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In Carroll's we read

...The Unruh effect teaches us the most important lesson of Quantum Field Theory (QFT) in curved spacetime, the idea that "vacuum" and "particles" are observer-dependent notions rather than fundamental concepts.

I wonder are we talking about the same observer or two different observers using two different frames?

Put it another way, can the same observer who observed nothing using a frame detect a thermal spectrum if switched to another frame that is uniformly accelerating with respect to his previous frame?

Does it apply both ways? I mean if an observer detects particles, does this observant-dependent notion of particle content of a given state, implies that he can switch to another frame in the blink of an eye, and detect nothing?

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Please specify the source you're quoting, and ideally provide a link. –  Emilio Pisanty Aug 12 at 10:10

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up vote 4 down vote accepted

That is exactly the point: if the field is in a vacuum with respect to observer A, and observer B accelerates uniformly with respect to A, then B will observe a field state with nonzero particle content.

It doesn't really matter whether you talk about different observers on different frames of reference, or of a single observer who 'switches' their frame of reference. The notion of 'observer' is not meant to imply a specific person, nor does the experimenter himself have to be at rest or in inertial motion with respect to those coordinates. The terms 'observer' and 'frame of reference' refer to ways of making sense of observations more than actual people.

Finally, note that the Unruh effect can sometimes work the other way - i.e. if observer A sees a field with particle content, there may exist a second observer B in uniformly-accelerating motion w.r.t. A for whom the field is in vacuum - but this is not guaranteed. What the effect teaches us is that such observers B will observe a different particle content than A, but in general this need not be the vacuum.

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+1, but i would be careful with the (not verified) Unruh effect, especially in regard to number of particles which should be an (relativistic) invariant –  Nikos M. Aug 11 at 15:22
That's sort of the point, too. Particle number is a relativistic invariant under the Poincaré group, but not under more general frame transformations. Whether it's experimentally verified/verifiable is another matter, but understanding the consequences is important. –  Emilio Pisanty Aug 11 at 15:27
i'll have to look at it more thoroughly, as i havent studied the unruh effect (and much of its associated conditions), tnx for the comment –  Nikos M. Aug 11 at 15:30
@EmilioPisanty Speaking of theoretical consequences, does this imply that if we are in a uniformly accelerating frame can observe, say, a huge collection of particles, e.g. a star or galaxy, that is not at all there, as observed in another reference frame? –  VictorM Aug 11 at 19:14
No, that is not the case. Some field states will appear as a vacuum to other observers, but that does not mean that all field states can do that. In general such states need to be thermal states, which rules out anything with as much structure as a galaxy. –  Emilio Pisanty Aug 12 at 10:10

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