Quantenfeldtheorie

Pierre Martinetti
Göttingen

The thermal time hypothesis: attempt at a physical interpretation of the modular group for the double cone

The "thermal time hypothesis" formulated by Connes and Rovelli in 94 is an attempt to give a physical meaning to Connes' discovery that "von Neumann algebras naturally evolve with time". The hypothesis is intended to be useful in quantum gravity where it could help to recover, at the classical limit, the intuitive notion of a unique proper time flow.
Besides such still-to-come applications, the thermal time hypothesis sheds interesting light on the physical interpretation of the modular group for various regions of Minkowski space-time.
In particular, by repeating on the double cone D the analysis made by Bisognano and Wichmann on the Rindler wedge (via Hislop- Longo theorem) we will see how one may generalize the Unruh effect (i.e. the thermalization of the vacuum for eternal uniformly accelerated observers) to observers with finite lifetime.

Although our result is plagued by strongly diverging transient effects, it has striking features. In particular we will argue that an observer with a finite lifetime should see the vacuum as a thermal state, whether he is accelerated or not.
--www.theorie.physik.uni-goettingen.de/forschung/qft/seminar/ab2002.html
Speaker: P. Martinetti
Title: The thermal time hypothesis.
Abstract:
We shall present an overview on the thermal time hypothesis (TTH) of Connes and
Rovelli which proposes a intrinsic definition of the notion of "physical flow of time" that may be interesting in a quantum gravity context. Here we shall illustrate the TTH by emphasizing some applications to general relativity and quantum field theories in curved spacetimes. Especially we will present our adaptation of the Unruh effect (i.e. the fact that the vacuum state of a quantum field theory on Minkovski spacetime is viewed as a thermal state for an eternal observer with constant acceleration) to observers with finite lifetime. Also we aim at discussing some recent application of the TTH
to de Sitter space.--conferences.phys.uoa.gr/nebxii/abstracts.htm

1994?
Maybe Ben should have heard more about this than he seems to have. There's some link to algebra automorphisms...?
What's this Unruh effect got to do with temperature?

Which testable predictions we can derive from thermal time hypothesis?

Maybe Ben should have heard more about this than he seems to have.

If it was published in 1994 and I haven't heard about it, that says more about the general acceptance of the idea by the community.

What's this Unruh effect got to do with temperature?

Basically, an accelerated observer sees blackbody radiation, whereas a non-accelerated observer sees no temperature.

http://en.wikipedia.org/wiki/Unruh_effect

Yes... and puts a whole new light on things. I have heard of the Unruh effect, but not the article. Very interesting.

Connes' discovery that "von Neumann algebras naturally evolve with time". The hypothesis is intended to be useful in quantum gravity where it could help to recover, at the classical limit, the intuitive notion of a unique proper time flow.Who would like to comment on von Neumman algebras (without posting links to wikipedia)? Why are the automorphisms thought to be important, and what does it have to do with non-commutativity, or whatever?

P.S. there's stuff about operators being looked at here and there. That's the mathematical/physical version of "operator". Again, this has something to do with non-commutative algebras. And QG theories. The notion of "time-free" physics at the quantum level seems to be a popular one.

Which testable predictions we can derive from thermal time hypothesis?
http://arxiv.org/abs/hep-th/0608221
A Lorentzian version of the non-commutative geometry of the standard model of particle physics
John W. Barrett
14 pages

"A formulation of the non-commutative geometry for the standard model of particle physics with a Lorentzian signature metric is presented. The elimination of the fermion doubling in the Lorentzian case is achieved by a modification of Connes' internal space geometry so that it has signature 6 (mod 8) rather than 0. The fermionic part of the Connes-Chamseddine spectral action can be formulated, and it is shown that it allows an extension with right-handed neutrinos and the correct mass terms for the see-saw mechanism of neutrino mass generation."

http://arxiv.org/abs/hep-th/0608226
Noncommutative Geometry and the standard model with neutrino mixing
Alain Connes
17 pages

"We show that allowing the metric dimension of a space to be independent of its KO-dimension and turning the finite noncommutative geometry F-- whose product with classical 4-dimensional space-time gives the standard model coupled with gravity--into a space of KO-dimension 6 by changing the grading on the antiparticle sector into its opposite, allows to solve three problems of the previous noncommutative geometry interpretation of the standard model of particle physics:
The finite geometry F is no longer put in "by hand" but a conceptual understanding of its structure and a classification of its metrics is given.
The fermion doubling problem in the fermionic part of the action is resolved.
The spectral action of our joint work with Chamseddine now automatically generates the full standard model coupled with gravity with neutrino mixing and see-saw mechanism for neutrino masses. The predictions of the Weinberg angle and the Higgs scattering parameter at unification scale are the same as in our joint work but we also find a mass relation (to be imposed at unification scale)."

.... article quoted...
Nice. Which testable predictions we can derive from "thermal time hypothesis"?

Frud---did you read those papers or did you just copy the abstracts from arXiv?

I don't think either of them deals with the thermal time hypothesis.

In fact, I know the second paper has nothing to do with thermal time because I read it.

I know the second paper has nothing to do with thermal time because I read it.Great, so you must want to explain, in great mathematical detail, why it has "nothing to do with thermal time"...? (or not)
Does it have anything to do with the work he is doing, that involves non-commutative geometry, and solving the operator problem (the Barret-Crane vertex)? I assumed it was related to the work he is doing on quantum gravity (it seems to be his thing). In response to a question about predictable stuff/testability.

Neutrino mixing is testable, isn't it?

P.S. If you're determined that this topic has no substance, that Connes & Rovelli are "wrong", and that there are no predictions, or, as Lubos Motl puts it: 'Carlo Rovelli has been working on his "background-independent graviton propagator", a combination of words that is an oxymoron because every propagator is by definition background-dependent', I'm not giving up yet.

Why is every propagator/operator background dependent? Is this a fundamental principle, or something?

Does it have anything to do with the work he is doing, that involves non-commutative geometry, and solving the operator problem (the Barret-Crane vertex)? I assumed it was related to the work he is doing on quantum gravity (it seems to be his thing). In response to a question about testability.

As far as I remember, this paper has nothing to do with quantum gravity. I think it is quite explicit in this assertion in the Introduction, claiming that this model does not have a UV completion. So this model has nothing to do with thermal time, because it has nothing to do with quantum gravity, where (aparently) this thermal time hypothesis is coming from. Of course, I don't know, because you have never given us a proper summary of the original article.

RE Neutrino mixing, it IS testable, but as I seem to recall the neutrino mass predicted by Connes model was WAY too big to be reasonable. But no one ever explained to me (and I never figured out) if this was actually a problem---it depends on WHERE he defines the neutrino mass. If he defines it at the UV cutoff, then uses the renormalization group to run the yukawa coupling down, it seems reasonable, but no one could ever answer this question for me, and it wasn't clear in my (quick) reading of the paper.

Note also that lots of theories predict neutrino masses, and thus neutrino mixing. One can write down a dimension five operator in the standard model, and neutrino masses are a standard prediction of SO(10) grand unified theories.

Yes, I'm well aware that this is one of many approaches to quantum gravity.
I'm more interested in a general overview, but I'm just trying to understand what the problems are with QG theories.

As for summarising some article--I don't feel like it, just now. Why is it a requirement that I summarise the article in New Scientist? I'm not that confident that they understood the concepts, for starters.

Why is it a requirement that I summarise the article in New Scientist?

Because you're the one who wants to talk about it, and you're the one who has read it.

Thread closed.

PM me when you feel like sumarizing the article.