Wilbert Zweistein's objection to the equivalence principle

ergospherical
I'd like to share the following competition problem:

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

atyy

Mentor
Possibly, but I don’t think that the Unruh effect is local and I would also think that it would be very difficult to distinguish it from Hawking radiation.

VVS2000, Demystifier and vanhees71
Homework Helper
Gold Member
2022 Award
Does the equivalence principle extend to all theories of quantum gravity?

vanhees71
ergospherical
Possibly, but I don’t think that the Unruh effect is local and I would also think that it would be very difficult to distinguish it from Hawking radiation.
But something like a star or a planet doesn’t emit Hawking radiation, right?

vanhees71
Mentor
My first reaction was that the thermometer will be able to measure heating due to the Unruh effect whilst his lab is accelerating.
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.

OTOH, if by "gravitational attraction" the question means coordinate acceleration towards a large mass, the lab would be in free fall in this case, and although there would indeed be no Unruh effect in this case, there would also be a reading of zero on the lab's accelerometer (which could be as simple as a bathroom scale), which would be a much easier and more straightforward way of distinguishing the two cases.

Orodruin, geshel, vanhees71 and 2 others
ergospherical
Oh, I didn’t know that. Can we ascribe a physical origin to the heating effect in the case of hovering (by means of rockets, say) outside a star?

Mentor
Can we ascribe a physical origin to the heating effect in the case of hovering (by means of rockets, say) outside a star?
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.

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 not a vacuum state for accelerated observers; instead, it turns out to look like a thermal state at the Unruh radiation temperature.

The reference from which I first learned all this is Wald's monograph, Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics. Unfortunately I have never found it online and I don't know of a good online discussion of the above, although there probably is one.

vanhees71 and ergospherical
ergospherical
Fascinating stuff. I’ll look for the book later this week (I recall it being referenced in H. Reall’s lecture notes); that’s probably more efficient than asking a bunch of groundwork questions here.

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

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.

vanhees71 and ergospherical
ergospherical
Thanks, I can go borrow it but the next couple of days are slightly nuts so probably won’t stop by the lib until the weekend. :)

Mentor
Thanks, I can go borrow it but the next couple of days are slightly nuts so probably won’t stop by the lib until the weekend. :)
If you can get through the book in a weekend you are definitely quicker at it than I am.

vanhees71
One thing or watch for in discussions of the equivalence principle is that it is local in time as well as space. Ohanian, for example, has published a number of alleged refutations of the principle that other physicists reject because they ignore the time element.

Orodruin, vanhees71 and PeterDonis
Gold Member
Does the equivalence principle extend to all theories of quantum gravity?
Does it extend to any theory of quantum gravity?

vanhees71 and PeroK