What properties of space determine gravity velocity?

[Emu]

It is my understanding that the velocity of gravity is assumed to be that of electromagnetic velocity i.e. “c” in General Relativity. We know from experiments that space has the properties of permittivity (electric capacitance per length) and permeability (magnetic inductance per length) and that these properties store energy by acting as inertia in conjunction with a restoring force. We also know that these two properties of space fix the velocity of electromagnetic waves to “c”. My question is; what properties of space determine the velocity of gravity?

 

[tiny-tim]

Welcome to PF!

It is my understanding that the velocity of gravity is assumed to be that of electromagnetic velocity i.e. “c” in General Relativity. We know from experiments that space has the properties of permittivity (electric capacitance per length) and permeability (magnetic inductance per length) and that these properties store energy by acting as inertia in conjunction with a restoring force. We also know that these two properties of space fix the velocity of electromagnetic waves to “c”. My question is; what properties of space determine the velocity of gravity?

Hi Emu! Welcome to PF!

Isn't it the other way round?

Isn't it the speed of c for electromagnetic waves that determines the permittivity and permeability of space?

 

[Nickelodeon]

It is my understanding that the velocity of gravity is assumed to be that of electromagnetic velocity i.e. “c” in General Relativity.

I would have thought that the speed of gravity is variable and dependent on the mass of the local celestial body.

If you drop a stone, say a few light years away, and assuming the Earth and the stone are the only things in existence, then it can't be too difficult to work out when and what speed the stone will eventually hit the Earth (for instance). That surely will be the 'local' gravity speed? I doubt if it will be anywhere near'c'.

 

[tiny-tim]

I would have thought that the speed of gravity is variable and dependent on the mass of the local celestial body.

If you drop a stone, say a few light years away, and assuming the Earth and the stone are the only things in existence, then it can't be too difficult to work out when and what speed the stone will eventually hit the Earth (for instance). That surely will be the 'local' gravity speed? I doubt if it will be anywhere near'c'.

Hi Nickelodeon!

No … he doesn't mean the speed of things moving under gravity … he means the speed of gravity itself.

For example, if the sun were to split in two, how long would it take before the gravitational effect was noticed on Earth?

 

[Emu]

Hi Emu! Welcome to PF!

Isn't it the other way round?

Isn't it the speed of c for electromagnetic waves that determines the permittivity and permeability of space?

It is my understanding that Maxwell first proposed the square of the speed of light to be equal to one over the permittivity times the permeability and that Hertz then did the experiments to confirm this equation. Being an equation, both sides are equal so determining the speed of light and using a constant of 4pi times 10 to the minus 7th power for the permeability allows us to determine the constant for the permittivity. It is also my understanding that the rational for this is to facilitate the use of easy to measure metrics such as meters as a function of the wavelength of a particular frequency of light. As far as which “came first”, it seems the change in permittivity and permeability change the speed of light in materials so I would presume that the properties of space may be determining factors.

 

[Emu]

I would have thought that the speed of gravity is variable and dependent on the mass of the local celestial body.

If you drop a stone, say a few light years away, and assuming the Earth and the stone are the only things in existence, then it can't be too difficult to work out when and what speed the stone will eventually hit the Earth (for instance). That surely will be the 'local' gravity speed? I doubt if it will be anywhere near'c'.

The "speed of gravity" usually is in reference to the time of flight for a gravitational event to reach a distant observer and also is the foundation for gravity waves. For example, if a very large mass was ejected from a star, would the gravity change be detectable first or would the light from the event be seen first or would both observations occur simultaneously. On the subject of gravity waves, if there is no property of space to store the gravitational energy even for a short while, then space cannot delay the effect of gravity and the possibility of gravity waves is greatly reduced.

 

[Mentz114]

It has to be Newton's G, surely ?

 

[HallsofIvy]

Not in relativity. There is no (number) "G" in relativity. You could argue that it would be Einstein's G tensor but that is determined by the local metric tensor so you wind up arguing that the speed of gravity over a path is determined by the local metric tensor at each point on that path which is true of everything!

 

[Mentz114]

Not in relativity. There is no (number) "G" in relativity. You could argue that it would be Einstein's G tensor but that is determined by the local metric tensor so you wind up arguing that the speed of gravity over a path is determined by the local metric tensor at each point on that path which is true of everything!

What about Einstein's $\kappa$ (kappa)? It certainly occurs in GR. But there isn't anything like mu₀ or epsilon₀.

Can Newtons G be considered a property of space-time, or is it just a constant of proportionality that fixes the dimensions ?

M

 

[Alex_B]

It is my understanding that the velocity of gravity is assumed to be that of electromagnetic velocity i.e. “c” in General Relativity. We know from experiments that space has the properties of permittivity (electric capacitance per length) and permeability (magnetic inductance per length) and that these properties store energy by acting as inertia in conjunction with a restoring force. We also know that these two properties of space fix the velocity of electromagnetic waves to “c”. My question is; what properties of space determine the velocity of gravity?

If we consider vacuum Maxwell's equations, we get solutions of EM waves with velocity cm if we consider Maxwell's equations in medium, we also may get wave solutions, correspoting to slower phase velocity, the speed of propagation of a signal remaining the same (equal to c!). In gravity, if we consider gravitational equations in medium, we may get solutions with lower phase velocity than c (perhaps), but velocity of gravity will remain c actually.