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If an observer moves in an accelerated frame in flat spacetime, the vacuum looks like a thermal distribution of particles to that observer. This is the Unruh effect.

  • Is it a special relativistic (SR) effect or a general relativistic (GR) effect? On one hand, it's flat spacetime which seems that SR is enough. But then it talks about the accelerated observer, which seems to suggest that it is a nontrivial GR effect. Please help.
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    $\begingroup$ For acceleration in SR: physics.stackexchange.com/questions/6742/… $\endgroup$ – Nihar Karve Nov 19 '20 at 15:43
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    $\begingroup$ This is really just a semantic question, right? I personally think of "anything that happens in the Minkowski spacetime" as "special relativity", but other people additionally require "inertial observers in Minkowski." There's no physics content in where you draw the line. $\endgroup$ – Andrew Nov 19 '20 at 16:00
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    $\begingroup$ I mean, an accelerated observer does not mean GR. Is that true? I am getting confused. Sometimes one says that GR is the extension of SR that includes accelerated frames of references. By this definition, the accelerated observers in flat spacetime without gravity will also be GR. Is that true? $\endgroup$ – mithusengupta123 Nov 19 '20 at 16:06
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    $\begingroup$ I would say "GR" means "gravity", which means "spacetime curvature induced by the presence of stress energy." An accelerating observer in a fixed, Minkowski spacetime definitely is not experiencing gravity (ie, there are no tidal forces), even though the equivalence principle means that locally gravity and acceleration are indistinguishable. But these terms get used by different people with different ideas and the boundaries blur over time. Your definition, which disagrees with mine, is certainly valid, if you are clear that this is your definition and use it consistently. $\endgroup$ – Andrew Nov 19 '20 at 16:09
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    $\begingroup$ @mithusengupta123 "Sometimes one says that GR is the extension of STR ..." That would mean STR universe is not a manifold. But then, what are inertial reference frames in STR about?Doesnt they already define an atlas and manifold structure on their own? My point is, you can extend STR for accelerated frames without any additional assumptions, you just need to use a little fancier math than what you might be used to. Seems to me analogical to Galileo saying to Newton his theory is not mechanics just because he uses derivatives and true mechanics is supposed to use only algebra $\endgroup$ – Umaxo Nov 19 '20 at 19:02
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It is a SR phenomenon since it would be true even if GR were false: no equivalence principle, no Einstein equations, etc. (and thus it is independent of it). The said effect is a consequence of properties of the unique Poincare invariant vacuum state which satisfies a peculiar property (KMS condition) with respect to the boost symmetry.

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  • $\begingroup$ By your own criteria Unruh effect is not a SR phenomenon since it could also be present in theories violating SR postulates (e.g. analog spacetime with a preferred reference frame). Moreover, your criteria of effect $E$ belonging to a theory $T$ may be unproveable in general since they necessitate blanket statements like “No other theory differing from $T$ will exhibit $E$”. This is not reverse mathematics, this is physics, and physical theory is not a formal object like ZFC but much more nebulous and even sociological construct (“GR is what GR researchers do”). $\endgroup$ – A.V.S. Dec 1 '20 at 9:42
  • $\begingroup$ So, It Is not a SR phenomenon. $\endgroup$ – Valter Moretti Dec 1 '20 at 10:26
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This is not an either - or situation. One should make a distinction between the physics of the effect, in this case the accelerating detector coupled to a quantum field registering the thermal spectrum of excitations of that field, and the conceptual framework used to explain the effect. Both GR and SR are such frameworks and each could be used to describe this effect.

Since the effect does not depend on the spacetime curvature, one does not need to use GR for the description, it is perfectly possible to describe the behaviour of accelerating detector using only notions of QFT in Minkowski spacetime (i.e. the SR theory). At the same time using the set of tools from general relativity (more specifically, from QFT in curved spacetime) also allows one to describe the very same physical situation. Moreover, there are multiple GR techniques that could be used to achieve quantitative description of the Unruh effect (Bogoliubov transformation method, WKB/tunneling method, anomaly cancellation method, etc.) each one offering new insights into the situation. The existence of such dual descriptions (SR and GR) is an important test of the formalisms employed and of our intuition built upon these sets of tools.

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  • $\begingroup$ Apart from that, I always thought the Unruh effect and Hawking radiation is basically the same thing (since the gravitational curvature at the black hole is equivalent to an accelarating frame of reference). So doesnt it mean while Unruh effect can be calculated in SR, its natural framework is more in GR? $\endgroup$ – lalala Nov 20 '20 at 8:06
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    $\begingroup$ While to me GR indeed seems more natural, there are methods for going the opposite way: reducing Hawking radiation to Unruh effect via so-called GEMS – global embedding Minkowskian spacetime see e.g. this. $\endgroup$ – A.V.S. Nov 20 '20 at 8:23

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