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First, we shoot a collection of particles (let's exclude gravitons from these, just for the sake of clarity) through a large region of spacetime in which the stress-energy tensor is zero and make them impact on a screen somewhere far away. A pattern will emerge.
Then we do the same with a second collection of particles (as much as possible identical to the first collection) but this time a gravitational wave is present.

We can vary a number of things. We can choose different particles (from photons to atoms). We can let the momenta of the particles have different angles (though they all are moving parallel wrt each other) wrt the direction in which the gravitational wave propagates. The same can be done but wrt to the screen. You can also vary the distance between the screen and the wave. The same can be done for the source of particles. For sure there will be different patterns visible in both cases. For example when the screen is placed far enough. Or not? Is it possible to detect gravitons with this construction (or, equivalently, to rule them out)?

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    $\begingroup$ This setup isn't very clear to me. Are you asking if you can do the double slit experiment with gravitons? If so the answer is in principle yes if you can produce a collimated beam of gravitons, develop a material that absorbs them with high probability so that it makes sense to talk about slits, and reliably detect them on a screen. In practice you will have major problems with all three of those steps. There's an interesting paper by Freeman Dyson about how it may be impossible in principle to detect gravitons: inspirehep.net/literature/1257811 $\endgroup$ – Andrew Apr 25 at 11:47
  • $\begingroup$ @Andrew You have: a collection of particles, confined to a volume. You try to make the collections look as much as possible the same. The collections are sent through space to a screen. One collection after the other. Without a gravitational wave, you'd expect a different pattern to be seen on the screen than with a wave. $\endgroup$ – Deschele Schilder Apr 25 at 12:03
  • $\begingroup$ How are you going to find a region of spacetime with zero energy momentum tensor? Just shooting the particles themselves guarantees that isn't true, not to mention things like the CMB/CNB that are ever present. $\endgroup$ – Triatticus Apr 25 at 12:41
  • $\begingroup$ @Triatticus Well, let's assume two spacetimes as empty as possible. They only differ by the presence of a gravitational wave.Of course the spacetime is not empty anymore when we shoot the particle field through it. The fields are tried to make as identical as possible. $\endgroup$ – Deschele Schilder Apr 25 at 12:56
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    $\begingroup$ @DescheleSchilder I'm still confused, are you trying to detect gravitons or gravitational waves (classical coherent states of gravitons?). When you "shoot a particle", what particle are you shooting? $\endgroup$ – Andrew Apr 25 at 13:13
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The problem is not the particles, it is that one cannot control and focus a gravitational wave. The gravitational waves detected by LIGO, the first evidence of gravitational waves, were coming from the merging of two black holes .

There is no way to detect or predict such occurrences, and the LIGO "screen" is continents long.

Gravitons are another layer of complexity , at the moment experiments are trying tof find their existence through polarization of the cosmic microwave background radiation. Having a beam of individual gravitons interact with individual particles is science fiction.

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  • $\begingroup$ What about projecting a photon field onto a screen? Isn't it possible to detect small spacetime fluctuations between the source and the screen? If the photon field stays constant (?) you would think that the observed pattern on the screen is changed when a gravitational field passes. $\endgroup$ – Deschele Schilder Apr 25 at 14:54
  • $\begingroup$ read the Ligo experiment, that is what happens, two perpendicular laser paths are interfered differently because of the spacecurvature changes from the gravitational field. Gravitons are another story. $\endgroup$ – anna v Apr 25 at 15:27
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You are describing LIGO: a beam of photons is sent through an empty region and allowed to interfere with a reference beam. When gravitational waves arrive they cause a shift of the interference fringes.

You may want the wave to be fully inside the test chamber rather than affecting it as a whole, but note that the effect of the wave - periodic changes in the distance to the target - happens in either case.

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I don't think you can produce gravitational waves at will. At least, strong enough to be measurable. Also, the setup used to measure gravitational waves is extremely sensitive and precise, because they are very weak. Noticing if a gravitational wave has any impact on a beam of particles is basically impossible at the moment, considering on top of everything else that those same particles will interact with each other with other forces.

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