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How fast is gravity?

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Suppose the sun were to suddenly vanish. The earth would of course go flying off on a (more-or-less) straight line, tangent to its orbit. My question is, would this happen instantly, or 8 minutes later (the time it takes for light to travel from sun to earth)? Can you justify your answer by solving GR equations?

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If you set Gij=(1/2)hij,kk, where Gij is the Einstein tensor and following the summation convention, you can derive an alternate form of Einsteins equations of gravity, which, when in an empty vacuum, look like grad2(hij)-(1/c2)(d2/dt2)hij=0, which is just a wave equation, showing the gravitational waves travel at the speed of light. Experimentally, of course, the speed of gravity has been shown to have an upper bound of 1.06c, although that is within experimental error.

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Thanks for your response, yourdadonapogos, and I'm sure you're right, but please indulge ..

 

First, I'm not thinking of an explosion. If the sun exploded, all the mass would still be there, presumably expanding at some rate far below c. The earth would continue to orbit the expanding mass with little change for quite a while, until it dispersed beyond our orbit (actually the explosion would blow the earth away by that time, but that's getting far off our topic). My question postulates that the sun literally vanishes - there's no mass at all left to orbit around. Obviously that's impossible; this is just a gedanken.

 

Second, the second part of my question is not just an afterthought - can the relevant GR equations be solved? (Full disclosure - this is a slightly tricky question).

 

Third, perhaps you have some other way to show that it would be 8 minutes (not using GR tensor equations). Can you please mention what it is?

 

Thanks very much, yourdadonapogos!

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Thanks for your response, Callipygous, and I'm sure you're right, but please indulge ..

 

The second part of my question is not just an afterthought - can the relevant GR equations be solved? (Full disclosure - this is a slightly tricky question).

 

Perhaps you have some other way to show that it would be instant (not using GR tensor equations). Can you please mention what it is?

 

Thanks very much, Callipygous!

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The second part of my question is not just an afterthought - can the relevant GR equations be solved? (Full disclosure - this is a slightly tricky question).

 

I just showed you above

 

 

Perhaps you have some other way to show that it would be instant (not using GR tensor equations). Can you please mention what it is?

 

The only form of gravity that is instant is Newtonian gravity, and we know Newtonian gravity isn't as accurate as GR, nor is N-gravity applicable here, because there is no such thing as a gravitational wave in N-gravity.

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Oh, and I don't get why you are saying not to use GR tensor equations...GR is not formulated in anything less abstract that tensors...it's not possible. But, I could show you with spinors, but that would just complicate things more (I'm assuming you want the proof without tensors because you don't know any tensor analysis).

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Thanks fuhrerkeebs, loos like you're right. I have to admit the last time I posed this question was a few years ago and I had a lot of fun with it then .. because it's impossible to even set up the relevant equations since GR doesn't allow initial conditions which specify disappearance of mass without any release of energy. I forgot to check if there were any recent results. When you confidently said it was less than 1.06 c I googled it. I see there's been a new experiment involving the light of a quasar passing Jupiter .. very similar to what I was dreaming of back then. I should have checked before asking, sorry to have bothered you!

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You're posting too fast for me, fuhrerkeebs! Above response was written without seeing your recent posts. Perhaps you see what I mean now. You can't set up GR equations for a vanishing sun because that's physically impossible (mass can't disappear without release of energy). That was the point of my "tricky" question. Unless I'm wrong about that .. ?

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Oh no, no bother at all...I quite like it when things I know about pop up on message boards. It isn't a recent result though, as I originally learned it in one of my dad's old tensor calc. books by D.F. Lawden, copyright 1962.

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You're posting too fast for me, fuhrerkeebs! Above response was written without seeing your recent posts. Perhaps you see what I mean now. You can't set up GR equations for a vanishing sun because that's physically impossible (mass can't disappear without release of energy). That was the point of my "tricky" question. Unless I'm wrong about that .. ?

 

The energy from the vanishing sun is the same energy the gravitational waves use to propagate.

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Well, yes, but there had always been the little issue of experimental proof (finally resolved).

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I'm sort of old fashioned - I don't believe the theory until the experiment backs it up. Makes it hard to take stuff like alternate worlds, multiple universes etc seriously!

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Yeah, theories like the MWI are quite hard to prove (requires "creating" intelligent quantums computers), but I guess you could say I'm the gullible type

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The math is so elegant, how could it be wrong? And since any proof (or disproof) will probably come long after we're dead, what's the harm in believing? If you want to publish these days, skepticism will only slow you down ..

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Yes, the technology to back/disprove a theory is always a bit behind the theory, but if we never published any of these theories, right or wrong, then we would not be motivation to develop the technology in the first place, so really, it is a win/win situation...

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Agree. But remember what Mr. Holmes said: ""It is a capital mistake to theorize in advance of the facts." If you're sure the butler did it you might not notice that the wife had a blood-stained knife in her dresser drawer .. Admittedly the last century of physics wouldn't have happened if they'd taken his advice literally. But I think his underlying point is still valid: go ahead and explore theories, but don't fall in love with them.

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What kind of moron still believes in the aether? I thought the existance of the aether has been consistently shown false by experiment...

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I've looked at your dynamic tensegrity link...it's hogwash. If we conclude that something is true without experiment and, where needed (such as the case here), without math, then anything could be true. Go back to school, get an education, quite spreading self-conjectured already-falsified information on the net...

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here is a simple explaination. information cannot travel at speeds above c. if the sun suddenly dissapeared, there would be no way for the eath to know it for around 8 minutes. (gravitons, if they exist, are believed to travel at c)

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Your "simple explanation" isn't an explanation...just because information cannot travel faster than the speed of light does not mean that gravity has to travel the speed of light.

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it means that is cannot be instantanious. also, the graviton is a theoretical massless particle that travels at c, so still not instantaneous.

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