# Dumb question on Unruh effect

1. Jul 11, 2008

### nrqed

Am not sure if this belongs more in quantum physics or in GR, it's at the intersection of the two.

If I understand correctly, the vacuum of the observer at rest corresponds to a thermal bath of particles for the accelerated observer.

Now the obvious question is: how does the observer at rest interprets the fact that a detector in the accelerated frame is recording particles even though the accelerated frame is moving in a vacuum?

In the field vs particle debate in QFT I have always sided with the "particle first" approach because in the end, what we actually detect are always particles. Even in the Unruh effect, one thing is clear for all observers: a detector will record particles or it won't. The only question is what is the interpretation as seen from different observers. The accelerated observer concludes that he/she is moving in a thermal bath of particles. But the observer at rest still sees clearly that the detector is recording particles with a thermal distribution. So what is the interpretation of what is going on from the point of view of the observer at rest?

Another question which may or may not be related to the first is where the energy of the observed particles come from. It is usually said that the energy comes from the force that is accelerating the frame. I am not sure how the energy is actually transfered and as far as I know, no calculation actually shows how this happens (I guess it woul require to also treat the force accelerating the frame quantum mechanically and as far as I know nobody has tried to do that, I am wrong?). But even if we sidestep the issue of transfer of energy, there is another question: energy is taken away from the source so that in order to maintain a constant acceleration, one must actually apply a larger force than what is calculated in GR textbook, right? Is this sort of calculation done somewhere?

Thanks

From the

2. Jul 11, 2008

### MeJennifer

See or instance "Spacetime and Geometry: An Introduction to General Relativity" by Carroll for a good introduction to the Unruh effect.

3. Jul 11, 2008

### George Jones

Staff Emeritus
I think Birrell and Davies attempts to answer some of these interesting question, but I don't have my copy with me right now. After looking at its table of contents on Amazon, section 3.3 "Meaning of the particle concept: particle detectors" looks relevant.

4. Jul 12, 2008

### yuiop

It seems curious that an observer suspended just above a black hole would see and measure particles being radiated from the horizon of the black hole (Hawking radiation being the gravitational equivalent of Unrah radiation) while a free falling observer at the same height would not detect any particles coming from the event horizon. Is that not slightly paradoxical?

5. Jul 14, 2008

### George Jones

Staff Emeritus
Yes, this book has a nice introduction to the Unruh effect, but I couldn't remember what it says with respect to nrqed's questions. Now I see that the last paragraph of the Unruh effect section gives a qualitative overview of the answers to nrqed's questions.

I don't think that this chapter, Quantum Field Theory in Curved Spacetime, is contained in the on-line notes that Carroll developed into the published book.

6. Jul 14, 2008

### MeJennifer

That is correct. I highly recommend Carroll's book.

By the way, a few words off topic on this: The above mentioned book costs about $100 in the US while in China one can obtain a legal copy for about$10. For instance Hawking and Ellis - "The Large Scale Structure of Space-Time" can be obtained for about the same price. A disturbing trend where major publishers provide science books at a significant discount to the Chinese market. A good thing for the Chinese students but I think it is unfair to Western students.

7. Jul 14, 2008

### Blackforest

I think too. This is a very interesting book and you certainly will find answers to your questions with a lot of explanations. Not so easy to read. Depending on the level you have in physics. You will also find a lot of paragraphs explaining why, even in vacuum, some observer see nothing and some other one will see a particle.

8. Jul 14, 2008

### nrqed

Thanks to all for the suggestions....I have to get my hands on copies of Carroll. A quick look at Birrell and Davies did not seem to answer my question but I skimmed only briefly.

I understand the point about the accelerated observer and the observer at rest not being in the same vaccuum. The question is of course about how the observer at rest would interpret the fact that the accelerated detector is recording particles. How would the observer at rest explain this. I am looking forward to seeing what Carroll says.

Thanks again for the feedback.

9. Jul 14, 2008

### Maaneli

Hey man,

Here is a treatment of the UD effect that I think addresses all your questions, using a self-field approach, rather than the standard vacuum fluctuations approach:

Quantum electrodynamics based on self-fields: On the origin of thermal radiation detected by an accelerating observer
http://prola.aps.org/abstract/PRA/v41/i5/p2277_1

Hope it helps.

10. Jul 15, 2008

### George Jones

Staff Emeritus
The last paragraph on page 54 and the first two paragraphs on page 55 might help.

Here is the last paragraph from Carroll's treatment of the Unruh effect: