Spacetime weave - Bit as the connection between Its or the informational content of spacetime by Torsten Asselmeyer-Maluga

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

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

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

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

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

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

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

Torsten,

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

The manifold constructed from the knot K is

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

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

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

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

F:bord_n^f --- > A

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

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

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

Cheers LC