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From Casimir effect, we know that when two plates are placed very close to each other in vacuum, they attract each other because the quantum fluctuations that press on the two plates' outer surfaces outweigh the quantum fluctuations on the inner surfaces. A recent paper published in Physical Review Letters by James Q. Quach (as reported by APS Physics synopsis) claims that:

New calculations by James Quach at the University of Tokyo, Japan, suggest that a gravitational Casimir attraction might be observable, provided the two mirrors have the unusual property of being able to reflect gravitational waves. Conventional solids would be transparent to the gravitational field. But theorists have suggested that superconducting materials may behave differently: the passage of gravitational waves through a superconductor would cause Cooper pairs, which are highly delocalized quantum objects, to move in a different way than the localized crystal ions. This effect, according to a recent proposal, could turn a thin superconducting sheet into an efficient reflector for gravitational waves.

Now here lies one of my doubts. Casimir effect, as we know, stems from Quantum Electrodynamics thereby proving the existence of virtual particles. How exactly can it claim to predict the existence of gravitational waves? Because as far as I know, Casimir effect has got nothing to do with gravitation.

The APS Physics synopsis further goes on to say that:

Building on this idea, Quach analyzed a scheme in which two films of superconducting lead, each a few nanometers thick, were separated by several micrometers, He calculated the gravitational contribution to the Casimir force that pulls the films together and showed it could exceed the electromagnetic one by an order of magnitude.

How exactly can we distinguish gravitational Casimir effect from the electromagnetic one (because if the former exists then the later would exist as well)? And, how come the gravitational Casimir effect (if it exists) outweigh the electromagnetic one?

The APS Physics synopsis further goes on to say that:

An experimental realization of his scheme could, he argues, offer a way to test quantum gravity theories and search for gravitons (the hypothetical quantum particles that mediate gravity).

Based on what I know, quantum gravitons are only in the linearized theory and perturbative Quantum Gravity. Even if we find it, would it change much of the problems for physicists working in the field of Quantum Gravity? Because based on the little I know, it took a lot of effort and time to quantize the electromagnetic field even though we discovered photon long ago. Also, hypothetically speaking, what would the result be if we replicate the same experiment (as proposed by James Q. Quach) in a BTZ black-hole? Since, a BTZ black hole in 2+1 dimensions has no propagating degrees of freedom, so there are no gravitons.

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  • $\begingroup$ Related: physics.stackexchange.com/q/167142/2451 $\endgroup$ – Qmechanic Feb 26 '15 at 10:37
  • $\begingroup$ Gravity is actually quite nicely and unambiguously quantizable on the energy scales needed for the computation of zero-point fluctuation and confirming at least the existence of such fluctuations beyond experimental doubt would be a strong proof of the fact that gravity is quantized at all. The fact is, however, that the "gravity-wave mirror" would probably be still not very efficient and the resulting fluctuations due to gravity beyond measurability. But I haven't been through the proposal of the mirror or the article, so don't take my word for it. $\endgroup$ – Void Mar 1 '15 at 19:07
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I cannot answer to all the questions but would like to stress something regarding what the Casimir effect tells us and what it doesn't.

If you look at how it is derived for the usual EM interaction, an experimental verification of the standard Casimir effect tells us that:

  • the EM field can have standing waves between two plates and outside them

  • There still exist such waves even in absence of an (average) EM field between and outside the plates at T = 0 i.e. there does exist zero point fluctuations of the EM field

There is nothing really about the actual existence of virtual particles. Of course, one can derive the Casimir interaction by expressing everything in term of photons; that's very convenient and maybe closer to reality than a wave picture (I personnaly do not think so but hey who knows...) but the Casimir interaction doesn't allow, as far as I understand it, to discriminate these two pictures.

Thus regarding gravity, if a Casimir-like effect were to be found, it would mean that there exist standing gravity waves between two plates and that the gravity field experiences zero point fluctuations which would be already awesome. Whether the zero point fluctuations can be captured by the graviton or virtual graviton concept is another problem.

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The key to the effect is the idea - really just a conjecture, and as the paper states, "these ideas have not been met without controversy" - that there are materials that are opaque to gravity waves in the same way that conductors are opaque to EM waves. If that's true, then the cavity between parallel plates will contain a reduced set of modes of the zero-point fluctuation relative to the region outside of them, just like in the EM CE, and there will be inward pressure. There exist theories/models of how classical matter and quantum fluids interact with gravity waves, and Quach uses those models to predict the magnitude of the effect. That's how he can distinguish between the gravitonic CE and the photonic CE. According to the model he uses, the gravitonic contribution dominates the photonic contribution by an order of magnitude for plates of superconducting lead 2 nm thick, separated by a distance on the order of microns. His proposal, then, is to repeat existing experiments under superconducting conditions and see if the order of magnitude of the CE matches the prediction including both the gravitionic and photonic contributions, or only the prediction including just the photonic prediction.

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I have read the paper and the gravitational explanation of the Casimir effect is not the main point, it's the experiment that provides evidence of the graviton's existence.

The paper starts by drawing a macroscopic analogy between Maxwell's equations and Einstein's linearized field equations (known as gravitoelectromagnetism). The author uses GEM because of something called the Heisenberg-Coloumb effect which uses a superconducting medium between two plates to prove the electromagnetic explanation of the Casimir effect. When some physicist decides to do the experiment the existence of the graviton depends on whether the EM or the GEM explanation is correct.

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