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Look at photons as an anology: you can manipulate matter using light in various ways: Light sails, optical tweesers, etc.

Now since a laser (or radio beam) can be seen as an oscillating E field and B field, and electrons are affected by the E field, all kinds of fun ensues.

A coherent beam of gravitons would have an Eg and everything is “charged” as far as the gravitational force is concerned, so why, fundimentally, is this not possible?

Likewise, why don’t gravitational waves slow down when passing through matter, since the mass should interact with the Eg field?

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    $\begingroup$ Why you think it is not possible? Regarding speed, they do not slow down because of the same reason photons do not slow down. $\endgroup$ – Anixx Dec 5 '16 at 2:14
  • $\begingroup$ Don't photons, effectively at least, slow down in materials such as glass?. $\endgroup$ – user108787 Dec 5 '16 at 2:53
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    $\begingroup$ @CountTo10 yes, that is discussed on several questions here. The E field interacts with the electrons and gices rise to quasiparticles called polarons. So, since matter reacts to gravity (from the Eg field) I ask the final paragraph of the post. $\endgroup$ – JDługosz Dec 5 '16 at 5:45
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They do not slow down, the polarons or virtual photons are just ways of describing the interactions inside the material, the scatterings, absorption and re-emissions. Any photon goes at c or does not exist. The slower speed is the macroscopic effect of all the interactions.

Same for gravitons. But gravitons interact weakly, about $10^{40}$ times weaker than electrons, so you'd see much less of an effect, if we could measure it. They do do stuff, they move matter (yes, as Feynmann showed they can do work), that is how we detected the gravitational waves in LIGO.

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