Unruh and Hawking Radiation Paradoxes?

[craigi]

Does the existence of observer dependent particles as predicted by the Unruh effect and Hawking radiation lead to paradoxes?

 

[Demystifier]

Does the existence of observer dependent particles as predicted by the Unruh effect and Hawking radiation lead to paradoxes?

Interesting question!
In my opinion, it is a paradox if you have a reason to believe that particles exist even when nobody observes them. If you don't have a reason to believe that, then there is no paradox.

 

[martinbn]

I don't think it has anything to do with observation. There would be a paradox if particle number is invariant. But why should it be?

 

[craigi]

I don't think it has anything to do with observation. There would be a paradox if particle number is invariant. But why should it be?

So suppose we accept that particle number isn't invariant under relative acceleration.

In order to conserve energy and avoid a paradox upon deceleration, do we require that free Unruh radiation is absorbed back into the vacuum and that particles that have absorbed Unruh radiation, at least statistically, release it back into the vacuum too?

 

[marcus]

Interesting question!
In my opinion, it is a paradox if you have a reason to believe that particles exist even when nobody observes them. If you don't have a reason to believe that, then there is no paradox.

So suppose we accept that particle number isn't invariant under relative acceleration...

AFAIK particle number is simply not an invariant. If the geometry is curved (as realistically speaking it always is, in nature) the particle number is poorly defined, ambiguous. Isn't that right?
Particles only "exist" as detection events.

So I would follow Demystifier's reasoning and say that there is no paradox.

One does not have to imagine some acceleration and deceleration story, in order to suppose that particle number is not invariant. It is simply, of itself, poorly defined in curved geometry.

There was a 2003 paper by Colosi and Rovelli about this which referred to an earlier paper by Paul Davies, but I think it is simply well-known and a reference is unnecessary.

 

[atyy]

Apparently the firewall paradox depends on an event horizon, but there is no firewall paradox for a Rindler horizon.
http://arxiv.org/abs/0909.1038
http://arxiv.org/abs/1309.6583
http://arxiv.org/abs/1207.3123
http://arxiv.org/abs/1307.4972

 

[MikeGomez]

So suppose we accept that particle number isn't invariant under relative acceleration.

In order to conserve energy and avoid a paradox upon deceleration, do we require that free Unruh radiation is absorbed back into the vacuum and that particles that have absorbed Unruh radiation, at least statistically, release it back into the vacuum too?

I don’t see the paradox, but I do see what you are saying about energy conservation. If the body heats up during acceleration, it seems reasonable to expect that it would either cool back down after deceleration, or leave the volume of space from which it came a little cooler. Whether or not it's possible to specify parameters for energy conservation in this situation is unclear. Here’s what DaleSpam has recently said in a different thread.

Unfortunately, in curved spacetimes there is no general global definition of energy. Here are a couple of nice FAQs on the topic:

http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html
https://www.physicsforums.com/showthread.php?t=506985
…

 

[bapowell]

I recall the "paradox" stemming from the fact that an accelerated particle detector will detect quanta (and an inertial detector will not), while both accelerated and inertial observers agree that the local stress-energy tensor vanishes: \langle 0_M|:T_{\mu \nu}:|0_M\rangle = \langle 0_M|:T'_{\mu \nu}:|0_M\rangle = 0. (Here T_{\mu \nu} is the inertial tensor and T'_{\mu \nu} is that in the accelerated frame, the ':' denotes normal ordering, and |0_M\rangle is the Minkowski vacuum.)