Big problem in gravity

[mourici]

Suppose a gama ray transformed into a positrom and electron , both have a positive rest mas ,so space time is bend a little according to Aienstien . Suppose now electron and positron combined again into a gamma ray and rest mass disappear spontaniously. the space time becomes plannar again. The quation is how the gravitation wave behaves in what direction and speed gravitation wave move and whats happens to gravitons , that leave a body with rest mass and move back to a the same place but mass dissapears/

[Spyman]

According to the theory of General Relativity by Einstein, energy bends spacetime equally as mass.

 

The gamma ray is already bending spacetime and the energy released by the annihilation will also bend spacetime to the same degree as the total mass of the electron and the positron.

 

Gravity waves travels with the speed of light in vacuum.

 

Gravitons is still considered a hypothetical particle.

 

http://en.wikipedia.org/wiki/General_relativity

http://en.wikipedia.org/wiki/Gravitational_wave

http://en.wikipedia.org/wiki/Graviton

[ajb]

Photons carry energy-momentum and so couple to the space-time metric via the field equations. I don't think that space time becomes "plannar" as you put it when a positron and electron annihilate. What Spyman says is correct, at least not very close to the pair you would not notice any effect.

 

I don't know how you could calculate what happens. You could certainly study QED on a fixed background or maybe even get some low order results if you coupled linearised gravity to QED. The second approach would be the only way to tackle what happens to gravitons.

[lakmilis]

hmm, but does relativity predict graivty waves travel at speed of light? I thought newtonian mechanics did so and that was some of the problems with it, gravity acts with respect to some objects position earlier in time , a ct distance away from the other body....

[timo]

hmm, but does relativity predict graivty waves travel at speed of light?

Yes, some approximations do.

 

I thought newtonian mechanics did so ...

I don't think so.

 

and that was some of the problems with it, ...

The commonly expressed problem is that newtonian gravity would allow for instantaneous reaction following from some action at some distant place, e.g. when the source of gravity moves.

 

Gravity acts with respect to some objects position earlier in time , a ct distance away from the other body....

It's actually desirable to have reactions follow to events in the past. The reason is that there are three classes how two different events E1 and E2 can be connected:

1) E1 came before E2.

2) E2 came before E1.

3) Depending on your point of view (in smart: "Frame of reference") either E1 came before E2 or E2 came before E1 or they both happened simultaneously.

 

From 3) you can see the relativistic problem with cause and effect happening at the same time: If you label one of those events as cause and the other as effect, then depending on your point of view, the cause can happen before the effect, can happen after the effect (which is considered non-sensical) or at the same time. A "physically real" simulaneously between E1 and E2 cannot exist.

[swansont]

Newtonian gravity predicts infinite propagation speed.

[lakmilis]

Newtonian gravity predicts infinite propagation speed.

 

yes swansont, thats what I thought [and meant] sorry.

 

to atheist, ok, sorry my mind is getting rather tired, heading to bed soon.

[timo]

Newtonian gravity predicts infinite propagation speed.

I am not sure I'd suscribe to that statement. It boils down to the question how you define "propagation speed":

Propagation speed of what? I classical physics, you can (at least I think so, I'm not completely sure about that) take a test-mass and a source of gravity at postion x and then instantaneously displace the source to y. In the same instant, the gravitational field at the test-mass will change. You could possibly interpret that as infinite speed with which the information about the gravitational field changed. You can try to do exactly the same thing in GR using the Schwarzschild metric instead of the term for Newtonian gravity and get exactly the same result, the difference being that the instantaneous displacement is invalid (and also kind-of violates the assumptions put into the Schwarzschild metric) - for basically the same reasons that the example would be invalid in electrodynamics (violation of equation of continiuity equation and omission of the motion-dependent part of the potential).

That's basically the same discussion we had about electrostatics/electrodynamics some time ago. There (in the relativistic theory of electromagnetism), the speed of propagation is understood (more precisely: Has been understood by me, so far) as the speed of the wave resulting from the wave-equation [math] \box A_\mu = 0 [/math] in the Lorentz gauge, from which v=c follows. In a suitable approximation of GR, you get the similar wave equation [math] \box \psi_{\mu \nu} = 0 [/math] in harmonic gauge (where [math]\psi[/math] is defined by [math] g_{\mu \nu} = \eta_{\mu \nu} + \psi_{\mu \nu} [/math], g being the metric and eta being the minkowsky metric), also leading to waves with v=c. Problem: Starting from this understanding of "speed of propagation", how do I translate this understanding to classical electrostatics or Newtonian gravity? What would the wave solutions (for a wave with infinite speed) be? 1? exp(-wt)? A exp(-wt) + B exp(wt)? Something else?

 

Or simply stated: How do you define and understand propagation speed such that the same term has a meaning both in classical and relativistic theory?

[swansont]

Newtonian gravity doesn't have retardation; the force you feel depends on where the mass is now. If the mass moves (and it doesn't have to be instantaneous motion) the force changes immediately, unlike in electrostatics, and this requires infinite propagation speed. GR gets around this problem because the curvature is always present, and the retardation effects appear only when the mass is accelerated, AFAIK.

[timo]

Hm, we might be talking about different things. When comparing electrostatics and newtonian gravity, I am talking about a potential "V = some_constant * charge_of_source / distance" for both cases (with V charge being electric charge and mass, respectively).

[swansont]

Propagation speed, as I was using it, is how fast does a change in the source configuration show up as an effect at some r. Or, where does the force vector point — it should point at where the source was at t = d/v (but that, of course, is where GR deviates from Newton — mass doesn't affect motion directly; mass warps space, and warped space affects motion)

[Farsight]

Gravity is normally considered to be "curved spacetime", but I like to think of it as the "reaction" to "action", the latter being closely associated with energy. This energy might be in the form of a 1022KeV gamma photon, or an electron/positron pair. It doesn't matter which. This energy propagates at a maximum velocity c. If the action is limited to c, then I can see no way in which the reaction can move any faster. The two are always intimately linked. So I can't envisage a change in gravity propagating at a velocity that exceeds c.

[timo]

Still off-topic and supposed to end my little off-topic disgression:

 

Intuitively, the notion of "infinite propagation speed", which suggests being some limit of some however-defined propagation speed, seems as if it might create problems. The two meanings of propagation speed sketched (speed of the solutions of the free wave equation and the "instantaneous change" of the field) might be incompatible (for that there seems to be no such thing as a free wave equation in Newtonian gravity in the one direction and no such thing as "identify field at (x,t2) with the one being created by a cause at (y,t1)" in the other direction of equivalence).

Yet, since you can approach the field equation of Newtonian gravity by something like [math] \left( \lim_{a \rightarrow 0} a \partial_t^2 - \nabla^2 \right) V \sim \rho [/math], the two meaning might be compatible in the end. Right now, I'm a bit confused on how "speed of gravity" and similar terms should be understood (and if they have a comparable meaning in relativistic and non-relativistic theories at all). I'll have to think about it and will probably start a seperate thread about it in case I come to some noteworthy conclusions.

[lakmilis]

well, like I said, I confused myself earlier, but what swansont is saying is that in classical physics there is no retardation of the gravity vector between two objects, i.e. no matter how fast the two objects displace w.r.t each other, the gravity vector instantenously follows the direct line between the two...the straight line being in newtonian space..or I guess I should rather say Euclidean.