The general consensus among scientists is that gravity (or rather gravitational changes to be more precise) travels at the speed of light but in reality no one really knows because it has never actually been measured.
Is there any reason to believe there could be any possibility gravity could be instantaneous? The answer to that is “sort of”, but it’s far too complicated to get into that discussion here. (The phenomena of entanglement also behaves as though it is instantaneous)
This needs to be reiterated. The “speed” of gravity is [apparently] instantaneous; the “speed” of light is also [apparently] instantaneous. But “instantaneous” turns out not to mean anything in spacetime, it’s mediated by an absolute constant called the speed of light.
as I understand it, all particles and mass are interchangeable at some level, eg you can create particles from other particles with various manipulations or change one to another with enough energy input.
Is there any theory which predicts a method by which you might be able to create gravity waves somehow by turning other particles into gravitrons?
A chap named Tom Van Flandern was really big in the “FTL Gravity” field, and it’s not really clear whether he was a crank or just a guy with an alternative theory. I’ve read his lengthy debates with others on the subject, and he handled himself relatively well.
The two big issues are that the GR equations all show gravity as a speed-of-light phenomenon, and there isn’t another working model that has equations showing otherwise…and if gravity moves FTL, then causality can break down allowing consequences to precede their causes. No one feels quite comfortable with that.
Boom-tish. 
Wait, what gravitational influence would a supernova have on us, assuming it’s thousands of parsecs away?
Not much. Apparently two spiralling and merging black holes would “distort the 4 kilometer mirror spacing by about 10−18 m, less than one-thousandth the charge diameter of a proton.”
From the page on LIGO
Yup. It’s kind of ridiculous how sensitive this experiment has to be to be able to detect anything at all. The original LIGO experiment ran for about 10 years and saw no signals. They then turned it off and spent five years upgrading the hardware to make it about ten times more sensitive, and turned it back on last year. The hope is that the increased sensitivity will lead to a much larger rate of signals, i.e., one that is at least one signal per ten years.
Rumors have been swirling around since last fall about a possible detection or two, so let’s keep our fingers crossed.
I don’t know if this is quite what you mean, but you can drop the other particles into a black hole, and then wait for the hole to evaporate out that much mass. Some nonnegligible proportion of Hawking radiation will be composed of gravitons [note spelling].
On the topic of supernovae, a spherically-symmetric supernova would emit no gravitational waves at all. The simplest models we have of supernovae are spherically symmetric, but then, those simplest models also have an annoying tendency to refuse to explode. More realistically, supernovae are almost certainly asymmetric to some degree (such as the core remnant being propelled in one direction, with the ejecta propelled disproportionately in the opposite direction), and that asymmetry would allow them to produce gravitational waves.
EDIT: The “10-18 m” that coremelt quoted should actually say “10[sup]-18[/sup] m”, or ten-to-the-minus-eighteenth-power. It’s not “ten to eighteen meters”.
The observed decay of pulsar orbits Hulse–Taylor pulsar - Wikipedia is consistent with GR (and thus with the speed of gravity being c. I don’t think an instantaneous gravity theory would predict any decay at all.
I think that a symmetrical explosion (as in a supernova) would not produce gravity waves - you need an event that is not spherically or cylindrically symmetric to get gravity waves (ruining my hopes of detecting the rotation of Ringworld).
Thats not quite what I meant. We can manipulate photons, electrons, neutrons, x rays, EM waves etc in many various ways. What I’m talking about is similarly manipulating gravity by changing other particles into gravitrons or blocking / deflecting gravitrons? Does any of the math suggest it might in theory be possible to do that?
I’m guessing that even if its possible the energy levels involved might make it wildly impractical?
Again, it’s “graviton”, not “gravitron”. A gravitron is a carnival ride.
There aren’t many situations where you can convert some other particle into gravitons, but then, the same is true of photons: Various conservation laws tend to get in the way. About the only way you can convert other particles to either is in antimatter annihilations. Any matter-antimatter reaction which converts to photons presumably could, in principle, convert to gravitons, instead, but it’d be phenomenally unlikely, because gravity is so much weaker than electromagnetism (or, more precisely, the masses of typical particles are so much less than their charges).
Most interactions which produce photons, they’re emitted from some other particle, which also sticks around. This can also be done with gravitons, quite easily: Any time you shake a mass around, you’re emitting gravitons. For various reasons, though (including the mass/charge ratio and the typical frequencies involved), these gravitons are almost impossible to detect, even in aggregate.
But most of the fun things we do with electricity don’t involve the emission of real photons. Mostly, it’s just moving charges, and the virtual photons which mediate forces between them. Again, the same thing is possible with gravity, but it means moving masses around, and it takes a planet-sized mass to produce a significant gravitational field (there’s that pesky mass/charge ratio again).
So in short, yes, you can do most of the same things with gravity that you can with electromagnetism, but no, it doesn’t do much practical good.
Damn, still no flying car then 
Press conference tomorrow.
Chronos, did you forget that you wrote a SDSAB column on that subject?
Hm, yes, I did forget about that column. Not one of my best works, I’m afraid: Ed and I had a tough time balancing accuracy and readability there.
And fingers crossed on that press conference tomorrow! Hopefully they’ll have a verified detection, and it’ll be enough to lead to further, more effective, instruments.
… And 21 months later, that’s almost exactly what happened. Technically, the event was detected in August, but wasn’t announced until earlier this month. Also, technically, the event was the collision of two neutron stars (a “kilonova”) rather than a supernova. But the basic idea is the same.
Using these observations, and under certain (pretty reasonable) assumptions, the speed of gravitational waves differs from the speed of light by no more than one part in one quadrillion (10[sup]15[/sup]) or so. See Section 4.1 of the linked paper for all the gory details.
Which also, incidentally, puts extremely tight bounds on the mass of the graviton. The models generally describe the graviton (and the photon and the gluon) as massless, but that’s not actually something we can test experimentally: All you can actually do is say that, if it does have a mass, it’s less than some value implied by your experiment. Or alternately, of course, you can find that it isn’t actually massless after all, but is in fact greater than some value derived from your experiment: Until a decade or two ago, it was generally assumed that neutrinos were massless, but that’s now known to be false.
Well, one consequence of a particle’s mass is its speed. If a particle is truly massless, then it’ll travel at exactly c (and vice-versa). If a particle has some nonzero mass, then its speed will depend on the ratio of its energy to its mass: A very large ratio will get you very close to c, or equivalently, a speed very close to c implies a very large ratio of energy to mass. And the gravitons in these gravitational waves would have a very small energy to begin with, and so their masses must be far smaller yet, in order to get such a high speed.
Note, though, that this isn’t how the tightest mass limits are set even with the phenomenal leap in velocity precision obtained with the recent multi-messenger observations. Based on the velocity measurements, I estimate a mass limit about an order of magnitude shy of the best limits, which are set by looking at the (non-)dispersion of the gravitational waves themselves, without reference to light.
In essence, it is more powerful to compare the speed of high-frequency (high-energy) gravitational waves to the speed of low-frequency (low-energy) gravitational waves from the same source than to compare gravitational waves to light. Notably, the latter comparison suffers from uncertainties in the astrophysics governing the delay between the emission of light and gravitational waves. In fact, the new velocity limits are two-sided due to these astrophysical uncertainties. At present, we will learn more about neutron star mergers by assuming v[sub]g[/sub]=v[sub]l[/sub]=c than we will learn about v[sub]g[/sub] or v[sub]l[/sub] from prior understanding of neutron star mergers.
Ah, true. “High-energy gravitational waves” are far, far lower energy than anything anyone’d describe as “light” (especially gamma rays), but you’re right that the uncertainties are dominated by the astrophysical unknowns.
Either method, though, is many orders of magnitude better than the previous best upper bound, determined from Solar System orbits. And even that limit was much better than the best limits on the photon mass: One might even say that we’re more confident that gravity travels at c than we are that light does.