Hawking Versus Unruh Temperature as a Measure of the Health of the Equivalence Principle by Douglas Alexander Singleton

Gheorghe-Sorin Paraoanu

Hi Doug,

I find the point that you raise in your essay extremely interesting.

I even went to read your PRL from 2011 to clarify for myself a few technical points.

Though I think the discussion above with Jack Mallah needs to be continued. I would like to reformulate a bit here what is at stake. Suppose that we are in an Einstein's elevator: the equivalence principle tells us that we cannot know if we are in an accelerated system or in a gravitational field - the physics that we "experience" is the same. Yet one can simply open the door of the elevator and check what is the actual situation: are we standing on some planet or are we in some accelerating spaceship, etc. Is the measurement of the Unruh versus Hawking temperature and correlations that you describe in any way different from the situation described above? Somewhat I would think that what happens is that you find a way to extract global information from a local measurement of the radiation. This is still interesting of course, but does it mean at all that the equivalence principle is broken? In some sense, there could be something more fundamental here that I am not catching, for example one would think that the Hawking and Unruh effects are a inescapable consequence of QFT, therefore the situation is different from just opening the door of the elevator and acquiring information about the surroundings. In this sense one can say that global information will inevitably be present in any local frame. Though I find this argument weak, because also with the Hawking/unruh radiation I can choose to shield them by "metalizing" my elevator (making it a Faraday cage).

[deleted]

Hi Gheorghe,

Thanks for reading my essay and as well the journal paper which was the basis of the first part of the essay.

In regard to your question " Is the measurement of the Unruh versus Hawking temperature and correlations that you describe in any way different from the situation described above?"

My contention is that it is different. The Unruh-DeWitt allows one to make local measurements of the temperature and transition rate. The physical picture I like to keep in mind for the UD detector is an electron in a magnetic field. This has two states and one can measure the rate at which the upper state gets excited in a particular space-time (e.g. Schwarzschild) or for a particular space-time path (Rindler observer). The conceptual reason for why the local measurement with an UD detector can obtain global information about the space-time or space-time path is that its transition rate depends on the field modes which depend on the global structure of the space-time or space-time path. Also QM in general has non-local features (such as entanglement) and the EP is local.

The question of shielding the radiation is interesting and I have not fully understood this. Certainly, under normal circumstances, one can shield the UD detector from Hawking radiation (By "under normal conditions" I mean at all points in the BH evaporation process except at the very end when it will emit gamma rays of increasingly high energy and short wavelength. At some point the wavelengths of the gamma ray photons emitted by the small BH will be much smaller than the interatomic spacing and it will not be possible to shield them).

On the other hand I am not sure if it is at all possible to shield an UD detector from Unruh radiation.

Best,

Doug

Sergey Fedosin

If you do not understand why your rating dropped down. As I found ratings in the contest are calculated in the next way. Suppose your rating is [math]R_1 [/math] and [math]N_1 [/math] was the quantity of people which gave you ratings. Then you have [math]S_1=R_1 N_1 [/math] of points. After it anyone give you [math]dS [/math] of points so you have [math]S_2=S_1+ dS [/math] of points and [math]N_2=N_1+1 [/math] is the common quantity of the people which gave you ratings. At the same time you will have [math]S_2=R_2 N_2 [/math] of points. From here, if you want to be R2 > R1 there must be: [math]S_2/ N_2>S_1/ N_1 [/math] or [math] (S_1+ dS) / (N_1+1) >S_1/ N_1 [/math] or [math] dS >S_1/ N_1 =R_1[/math] In other words if you want to increase rating of anyone you must give him more points [math]dS [/math] then the participant`s rating [math]R_1 [/math] was at the moment you rated him. From here it is seen that in the contest are special rules for ratings. And from here there are misunderstanding of some participants what is happened with their ratings. Moreover since community ratings are hided some participants do not sure how increase ratings of others and gives them maximum 10 points. But in the case the scale from 1 to 10 of points do not work, and some essays are overestimated and some essays are drop down. In my opinion it is a bad problem with this Contest rating process. I hope the FQXI community will change the rating process.

Sergey Fedosin

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