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“Speed” of Gravity and Speed of Light

I'm wondering if gravitational waves have the same speed of light? They must if gravity is mediated by a graviton spin 2 massless boson. One can argue that since gravity is a long range force, then its boson must have zero mass. But neutrinos travel through the universe too and despite their tiny mass yet have non zero mass. So, I'm wondering if there is a deeper justification for believing that gravity's speed =c?

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marked as duplicate by Qmechanic, David Z Apr 14 '12 at 21:47

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Well, if you are on board with GR, and you are on board with gravity waves, take a look at the gravitational wave equations's derivation and consider the meaning this equation has. It hasn't changed, it's still the wave equation. If we open up the D'lambertian, it's $$\Box=\boxed{\frac{1}{c^2}}\frac{\partial^2}{\partial t^2}-\nabla^2$$ In one sign convention, and remember that the wave's velocity squared is the inverse of that thing by the time derivatives. That's $c$. Why doubt GR, or the wave equation at this point? Especially in the classical regime.

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