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I was recently thinking of a thought experiment:

Assumptions

  1. Graviton detectors can exist
  2. The equivalence principle will hold in the final theory of quantum gravity
  3. We can accelerate the graviton detector

Thought Experiment

Lets say I have a graviton detector (it detects the number of gravitons). In presence of a gravitational field we expect it to detect the graviton. However, in absence of a gravitational field we can also make it detect gravitons by accelerating the detector (by the equivalence principle). However, if we accelerate the detector then how many times will the detector "click"? Will it "click" at all?

Resolution

  1. If it clicks (under acceleration): it will imply that acceleration too is quantized
  2. If it doesn't click: It would imply there is no such thing as a graviton or a graviton detector (personally I think there's no need for a "or"). It could also imply the equivalence principle does not hold.
  3. It is impossible to accelerate the graviton detector and for it too remain a graviton detector: I don't think this is likely but wrote it for completeness sake

Question

Is the premise of the experiment even correct? (I think I must be missing something)? If it is correct what is the resolution of the paradox?

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  • $\begingroup$ I am afraid that the reality of quantum gravity is a little bit more complicated than that, but you are kind of on the money that a graviton detector would click when it is being accelerated. Having said that, the energy of an individual graviton at macroscopically achievable accelerations is far too small to be measurable directly and graviton detectors of this kind will remain elusive. That's no different from detectors for low energy photons, by the way. Even the most sensitive bolometers today can not resolve individual photons much below the THz range. $\endgroup$ – CuriousOne Jan 31 '16 at 10:17
  • $\begingroup$ @CuriousOne If I get you right you say it will click but you don't seem to agree that would imply acceleration would be quantized. Can you elaborate more on this point? $\endgroup$ – drewdles Jan 31 '16 at 10:27
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    $\begingroup$ I am not a theorist, so I can't give you the details, but when you want to quantize gravity, you aren't quantizing the variables of classical mechanics (like acceleration or position), but those of general relativity, i.e. the values of tensor fields. Direct quantization doesn't seem to work, but one seems to be able to quantize a transformed version of the field equations. The quantized entities become small pieces of area and volume (rather than distance). Classical variables like acceleration then become expectation values over macroscopic pieces of matter. $\endgroup$ – CuriousOne Jan 31 '16 at 10:35
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Your experiment looks ok to me. There is no resolution of the paradox, so it's one way to look at the root of the 'quantize gravity problem'.

Another experiment with the same detector: If the detector is in on a shelf, when it drops off the shelf, it is supposed to mysteriously stop seeing gravitons, even though the 'flux' has not changed. Note that the speed of the detector has not changed appreciably when it first starts to fall. "All experimental quantities are unchanged". Your nice question shows why its impossible to create a naive form of quantum gravity.

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  • $\begingroup$ Gravitons aren't detectable from static gravity wells. :( $\endgroup$ – Joshua Nov 21 '16 at 16:16

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