# Connes Rovelli paper on time in gen. cov. quantum theories

1. Apr 6, 2010

### marcus

This paper was a "sleeper" for much of the past 16 years. But in the past 12 months, since March 2009, it has received 8 citations. Just random fluctuation or can we point to something that stirred up interest?

http://arxiv.org/abs/gr-qc/9406019
Von Neumann Algebra Automorphisms and Time--Thermodynamics Relation in General Covariant Quantum Theories
A. Connes, C. Rovelli
(Submitted on 14 Jun 1994)
"We consider the cluster of problems raised by the relation between the notion of time, gravitational theory, quantum theory and thermodynamics; in particular, we address the problem of relating the 'timelessness' of the hypothetical fundamental general covariant quantum field theory with the 'evidence' of the flow of time. By using the algebraic formulation of quantum theory, we propose a unifying perspective on these problems, based on the hypothesis that in a generally covariant quantum theory the physical time-flow is not a universal property of the mechanical theory, but rather it is determined by the thermodynamical state of the system ('thermal time hypothesis'). We implement this hypothesis by using a key structural property of von Neumann algebras: the Tomita-Takesaki theorem, which allows to derive a time-flow, namely a one-parameter group of automorphisms of the observable algebra, from a generic thermal physical state. We study this time-flow, its classical limit, and we relate it to various characteristic theoretical facts, as the Unruh temperature and the Hawking radiation. We also point out the existence of a state-independent notion of 'time', given by the canonical one-parameter subgroup of outer automorphisms provided by the Cocycle Radon-Nikodym theorem."

The citation history is that Connes Rovelli garnered 57 cites in the 16 years to date, an average of about 3.5 per year. Instead of trailing off, as happens with many papers, interest seems to keep coming back. The interest is from wide range of authors: I haven't heard of most of them.

General covariance means diffeomorphism invariant. The equations of the theory do not change no matter how you moosh and morph the continuum. Solutions remain solutions no matter how you squoosh the picture. In effect, space and time have no identity, no definite physical meaning, no objective reality. Only relationships among events. Einstein pointed this out in 1916.

General covariance is at the root of why 1915 General Relativity is background independent. As are some other theories which derive from GR. Mathematically speaking, the gravitational field, in GR, is not actually a metric tensor defined on a given manifold. It is an equivalence class of all the possible metric tensors on all possible manifolds which can be morphed into each other. It is the abstract idea of a geometry, after the underlying continuum has been thrown away.

The basic lesson of Gen Rel is that fundamental physical theories should eventually be made general covariant. Space and time are not real, only the web of relations, the geometry. It must be possible to throw away the spacetime continuum on which any particular solution is constructed, and retain the class of all solutions which are equivalent under diffeomorphism to the given one. Nothing must depend on the background.

OK so what does time mean in that case?

In 1994 Connes and Rovelli proposed an answer to that question. We'll see. Maybe their idea "has legs". The question of time is not settled yet.

Last edited: Apr 6, 2010
2. Apr 6, 2010

### marcus

Cosmology buffs will recall that although GR has no distinguished time (each observer has its own proper time) and despite the fact that cosmology is founded on GR, cosmology has its own "universe time". Sometimes called Friedman-Robertson-Walker (FRW) time because the standard cosmo model runs on it. This is an observer-independent universal time that confronts you as soon as you admit the background of oldest light into your picture of the universe.

By admitting the cosmic microwave background, one is acknowledging that the universe is in a particular thermodynamic state. One is particularizing. The light arose from particular conditions of temperature density and expansion-rate which allowed photons effectively infinite mean free path. Thermodynamic conditions.

The standard cosmo model is essentially the picture seen by observers at rest relative to cosmic background.

Connes Rovelli 1994 cites a paper by Rovelli in 1993 where he shows that the thermal time which was featured in Connes Rovelli is the same as the FRW model's universe time.

In other words, a general covariant system which at first sight has no distinguished time may yet have a distinguished pan-observer time which arises from the thermodynamic state of the system.

There are two relevant 1993 papers by Rovelli, published back-to-back in the same August 1993 issue of Classical and Quantum Gravity.
Statistical mechanics of gravity and the thermodynamical origin of time
C Rovelli
doi: 10.1088/0264-9381/10/8/015 Full text PDF (984 KB)
The statistical state of the universe
C Rovelli
doi: 10.1088/0264-9381/10/8/016 Full text PDF (579 KB)
http://iopscience.iop.org/0264-9381/10/8
Arxiv does not have online preprints of these articles.

3. Apr 7, 2010

### Fra

This is a really good key question IMO.

Thanks for posting this Marcus. I am so far not much aware of Connes thinking. So far my impression is that his work is mostly in pure mathematical physics rather than fundamental physics per see but maybe I'm wrong.

I'll try to get around skimming those papers and see.

/Fredrik

4. Apr 7, 2010

### humanino

In a french interview (with a journalist from arte, the German-French cultural channel), Connes relates how he had been invited in a quantum gravity workshop, and accepted because he thought he would learn something. It turned out he did not understand much of the presentations and was pretty bored. But Rovelli had a talk with a provocative title ("we know what quantum gravity is"), which he found quite stimulating. Later at the dinner, he decided to seat next to Rovelli. He began to describe his current thoughts about the issue of time. According to Connes, Rovelli left the table without a word, and Connes thought he had somehow offended Rovelli.

As it turns out, Rovelli came back later to Connes with a copy of one of the article above (I do not remember which). Connes describes "He had re-derived my formula for the inner automorphisms from pure philosophical thinking" by reflection on the statistical mechanics of curved spaces. Although probably a bit exagerated, I find his description worth mentioning.

Last edited: Apr 7, 2010
5. Apr 7, 2010

### bcrowell

Staff Emeritus
As a nonspecialist with a dilettante's interest in quantum gravity, I feel like sending a dozen red roses to anyone who can write the first few sentences of a quantum gravity paper in such a way that I have some idea what is being said. This paper passes that test.

Reference [4], to a 1993 paper by Rovelli, seems to be very important here. The paper isn't available on arxiv, but the latex source code is available here: http://www.phyast.pitt.edu/~rovelli/Papers/ (termodinamica.tex). This paper is written so well that I can understand page after page of the introductory material! Ah, bliss! Time to go to bed now, but I will definitely want to study this more carefully.

The conception of time as arising from thermodynamics seems like it might have some connection to some of the recent thermodynamic ideas we've been hearing about gravity.

6. Apr 7, 2010

### Fra

This was my hope as well, as my personal ideas also involves a kind of statistical inference to unify the timeless and the evolving pictures, but judging from my rovelli's reasoning in the past where he avoids the physical basis of that, I could guess how rovell's means with this. I was hoping that connes had some new angles I haven't seen before. Some of the recent papers on entropic cause of gravity does IMO miss certain traits. Although the general trends are to my liking. I'll try to read it tonight.

/Fredrik

7. Apr 7, 2010

### Fra

I haven't read the entire paper yet but just started skimming the intro during a break and noticed a quite biased way (in line with rovelli's thinking) of characterizing the agreed key question of how to unify the timeless picture with the evolving picture.

On page three he writes...

"Thus, a basic open problem is to understand how the physical time flow that characterizes the world in which we live may emerge from the fundamental “timeless” general covariant quantum field theory"

I think a more non-biased phrasing is that there exists somehow an incoherence between on one hand the timeless character of physical law (diff invariance), and the evolution of states and information as inferred from actual measurements with time.

The scheme of explanation expressed that

1. the apperance of time, is emergent from a timeless picture is one possibility to resolve the incoherence

the other possibility is that

2. the apperance of a timeless picture is emergent from an evolving picture.

Not only has neither approach yet succeded, but we don't even know which approach is is the better one. I personally think there is a duality here, where the two views can be consistent although conceptually I think the second view seems "less realist-style" and more focused on the inference process and thus to me preferred.

/Fredrik

8. Apr 9, 2010

### Fra

I appreciate some ideas, and I can appreciate the reasoning with an extra emphasis on the following remark of theirs, in conclusions in the end of the paper.

(1)
" We leave a large number of issues open. It is not clear to us, for instance,
whether one should consider all the states of a general covariant quantum system
on the same ground, or whether some kind of maximal entropy mechanism able
to select among states may make sense physically."
-- http://arxiv.org/abs/gr-qc/9406019

(2)
"In spite of this incompleteness, we find that the number of independent facts
that are connected by the thermal time hypothesis suggests that this hypothesis
could be an ingredient of the fundamental, still undiscovered, generally covariant
quantum theory.
"
-- http://arxiv.org/abs/gr-qc/9406019

The important part that I would have objected to unless they've admitted on their own the incompletness is that implicit assumption of the equiblirum of the statistical state beeing implicit in the gibbs state.

The problems they get, quite expectedly is that they don't know how to choose this lets call it "prior" distribution.

I appreciate the idea of representing the lets say "master symmetry" by a statistical kind of state, but I'd prefer to see this differently, and that the state must be connected to an inside observer, and that the "choice of this prior", instead of beeing arbitrarity chosen, or chosen by some ad hoc objective entropic principle, could instead hopefully be seen as a result of evolution, where the correspondennce to the "timeless gibbs states that he talks" about, instead just represents an equilibrium case, in the meaning of "equilibrated observers", like there as an "equilibrium" in an ecological system, but while it's possible to disturb this.

This idea would still be consistent with entropic emergence, it's just that the point is that since we are seeking here an intrinisic measurement theory, observer invariant measures of entropy hardly existst. Instead each observer, encodes it's own measure of disorder, which is evolving. This is as I see it the big difference in visions... some people look for such evolving picture, smoling sniffed it, but most others look for sometihng more in structural realist style.

I think that in order to provide a fraemwork to explain stuff like the origin of the universe, and the unification of *all* interactions un understanding of the non-equilibrium case is needed.

I think most people who reject this evolving stuff as too subjective or lack of decidability, wants to be more decidable than what is in fact possible, and they end up with the problem of having to choose between a landscape of various paramters - a choice that is unphysical. So in the end, full decidability is neverthenless absent. Either you try do deny this, or embrace it and take it to be one of the constructing principles of nature and exploit it, and be able to actuall be more predictive, not less. The only physicist I've seen have the guts to raise this in public is smolin, although it's clear that the argument seems to come from unger, although not a physicist he seems to have a great understanding of this logic.

Other than that I can buy that the idea provided is a possible component, but I have a feeling that the reasoning characterized in that paper, and that characterizes rovelli as far as I know is that they rather are looking for an eternal logic, to select for this, rather than see it as evolved. I personally don't think the realist picture will prove viable in this problem.

/Fredrik

Last edited: Apr 9, 2010
9. Jul 12, 2010

### marcus

To continue the story of this 1994 paper and the germinating idea of time which is present in it, in May 2010 a new paper came out by Rovelli and Smerlak.

Here is the first paragraph, to clarify the connection:

The “thermal time hypothesis” (TTH) was proposed by Connes and one of the present authors[1, 2] as a basis for a fully general-relativistic (and quantum) thermodynamics-–a problem which is still open [2–5]. In a nutshell, the TTH proposes that the most characteristic features of the “ﬂowof time” are essentially thermodynamical, and can emerge statistically also in a quantum gravitational context where other notions of time are meaningless[6].

http://arxiv.org/abs/1005.2985

Last edited: Jul 12, 2010
10. Jul 12, 2010

### marcus

I detect a slight oddity. The Rovelli Smerlak paper is on the "MIP poll" list. And (although it is not about the most discussed topics in our forum) it so far got more votes than any other of the 15 papers!

And those who voted for it are mostly people I don't know, either new or haven't posted as actively in Beyond forum as some of us. I didn't vote for it, or Fra (for instance ) but somehow some strangers noticed it.

Rovelli Smerlak
Thermal time and the Tolman-Ehrenfest effect: temperature as the "speed of time"
http://arxiv.org/abs/1005.2985
(Submitted on 17 May 2010)
"The thermal time hypothesis has been introduced as a possible basis for a fully general-relativistic thermodynamics. Here we use the notion of thermal time to study thermal equilibrium on stationary spacetimes. Notably, we show that the Tolman-Ehrenfest effect (the variation of temperature in space so that $$T\sqrt{g_{00}}$$ remains constant) can be reappraised as a manifestation of this fact: at thermal equilibrium, temperature is locally the rate of flow of thermal time with respect to proper time - pictorially, "the speed of (thermal) time". Our derivation of the Tolman-Ehrenfest effect makes no reference to the physical mechanisms underlying thermalization, thus illustrating the import of the notion of thermal time."

Last edited: Jul 12, 2010
11. Apr 8, 2011

### marcus

It has been another 12 months since this thread was started, so perhaps we should check to see how the paper is doing citewise.
Just going one the basis of cites, which is not a perfect measure, interest did not stay at that high level.
Here is the DESY spires link:
http://www-library.desy.de/cgi-bin/spiface/find/hep/www?rawcmd=FIND+EPRINT+GR-QC/9406019 [Broken].

If I counted right, in the 12 months ending 1st April 2010 it got 8 cites.
However in the 12 months ending 1st April 2011 it got 3.
http://www-library.desy.de/cgi-bin/spiface/find/hep?c=CQGRD,11,2899 [Broken]

Still I think it's intrinsically interesting and still has something to tell us. The story of this thermal time idea is probably still unfolding.

One question that occurred to me recently is what happens to time during the Loop cosmology bounce. This is a very brief interval (if that is meaningful) during which the density of the universe is very high and Loop gravity predicts that quantum corrections make gravity repellent.

So the familiar evolution from uniformity towards "lumpiness" that we see in both the distribution of matter and the gravitational field is briefly reversed. Does the concept of physical time even make sense during that seemingly brief high-density episode?

Last edited by a moderator: May 5, 2017
12. Apr 8, 2011

### marcus

A good summary of results in Loop cosmology which raises this question about time appears on pages 15 and 16 of http://arxiv.org/abs/1012.4707 , Rovelli's December 2010 review paper "LQG, the first 25 years." This turns out to be a generally useful up-to-date reference, covering a range of topics.