One of the tenets of Einstein's theory of general relativity is that an observer, carrying out local measurements, cannot determine if they are being accelerated in the absence of gravitational fields or stationary but in the vicinity of a large gravitational field. That is to say, if you are in a locked laboratory with no way to examine the outside, you could not tell if you were sitting on a beach on Earth, or in the back end of a spaceship speeding up at a rate of 32.2 feet per second per second. Some new thought experiments, however, suggest that the "simple" act of measuring temperature may throw this truism into turmoil.

There are a few caveats. First, the gravitational field cannot be so strong, or the reference frame so large, that tidal forces are present (a fancy way of saying that the gravitational field does not change over the range of the observable space). Second, you can only make a local measurement.

Einstein proposed the equivalence principle in 1907, a full nine years before his publication of general relativity. The idea, however, guided the development of general relativity. When combined with Einstein's theory of special relativity, it gave rise to the prediction that clocks will run at different speeds in gravitational fields with differing strengths, and that light would be bent by gravitational fields.

Numerous experiments, measuring all types of phenomena, have proven that the equivalence principle holds. However, a new thought experiment published in a recent version of Physical Review Letters demonstrates that, depending on how you measure temperature, a scientist in the sealed laboratory could tell where she is. On the surface, this result would seem to suggest that the equivalence principle it not valid under all conditions, but there is a wrinkle—the researchers here suggest making a local quantum mechanical measurement. The fact that quantum mechanics is an inherently non-local phenomenon may provide a way of cheating the prerequisites that Einstein put on his equivalence principle.

In the paper, the authors consider two cases: a laboratory that is parked some distance from a Schwarzschild black hole, and one that is being accelerated at a constant value a, equivalent to the gravitational field strength imparted by the black hole at the given distance. Both cases have a temperature associated with them. A black hole isn't really black because it gives off Hawking radiation. A body accelerating through a vacuum will also measure a temperature due to the Unruh effect—which depends on its acceleration.

Turns out that under the conditions for the second case (where spacetime is described by the Rindler metric and a vacuum described by Minkowski space) the temperature measured in the laboratory will be lower than the first case (where spacetime is described by the Schwarzschild metric and an Unruh vacuum state). This presents a local measurement of a non-local phenomenon that seemingly violates the equivalence principle.

However, the Universe proves Einstein is correct as the fixed laboratory moves towards the black hole's Schwarzschild radius, where not even light can escape. As this happens, the accelerating laboratory keeps speeding up to keep the apparent forces the same. In these limiting cases, the temperature measured would become infinite and our intrepid scientist can no longer determine which type of laboratory they are in (fixed or accelerating).

The authors of the paper even give a concise set of directions to use if you are ever trapped in a box and need to know if you are still on Earth or merely accelerating in deep space: "The procedure for an observer equipped with a means of measuring local acceleration and an Unruh-Dewitt detector for measuring temperature is as follows: (i) Measure the local acceleration. (ii) Insert this into (eq. 8). (iii) Measure the temperature via the Unruh-Dewitt detector. If the temperature is higher than that calculated in step (ii) then one is in a gravitational field and not in an accelerating frame."

I suppose a "*some assembly required" disclaimer would be needed on this were it part of an actual emergency kit. The authors conclude by postulating that this result could be "optimistically" taken as a hint that gravity and quantum mechanics begin to merge into a consistent theory of quantum gravitation at high energies or extreme gravitational fields.

Physical Review Letters, 2011. DOI: 10.1103/PhysRevLett.107.081102