How Does the Unruh Effect Differ Between Observers in Motion and at Rest?

[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 transferred 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

 

[MeJennifer]

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

 

[George Jones]

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.

 

[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?

 

[George Jones]

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

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.

 

[MeJennifer]

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.

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.

 

[member 11137]

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.

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.

 

[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.

 

[Maaneli]

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 transferred 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

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.

 

[George Jones]

A quick look at Birrell and Davies did not seem to answer my question but I skimmed only briefly.

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:

The Unruh effect tells us that an accelerated observer will detect particles in the Minkowski vacuum state. An inertial observer, of course, would describe the same state as being completely empty; indeed, the expectation value of the energy-momentum tensor would be \left< T_{\mu \nu} \right> = 0. But if there is no energy-momentum, how can the Rindler observers detect particles? This is a subtle issue, but by no means a contradiction. If the Rindler observer is to detect background particles, she must carry a detector - some sort of apparatus coupled to the particles being detected. But if a detector is being maintained at constant acceleration, energy is not conserved; we need to do work constantly on the detector to keep it accelerating. From the point of view of the Minkowski observer, the Rindler detector emits as well as absorbs particles; once the coupling is introduced, the possibility of emission is unavoidable. When the detector registers a particle, the inertial observer would say that it had emitted a particle and felt a radiation-reaction force in response. Ultimately, then, the energy needed to excite the Rindler detector does not come from the background energy-momentum tensor, but from the energy we put into the detector to keep it accelerating.