# B What limits the speed of a gravity wave to C

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1. Jun 2, 2017

### Rochelobe

The speed of light (in the vacuum) is a function of the permeability and permittivity of the vacuum. In other mediums the phase velocity will be different. It is assumed (by me) that the speed of a gravitational wave does not change depending on the medium i.e. a gravitational wave would not slow down while passing through the sun. This would cause diffraction and presumably dispersion of the wave. Why then is the speed of a gravitational wave limited by the speed of light in a vacuum? How did Einstein come to this conclusion?

2. Jun 2, 2017

### Staff: Mentor

Actually it's the other way around - the numerical values that we assign to the permeability and permittivity of the vacuum are determined by the speed of light. (That's not how these ideas were developed historically; it is only with the befit of hindsight that we could properly understand the role of the speed of light).
Einstein came to this conclusion the same way that Maxwell came to his conclusion about electromagnrtic radiation: he solved a differential equation and the answer came out to be waves travelling at speed $c$. It just about has be that way because gravitational waves must have the same property that light does, of having the same speed for all inertial observers regardless of their relative speed; and it is mathematically impossible for there to be more than one such speed. It's a historical accident that we call that one invariant speed "the speed of light"; it would be more accurate to call $c$ "the invariant speed that both light and gravitational radiation travels at". (The historical accident is that we knew the speed of light long before we knew what light was or that we were measuring the invariant speed limit of the universe, so we had already formed the habit of calling that particular speed "the speed of light").

3. Jun 2, 2017

### Orodruin

Staff Emeritus
To be fair, he only needed to find the appropriate differential equation and see that it is what we usually refer to as the wave equation. From there you already know the phenomenology and can identify the speed of the waves.

4. Jun 3, 2017

### vanhees71

Permeability and permittivity are just an artifact of our men-made SI units. They are conversion factors to the natural units.

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