- #1

marcus

Science Advisor

Gold Member

Dearly Missed

- 24,738

- 788

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

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

General covariance is at the root of why 1915 General Relativity is

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

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.

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: