It has been my understanding that gravitational waves require a time varying quadrupole moment because the gravitational field has a retardation correction for both constant velocity and constant acceleration. This is unlike the electric field which only has a correction for constant velocity and therefore admits dipole radiation.
However the following link (and many others I have found) say that the quadrupole moment is required due to conservation of momentum. This explanation eludes me could someone explain?
“The gravitational waves are generated by accelerated masses as electromagnetic waves are produced by accelerated charges However, due to momentum conservation in a closed system, a gravitational dipole is not able to radiate. The first multi-pole component which produces waves is the quadrupole.”
Well, you can’t really make a gravitational dipole. When you move one mass back and forth (analogously to moving a charge back and forth to make EM radiation), there is always some other mass moving back and forth in the opposite direction. By conservation of momentum, the dipole contribution of this other mass always exactly cancels that of the first mass.
In the EM analogy, it would be like always having an equal charge moving in the opposite direction, so that the dipoole radition term is canceled.
Believe it or not, I had kind of thought of something like that, but what confused me was that with electromagnetic radiation charged particles are being driven by an electromagnetic field and the electromagnetic field also carries momentum.
On the other hand a time varying electric field sans charged particles will radiate on its own. Also the E field isn’t 180 degrees out of phase with the driven particles………I’m afraid I’m still confused.
Einstein’s general theory of relativity treats gravitation not as a force but as the curvature of space-time, and it’s the best theory we’ve got at this time.
Unfortunately it’s incompatible with QM at planck scales.
If a quantized gravity theory is ever produced (String theory?) then the virtual graviton would be the force carrier analogous to the virtual photon or gluon.
Of course, the quadrapole isn’t the only moment producing gravitational waves, wither, just the dominant one. You can also have octapoles, hexidecimal poles, etc.
The key to momentum’s significance is that if you multiply mass by velocity, you get (more or less) momentum, which is a conserved quantity. If, on the other hand, you multiply charge and velocity, you get something resembling current, which is not conserved.
Currently, gravity is studied in terms of curvature of space-time, but it’s believed and hoped that it’s also in some way consistent with a particle-mediated explanation. Find out how it’s consistent, and you’re likely to get fame, fortune, and babes. Well, OK, fame and fortune.
To clarify the other responses a bit, in classical GR, gravity is curvature of the spacetime, and there are no gravitons. With quantum gravity, it will be a force mediated by gravitons, and curved spacetime is just an approximation to what is really going on, one which gives a very accurate answer when quantum effects aren’t important. You don’t have both gravitions and curved space-time due to mass (or energy and momentum).
Presumably, space-time is then just flat, like what you’d have under special relativity (although you could still have a cosmological constant). I’m not certain on this last part. Actually, certain is a bit of a stretch on the first part too. Fairly certain might be better.
I’d be more inclined to say that gravitons are somehow a property of curved space, a quantum of curvature, if you will. Certainly, there’s some consequences of curvature which are hard to replicate in flat space, no matter what exotic particles you’ve got lying around. Of course, we won’t know for sure until some wise guy (meant in the best sense of the term :)) figures out a successful theory of quantum gravity.
