1. Mar 26, 2014

### craigi

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

2. Mar 27, 2014

### Demystifier

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.

3. Mar 27, 2014

### 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?

4. Mar 27, 2014

### craigi

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?

Last edited: Mar 27, 2014
5. Mar 27, 2014

### marcus

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.

6. Mar 27, 2014

### atyy

Last edited: Mar 27, 2014
7. Mar 28, 2014

### MikeGomez

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.

8. Mar 28, 2014

### 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.)