other contexts). Also there is not a single dessin leading to Mermin's square but many, why is it so? More work is necessary. This non-bijection is general for most geometries I have tried to reconstruct from the n-simplices to projective configurations such as Desargues, Cremona-Richmund (i.e. the doily W(2) of two-qubit commutatitivity) and others.

2) You are right that transitive action may not be a necessary condition. The geometry is constructed by having recourse to the stabilizer of each point in the permutation group relevant to the dessin.

3) Last remark, the geometry is of the projective type not the dessin. Here you have to refer to the theory that is well explained, for example in Lando and Zvonkin (my ref. [6]).

Torsten, please check that you vote was recorded.

Michel

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Author Torsten Asselmeyer-Maluga replied on Aug. 1, 2013 @ 08:13 GMT

Dear Michel,

I voted for you a longer time ago (Mid June) and it must be recorded because I'm unable to vote again.

But I had the same problem: many unfair votes.....

Best Torsten

Michel Planat replied on Aug. 1, 2013 @ 13:56 GMT

Dear Torsten,

I am trying to better understand your deep essay but it turns out to be quite difficult accounting for my poor knowledge of differential geometry.

I have a naive question. The (first) Hopf fibration S^3 can be seen as the sphere bundle over the Riemann sphere S^2 with fiber S^1. Could you explain what is the sphere bundle S^2 x [0,1] that you associate to the gravitational interaction? May it be considered as some sort of lift from dessins d'enfants on S^2 to S^2 x S^0, and the latter object lives in circles on S^3, right?

I have in mind Matlock's essay as well.

All the best,

Michel

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Author Torsten Asselmeyer-Maluga replied on Aug. 6, 2013 @ 12:13 GMT

Dear Michel,

the Hopf fibration is a non-trivial bundle but I had a trivial bundle in mind. So it is the simple cross product S^2x[0,1] but with a non-trivial foliation.

But it has some parallels to Matlock's construction in his essay.

All the best

Torsten

Sreenath B N wrote on Aug. 5, 2013 @ 17:21 GMT

Dear Torsten,

I haven't yet rated your essay and I want to know whether you have rated mine. If so/not, feel free to inform me at, bnsreenath@yahoo.co.in

Best,

Sreenath

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eAmazigh M. HANNOU wrote on Aug. 5, 2013 @ 23:08 GMT

Dear torsten,

We are at the end of this essay contest.

In conclusion, at the question to know if Information is more fundamental than Matter, there is a good reason to answer that Matter is made of an amazing mixture of eInfo and eEnergy, at the same time.

Matter is thus eInfo made with eEnergy rather than answer it is made with eEnergy and eInfo ; because eInfo is eEnergy, and the one does not go without the other one.

eEnergy and eInfo are the two basic Principles of the eUniverse. Nothing can exist if it is not eEnergy, and any object is eInfo, and therefore eEnergy.

And consequently our eReality is eInfo made with eEnergy. And the final verdict is : eReality is virtual, and virtuality is our fundamental eReality.

Good luck to the winners,

And see you soon, with good news on this topic, and the Theory of Everything.

Amazigh H.

I rated your essay.

Please visit My essay.

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Author Torsten Asselmeyer-Maluga replied on Aug. 6, 2013 @ 11:57 GMT

Dear Amazigh,

interesting essay. I agree that duality is important and for me it is a cornerstone in philosophy too.

Thats the reason why I rated you rather high.

Best

Torsten

Daryl Janzen wrote on Aug. 6, 2013 @ 20:06 GMT

Dear Torsten,

Thanks for drawing my attention to your essay. You're right that I'm interested in a geometrical explanation of accelerated expansion, and I'm glad that you picked this up from my comment on Sean Gryb's essay, and that it drew your attention to my essay. I see that we have some common interests, and will therefore read your essay with interest. In the meantime, I thought I'd direct you to the discussion thread I opened up on Ken Wharton's page (near yours at the top), because that pretty much outlines how I think a geometric description of the observed expansion rate should be handled.

Anyway, thanks for reading my essay. I'll comment again when I've read and rated yours. I hope you do rate mine as well before tomorrow night (since you've said you found it interesting ;)).

All the best,

Daryl

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Daryl Janzen replied on Aug. 6, 2013 @ 22:23 GMT

Dear Torsten,

I found your essay intriguing in many ways, yet highly technical (unfortunately, I think beyond the scope of this contest in that respect). I was also puzzled why, when you've already assumed a model that is spatially homogeneous and isotropic, you would be interested in recovering inflation? It doesn't seem to fit.

But those two things aside, you have some very interesting results, and I see a lot of overlap with what I'm thinking about, although we're approaching the problem in some ways differently. I wonder if, when the dust settles here, you'd be interested in reading through the discussion thread I began on Ken Wharton's essay page and emailing me your thoughts on what I've put there. I think I see a possibility from your essay that would really be of mutual benefit, and I imagine you'd pick that out as well from my posts.

As I said, interesting and intriguing essay. I rated it accordingly. I look forward to hearing more from you.

Best of luck, here and always,

Daryl

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Author Torsten Asselmeyer-Maluga replied on Aug. 7, 2013 @ 07:22 GMT

Dear Daryl,

thanks. I also rating your essay accordingly.

More later (hopefully)

Torsten

Yuri Danoyan wrote on Aug. 7, 2013 @ 03:25 GMT

Hi Torsten

Are you rated my essay?

Yuri

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Author Torsten Asselmeyer-Maluga replied on Aug. 7, 2013 @ 07:20 GMT

Hi Yuri,

I rated your interesting essay with a high rang.

Best

Torsten

Jonathan J. Dickau wrote on Aug. 7, 2013 @ 03:56 GMT

Greetings Torsten,

I found your essay deeply meaningful and engaging. It was not light or easy reading, but I found myself learning something meaningful with each paragraph I read. I think I was able to understand most of your technical points, although the depth of your coverage was astounding, which attests to the clarity of your exposition. I especially like the observation that the smooth and triangulated or PL constructions of the manifold are equivalent, and find greatly satisfying the idea of a tree-like branching spacetime.

There is much to like about your essay, and I gave you a high rating. I had started to read it at least twice before, but it was so dense with content as to take as much time as 3 or 4 lighter ones. However; I felt I needed to come back to it, before the deadline, and give you your due. You might enjoy my essay as well. I'll say more later, if there is time. Good Luck!

All the Best,

Jonathan

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Author Torsten Asselmeyer-Maluga replied on Aug. 7, 2013 @ 07:27 GMT

Dear Jonathan,

I also read your essay (giving them a high rang), it is really interesting.

But I will also read it again.

Best wishes

Torsten

Michael Helland wrote on Aug. 7, 2013 @ 19:19 GMT

Hello Torsten,

I liked your essay and rated yours a ten.

I hope you enjoy mine, and good luck.

http://www.fqxi.org/community/forum/topic/1616

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Author Torsten Asselmeyer-Maluga replied on Aug. 7, 2013 @ 19:43 GMT

Dear Michael,

thanks for your rating and I do the same for you.

very interesting essay, I agree with you completely, information has a hierachical structure with many layers (including also its semantic).

It was ghood that Matt brought us together.

All the best

Torsten

Jonathan J. Dickau wrote on Aug. 8, 2013 @ 23:40 GMT

Glad you could make it Torsten,

Your essay certainly deserves to win something. Good luck in the finals!

Regards,

Jonathan

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Author Torsten Asselmeyer-Maluga replied on Aug. 9, 2013 @ 09:02 GMT

Dear Jonathan,

thanks a lot for your words. Yes, finally I got it (with one of the last votes).

Congratulations for you rank.

Best

Torsten