# Speed of EM waves differ from GWs?

I understand that light travels at speed c in vacuum, when measured locally. This speed has an exact value, not an approximation, because it is defined as 299 792 458 m / s.

It is an exact value, because the meter is defined as the distance that light travels in a 1/299 792 458th of a second.

Now as per SR, all particles that have no rest mass must travel at speed c in vacuum, when measured locally.

This goes for photons (that build up the EM waves), and the (hypothetical) gravitons (that build up GWs). So both photons and gravitons have to travel at speed c. Both EM waves and GWs have to travel at this speed in vacuum when measure locally.

So theoretically there can be no difference between the speed of EM waves and GWs (assuming they propagate both in vacuum).

Then I found this:

http://iopscience.iop.org/article/10.3847/2041-8213/aa920c/pdf

And it talks about an experimental evidence about non-zero difference between the speed of EM waves and GWs. How is that possible? I thought the speed of light is an exact value, and it has to go for all massless particles.

Question:

1. How can there be experimental evidence of non-zero difference between the speed of EM waves and GWs?
• Quick comment: "because the meter is defined as the distance that light travels in a second" - I understand what you mean by this but the statement is obviously not true - a meter is not 1 light-second. The meter is defined as the distance light travels in 1/299792458th of a second. – enumaris Oct 4 '18 at 17:08
• @ÁrpádSzendrei It’s a good question so I upvoted. I would like to see how they are proven to be non-zero also. Ultimately I believe it will be found that they both come from the same thing or are the same thing. – Bill Alsept Oct 4 '18 at 17:19
• Having looked over the abstract, it seems this paper is talking about constraining an upper bound on the difference of speeds between EM waves and GWs (quite stringent at 1 part in $10^{15}$), and doesn't say that there is a difference in the speeds. Does the paper claim to have found a non-zero difference in the speeds later on? One would think that such a claim would be found in the abstract. – enumaris Oct 4 '18 at 17:36

## 2 Answers

Although I did not read the full paper, there might be some details contribuing to the answer.

In theory light and GW travel with the same speed, but the medium in which they travel is very different. Light travels through the current medium in space. GW perform changes to the space, that travel with the speed of light. So while GW are not affected from a medium, light is.

Now as you would expect the space to be completly empty, it isn't. Particles can form in pairs of particle and anti-particle for short times, due to the Heisenberg uncertainty principle (borrow energy for a short time -> create the mass for particle-anti-particle pairs -> give them back (annihilation) in time). This "fills" the vacuum with virtual particles, which create an effective medium and lowers the speed of light, if interactions of the photons and the virtual particles happen.

Since the paper observes light that traveled an enormous distance, there was enought time for such interactions to happen, hence the GW arrives faster that the photons.

Because GR is just one of the many models of gravity. From the observation of gravity's long range, classical GR is based upon masslessness of graviton. GR is the unique theory of massless spin 2 particles.

But you can give up masslessness and study the ensuing consequences of such a modified theory of gravity. Such models have massive gravitons. This is called Massive gravity.