# “Speed” of Gravity and Speed of Light

• The speed of gravity was not measured until today (at least there are no undebated papers to that effect).

• It seems common knowledge/belief among physicists that the speed of gravity is the same as the speed of light.

And this is my question: Is that speed of light = speed of gravity a result of GR or is that fed into the theory? Or is there some evidence from other sources than GR for this? Does the same speed imply some deep-lying relation between gravity and electromagnetism?

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Note that Newtonian gravity moves at infinite speed. –  Carl Brannen Mar 17 '11 at 0:45
duplicate? physics.stackexchange.com/q/5456 –  endolith Nov 18 '11 at 5:15

The special theory of relativity is really enough to see that gravitational signals have to propagate by the speed $c$ which we call "speed of light" because the light is the most commonly understood entity that is moving by this maximum speed. Special relativity is OK to describe infinitesimal deformations of spacetime.

All other massless particles also have to propagate by the same speed $c$ because this speed $c$ is needed to enhance the vanishing rest mass to a finite total relativistic energy. And gravitons are inevitably massless because they don't pick any preferred reference frame - or, alternatively, because gravity is a long-range force. Massive particles could only induce short-range forces (similar to the weak nuclear force caused by W,Z bosons).

Any particle - e.g. neutrino - whose energy is much greater than the rest mass is moving nearly by the speed of light, too. The same thing would hold for massless scalar particles such as the "moduli" (their quanta) if they existed. It's an elementary consequence of the formulae of special relativity. The speed of light is the maximum speed that the information and material objects may pick, by causality, and it's also the typical speed that massless (exactly) and light (approximately) particles actually choose.

So the answer to your last question is No, the appearance of the same speed $c$ doesn't imply any additional dynamical relationship between electromagnetism and gravity - it's a direct and elementary consequence of the special theory of relativity - and its kinematics - that was fully understood in 1905. The importance of the speed $c$ in the scheme of things - because of special relativity - is so high that adult physicists use units in which $c=1$ and they are never ever surprised when $c$ plays an important role - it's exactly the same degree of "surprise" as if the number $1$ appears somewhere in maths.

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You could,theoretically, have a theory of gravity where the graviton is massless, and then gravity would propagate with $v<c$. That gravitational signals propagate with $c$ is most certainly a result derived from GR (and most competing theories of gravity, admittedly). –  Jerry Schirmer Mar 16 '11 at 23:55
@Jerry Schirmer, Is this a typo? Didn't You want to say ""where graviton is not massless? –  Georg Mar 17 '11 at 9:31
@Georg: yes. That indeed is a typo. –  Jerry Schirmer Mar 17 '11 at 16:08
Dear @JerrySchirmer, if the "graviton" were massive, then the force wouldn't decrease as $1/r^2$ but approximately exponentially and it wouldn't be long-range. Consequently, it would never be called "gravity" because it wouldn't produce a detectable force from the planets. Gravity means that it is a long-range force linked to the spacetime geometry, as we know from Einstein, and such a graviton has to be massless. –  Luboš Motl Aug 30 '13 at 9:55
We may also use the word "gravity" in a generalized way - surely for massive KK modes of higher-dimensional gravity and perhaps for speculative theories with massive spin-2 particles - but it is not "the" gravity. –  Luboš Motl Aug 30 '13 at 9:56

I think the main argument would be causality. If gravitational disturbances traveled faster than light, presumably you could use them to convey information backwards in time. Although now that I think about it, that argument is based on special relativity. I can't think of a reason it wouldn't carry over to GR, but I don't know whether anyone has explicitly checked.

You can derive from GR the fact that gravitational waves (disturbances in the weak-field approximation) propagate at speed $c$.

I'm not aware that any experimental measurements have been done, since gravity is a weak force and is difficult to measure. Building a "gravity telescope" is a lot more complicated than a regular telescope, although there are plans in place, e.g. LISA, which might be able to detect gravitational waves for the first time, if it gets funded and built.

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Yes, there is another derivation: String Theory. The action and its QFT implies the existence of not only tachyons (which would move faster than $c$), but two massless particles of spin $1$ and $2$ ... the spin-1 particle is the photon, and the spin-2 particle is the graviton (both must necessarily travel at speed $c$ because of their mass).

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