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ergospherical

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My first reaction was that the thermometer will be able to measure heating due to the Unruh effect whilst his lab is accelerating.

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ergospherical

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My first reaction was that the thermometer will be able to measure heating due to the Unruh effect whilst his lab is accelerating.

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Dale

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Does the equivalence principle extend to all theories of quantum gravity?

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ergospherical

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But something like a star or a planet doesn’t emit Hawking radiation, right?

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PeterDonis

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The Unruh effect is due to proper acceleration, and would be there, in principle, whether the lab was accelerating in free space or was sitting at rest in the gravitational field of a large mass. So it could not be used to distinguish those two cases.My first reaction was that the thermometer will be able to measure heating due to the Unruh effect whilst his lab is accelerating.

OTOH, if by "gravitational attraction" the question means

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ergospherical

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PeterDonis

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I should actually rephrase my previous statement. The Unruh effect is derived assuming flat spacetime and the quantum field being in the vacuum state according to inertial observers. (See below for why the qualifier "according to inertial observers" is necessary.) If a gravitating mass is present, spacetime is neither flat nor in the vacuum state according to inertial observers, so it's not clear whether the Unruh effect would even be predicted in this case. If we assume it would be predicted in the "hovering in the vacuum region above a gravitating mass" case based on something like the equivalence principle, then its physical origin would be what I describe below.Can we ascribe a physical origin to the heating effect in the case of hovering (by means of rockets, say) outside a star?

The qualifier I gave above about the vacuum state is necessary because the reason the Unruh effect is predicted at all is that which state of the quantum field is the "vacuum" is different for inertial observers and accelerated observers. More precisely, the concept of "vacuum state" for the quantum field requires a concept of "time translations" for its definition, and inertial observers and accelerated observers have different concepts of "time translations" (roughly speaking, because the inertial Killing vector field and the boost Killing vector field in Minkowski spacetime are different). The derivation of the Unruh effect amounts to showing that the state of the quantum field that is a vacuum state in flat spacetime for inertial observers is

The reference from which I first learned all this is Wald's monograph,

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ergospherical

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PeterDonis

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It's on Amazon:I’ll look for the book later this week

https://www.amazon.com/dp/0226870278/?tag=pfamazon01-20

When I said I have never found it online, I meant I have never found a digital version of it, or, for example, a preprint on arxiv.org or some other similar freely available online source that covers the same material.

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ergospherical

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PeterDonis

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If you can get through the book in a weekend you are definitely quicker at it than I am.

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PAllen

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Does it extend toDoes the equivalence principle extend to all theories of quantum gravity?

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As demonstrated by this discussion the problem with the equivalence principle or rather the equivalence principles is that it is usually discussed in the heuristic introductions to GR and then not further qualified given the fully exposed theory (a fate it shares with the discussions of the Michelson Morley experiment, which is usually also only discussed as a "crucial experiment" for the heuristical motivation of SR).

A clear way to state the principle is that the GR spacetime model is a Pseudo-Riemannian manifold with the fundamental form of the signature (1,3) or, equivalently (3,1). Physically that means that the notion of inertial frames is local an that at any point in spacetime there's always a local inertial frame of reference. That's of course not a good way to heuristically motivate GR but it should be the final clarifying statement about the content of the (then even strong!) equivalence principle.

For particle physicists another convincing semi-heuristic argument is that relativistic models of the gravitational interaction can be built by "gauging" Poincare invariance, which becomes then a local symmetry and thus you have a gauge theory with the general diffeomorphism invariance as the gauge group, which usually is called "general covariance". Together with the fact that there are particles with spin that leads to the statement that GR spacetime is described as a Einstein-Cartan manifold with torsion. In the usual "macroscopic" phenomenology, where gravitation plays a practical role, all you have is classical matter ("continuum mechanics") and the em. field as sources, and there the theory specializes to usual GR. If there is torsion, it's inside "polarized matter" and thus pretty difficult to observe.

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