Thermodynamics of Spacetime: The Einstein Equation of State?

[mtak0114]

Hi,

I have recently been delving into Quantum gravity related material... and I came across a paper by Ted Jacobson "Thermodynamics of Spacetime: The Einstein Equation of State" http://arxiv.org/abs/gr-qc/9504004 and as far as I understand the argument it is very impressive who would have thought that three seemingly unrelated theories could be so closely tied (GR, thermo and QFT). But I have two questions:

1) Why starting from the 2nd law which assumes an arrow of time can we extract a theory which is time reversal invariant GR? (this is probably closely related to the work of Hawking which I am unfamiliar with)

2) His interpretation of heat puzzles me:

"In thermodynamics, heat is energy that flows between degrees of freedom
that are not macroscopically observable. In spacetime dynamics, we shall
define heat as energy that flows across a causal horizon."

specifically he identifies $$Q$$ (the heat) with $$T^{\alpha\beta}$$ (the energy momentum tensor.)

cheers

M

 

[Naty1]

This seems dependent on the holographic principle/conjecture...and all these things tie together when entropy is considered as information...

entropy is a measure of hidden information (not macroscopically observable) with heat and entropy closely related.

wiki has some insights at: http://en.wikipedia.org/wiki/Laws_of_black_hole_mechanics

I hesitate to make any other comments as I would be as likely to mislead as enlighten.

Leonard Susskind has good discussion on this general subject, THE BLACK HOLE WAR, in various places under thermo/heat/entropy as does Charles Seife, DECODING THE UNIVERSE, including pages 70 to 85...

 

[Entropia]

Hello M,

Thank you for bringing up this interesting paper by Ted Jacobson on the thermodynamics of spacetime. The idea of relating thermodynamics and gravity is not new, as it has been explored by many physicists including Hawking and Bekenstein. However, Jacobson's approach is unique in that he derives the Einstein equation of state using only thermodynamic principles.

To address your first question, the second law of thermodynamics states that the entropy of a closed system always increases or remains constant. This implies that there is an arrow of time, as the direction of time is associated with the increase of entropy. However, in general relativity, there is no preferred direction of time. The equations of GR are time-reversal invariant, meaning they hold true regardless of the direction of time. So, it may seem contradictory that Jacobson is able to derive GR from thermodynamics, which assumes an arrow of time. The key here is that Jacobson is not using the second law directly, but rather he is using the concept of entropy and its relationship to energy and temperature. By assuming that the Einstein equation must have an associated entropy, he is able to derive the equation in a thermodynamic framework.

Regarding your second question, Jacobson's interpretation of heat as energy that flows across a causal horizon is a bit unconventional. In classical thermodynamics, heat is defined as energy transferred between two systems due to a temperature difference. However, in the context of spacetime dynamics, Jacobson is relating heat to the flow of energy across a horizon, which is a boundary between two regions of spacetime. This concept is not limited to black hole horizons, but can also be applied to any causal horizon in spacetime. The identification of heat with the energy-momentum tensor is based on the fact that the energy-momentum tensor is a conserved quantity in GR, and it plays a role in determining the causal structure of spacetime.

I hope this helps to clarify some of the concepts in Jacobson's paper. Overall, his work is a fascinating exploration of the connection between thermodynamics and gravity, and it provides a new perspective on the fundamental principles of spacetime. Thank you for bringing it to my attention.