# Is the Unruh effect a special relativistic effect or a general relativistic effect?

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.
• For acceleration in SR: physics.stackexchange.com/questions/6742/… – Nihar Karve Nov 19 '20 at 15:43
• 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. – Andrew Nov 19 '20 at 16:00
• 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? – mithusengupta123 Nov 19 '20 at 16:06
• 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. – Andrew Nov 19 '20 at 16:09
• @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 – Umaxo Nov 19 '20 at 19:02

• 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”). – A.V.S. Dec 1 '20 at 9:42