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

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

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

Hi Torsten,

there's no need for apologies, the way this forum is structured, I keep losing the thread ('verliere den Faden') myself constantly. All the information one gets via the email updates is that *somewhere* within the 100-something replies in a thread, someone has added something... I think there's maybe room for improvement.

Unfortunately, our university library does not seem to have a copy of your book in stock, I will check whether it is available via remote order. I will have to step up my game if I want to have a meaningful discussion on the subject...

I think I've heard someone flaunting the idea that in the path integral, one should somehow integrate over all geometries (though how exactly that works, I'm not sure), and R^4 then may be singled out as giving the dominant contribution due to the plethora of smoothness structures---but I'm unsure as to how viable this is, or whether I am remembering correctly.

Anyway, thanks for your reply,

Jochen

Dear Torsten!

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

Dear Torsten,

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

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

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

Best wishes

Antony

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

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

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

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

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

Cheers LC

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

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