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It is speculated that Unruh radiation exists for accelerating observers in flat spacetime. A thermometer in the frame will point at a higher value than for someone in a stationary frame. In the spacetime of the accelerating observer, creation operators exist which create real particles that can affect the thermometer (assume the observer is shielded from the CMBR).
But how can this be? If the acceleration is constant and a pair of particles is created, won't these particles get the same acceleration both? I can imagine that if the particles are accelerated differently, like in the spacetime of a black hole, they become real, but not if they are accelerated exactly the same. Not even if you let a frame accelerate in the most strange ways. Where does the energy come from to make them real? Aren't tidal forces required to make them real?

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  • $\begingroup$ Note that the Unruh effect tells us that for an accelerated observer with respect to some referential $(R)$, the number of particles in another referential which is not accelerated with respect to $(R)$ is not zero. This does not mean that the accelerated observer will see these particles because, in his own referential, he is in vacuum. Moreover in his own referential, an observer which is static with respect to $(R)$ is also in the vacuum. $\endgroup$ Jun 7, 2021 at 10:52
  • $\begingroup$ @JeanbaptisteRoux So the particles are seen in the rest frame? That is from the point of view of the accelerated observer? Why doesn't the person in the rest frame see them? Are they real particles? $\endgroup$
    – user303670
    Jun 7, 2021 at 12:45
  • $\begingroup$ Note that the unruh effect is not really debated or controversial, the real deal of discussion is the unruh radiation. $\endgroup$
    – Quillo
    Sep 19, 2022 at 10:06

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The Unruh effect is the hypothetical prediction that an accelerating observer will observe a thermal bath, like blackbody radiation, there where an inertial observer sees the vacuum (no particle). In other words, the inertial observer sees no particle, while the non-inertial observer sees a thermal distribution of particle with temperature related to her/his acceleration. The concept of particle is Lorentz invariant, but it is not generally covariant. If you work with non inertial frames you cannot talk about particles in an absolute way: you have to say to which observer you are referring to. This is like time in special relativity (versus time in Newtonian theory). In Newtonian theory time is absolute, you don't have to say to which observer you are referring to, but in special reativity the time coordinate depends on the observer.

Coming back to the particles of the bath, I don't think we can say that they are real: as soon as the non-inertial observer stops he would see exactly the same vacuum (no particle) as any other inertial observer. This is in some sense similar to the length contraction in special relativity: as soon as the observer in motion stops she/he will see the same length as the one measured in the LAB frame. Notice that length contraction is very different than time dilation, which is a real effect: if you move with very high velocity with respect to the LAB frame, then you stop and compare your watch with the one of the LAB frame you will see that your watch slowed down!

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  • $\begingroup$ That they are not real is the most important thing! So the particles in Unruh are different from (real) Hawking radiation? Are they connected? Does the gravity field just make them real? $\endgroup$
    – user303670
    Jun 8, 2021 at 7:56
  • $\begingroup$ The math is similar, but the results have different meaning. For the Hawking radiation take a two dimensional (for simplicity) collapsing shell (the result happens to be independent on the shape) and a scalar field. The modes of the field are everywhere: inside and outside the shell. When the radius of the shell reaches the Schwarzschild radius, the part of the wave mode inside the horizon gets suck, while the part outside the shell is free to propagate and the flux of this wave (exponentially redshifted) can be measured. This is a qualitative explanation of the Hawking radiation. $\endgroup$
    – Voltrack
    Jun 8, 2021 at 8:42
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    $\begingroup$ Notice that length contraction is very different than time dilation, which is a real effect I think you are comparing apples and oranges here. In the case of length contraction, you are talking about new measurements made after you stopped, but in the case of time dilation you are talking about measurements along your entire path. If you would also look at time measurements after you stopped, they would be also the same as in lab frame. Similarly, if you would look at the distance you think you traveled between two static objects, it would be smaller than in the lab frame ... $\endgroup$
    – Umaxo
    Sep 19, 2022 at 4:53
  • $\begingroup$ ... there is no other reconcile with the fact, that you just traveled subluminally the distance that is in LAB frame 2 light years within one year of your own time. $\endgroup$
    – Umaxo
    Sep 19, 2022 at 4:53

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