Do Different Observers Agree on Entropy in the Unruh Effect?

[naima]

If $|0_M\rangle$ is the Minkowski vacuum we have a $a |0_M\rangle = 0$
if $|0_R\rangle$ is the Rindler vacuum we have $b |0_R = 0\rangle$
and $\langle 0_M| b^\dagger b | 0_M \rangle$ is the mean value of the number of particles that an accelerated Rindler observer will be able to measure if he has an appropriate setup (selectivity = 1) If he uses a bad setup he will detect only a part of the particles. In this case the coupling constant appears in the result. This does not mean that the bath depends on the coupling constant.
IMHO of course!

 

[Demystifier]

Are you familiar with the concept of quantum contextuality?

 

[naima]

I can understand that when you have non commutative observables like spins in different directions, the result of the spin output depends on the direction of the setup.
Has the accelerated observer the choice between non commutative measures for the bath?

 

[Jimster41]

Is "quantum contextuality" sort of just Gleason's theorem? (Not that Gleason's Theorem is anything to sneeze at)

I landed on it drilling into the wiki on Quantum Contextuality.
Then that went off into "p-adic QM" which is totally breaking my head at the moment. Seems very interesting... Never heard of it. P-adic numbers remind me pretty strongly of Smolin's "variety" metric

 

[Demystifier]

I can understand that when you have non commutative observables like spins in different directions, the result of the spin output depends on the direction of the setup.
Has the accelerated observer the choice between non commutative measures for the bath?

Yes, the Unruh effect is very similar to the measurement of spin. The Minkowski number operator does not commute with the Rindler number (RN) operator. Actually, there is no one RN operator but a whole class of different RN operators - one for each possible acceleration. They do not commute with each other. An observer has the choice to measure any of these number operators. Operationally, he can measure different number operators by accelerating his detector to different accelerations. This is similar to the measurement of spin, where observer can measure spins in different directions by rotating his detector to different directions.

 

[naima]

As i was looking for what happens with a non eternally accelarated thermometer, i found this paper http://arxiv.org/abs/1307.4360
It is not surprising that if the thermometer's acceleration jumps from 0 to a at time 0 it will not "see" immediatly a thermal bath at temperature T.
This is not my problem. I read in this paper:
Unruh's classic paper offers an illustrative analog for the Hawking effect in black holes, often explained in terms of the geometric notion of an event horizon. However, there is no horizon for detectors undergoing non-uniform or finite-time acceleration.
I have problem with this sentence.
Does he say that at a given moment a Black Hole has no horizon for non eternal observers?

 

[Demystifier]

Does he say that at a given moment a Black Hole has no horizon for non eternal observers?

No, he does not say that. He does not talk about black holes, but about acceleration in Minkowski spacetime.

Concerning radiation from a black hole, the relevant horizon is the apparent horizon, not the event horizon. The event horizon is a property in the infinite future, while the apparent horizon is a property "now". For more details see also
http://lanl.arxiv.org/abs/hep-th/0106111

 

[naima]

Thank you very much Demystifier:
I did not know that there is a difference between these different horizons.
The "apparent horizon" in wiki is not obvious.
In his book Penrose writes that once a BH exists there is an horizon of points. behind it emitted light always moves inward. He calls that an event horizon or absolute horizon. Isnt it what other authors call "apparent horizon"?
Have you a link with clear definitions?Edit:
I found this link about http://www.fysik.su.se/~ingemar/relteori/Emmaslic.pdf
An apparent horizon is the boundary of trapped points. A point is trapped if it belongs to a trapped surface

 

[craigi]

http://arxiv.org/abs/hep-th/0403142

Abstract:The geometric entropy in quantum field theory is not a Lorentz scalar and has no invariant meaning, while the black hole entropy is invariant. Renormalization of entropy and energy for reduced density matrices may lead to the negative free energy even if no boundary conditions are imposed. Presence of particles outside the horizon of a uniformly accelerated observer prevents the description in terms of a single Unruh temperature.