Gravitational Waves: Speed, Catching Up & Rules

[tionis]

Could I catch-up to a gravitational wave? Do the same rules apply as with light -- meaning the speed of GRs are frame independent, etc?

Thanks.

 

[PeterDonis]

Gravitational waves travel at $c$, like light. So their speed works the same as the speed of light, and you can't catch up to them, just as you can't catch up to a light beam.

 

[tionis]

Thanks, Peter. So can we now say that the speed of gravitational waves not only in vacuum, but everywhere is the same for all observers, regardless of the motion of the producing source?

 

[PeterDonis]

can we now say that the speed of gravitational waves not only in vacuum, but everywhere is the same

In principle, the speed of GWs in a non-vacuum could be different from $c$, just as the speed of light waves in a medium can be different from $c$. However, as I understand it, the deviations are expected to be much smaller for GWs, whereas the deviations for light are easily observable in many materials (for example, the speed of light in water is about 3/4 of its speed in vacuum).

 

[tionis]

Should the speed of gravitational waves now become a new postulate, and if so, would it be of special relativity or general relativity?

 

[bcrowell]

Should the speed of gravitational waves now become a new postulate, and if so, would it be of special relativity or general relativity?

FAQ: Is the c in relativity the speed of light?

Not really. The modern way of looking at this is that c is the maximum speed of cause and effect. Einstein originally worked out special relativity from a set of postulates that assumed a constant speed of light, but from a modern point of view that isn't the most logical foundation, because light is just one particular classical field -- it just happened to be the only classical field theory that was known at the time. For derivations of the Lorentz transformation that don't take a constant c as a postulate, see, e.g., Morin or Rindler.

One way of seeing that it's not fundamentally right to think of relativity's c as the speed of light is that we don't even know for sure that light travels at c. We used to think that neutrinos traveled at c, but then we found out that they had nonvanishing rest masses, so they must travel at less than c. The same could happen with the photon; see Lakes (1998).

Morin, Introduction to Classical Mechanics, Cambridge, 1st ed., 2008

Rindler, Essential Relativity: Special, General, and Cosmological, 1979, p. 51

R.S. Lakes, "Experimental limits on the photon mass and cosmic magnetic vector potential", Physical Review Letters 80 (1998) 1826, http://silver.neep.wisc.edu/~lakes/mu.html

 

[PeterDonis]

Should the speed of gravitational waves now become a new postulate

No; as bcrowell says, the current postulate is not that light travels at $c$, it's that $c$ is the maximum speed of causal influences. Given that postulate, it can be shown that a massless causal influence ("massless" meaning "zero invariant mass") will travel at this maximum speed, and a causal influence with nonzero invariant mass will travel at a slower speed.

 

[tionis]

Thank you, Peter and professor Crowell. I hope to read a FAQ entry about gravitational waves from you guys soon.