Gravitational Potential & Field: Doubts & Solutions

[Dale]

I tried to think of a practical example of applying GPE where it could actually help to use anything other than Infinity - except for the obvious ones where we are starting off from Earth and falling back again.

I think that the obvious example is a fine one. If you can do it in the obvious case, then you obviously can do it. Also, the obvious case you mention answers the OP's question since it would set the potential to 0 at the surface where the field is non-zero.

Also, you wouldn't necessarily use the mgh approximation, e.g. in launching a satellite or ICBM.

That could be why I come out in spots at the mention of gravitons - except when the person who introduces them is a BRAIN.

I agree. Gravitons are completely irrelevant to this discussion.

 

[sophiecentaur]

One other thing in favour of defining GPE relative to Infinity, of course, is the universality of it. We could have an excellent gravitational conversation with the scientists on the planet Zog, ten light years away and we'd all be talking the same language. We'd show them Hydrogen lines and a few other common phenomena to get our units agreeing and scaled up, then we would all know what we meant. The dimensions of the third rock from the Sun would probably not interest them very much, scientifically.
Not that it is a likely scenario for some while. Get a move on please, SETI..

 

[MikeGomez]

I suppose we are all in agreement that the measurement of gravitational potential energy at the center Earth as zero, assuming a reference of zero potential at an infinite distance form the earth.

OMG, what the heck was I thinking! Of course the logical location to assign zero potential gravity is at the surface of the Earth and a maximum at infinity.

I became extremely flustered when Darwin flipped the Bozo switch on me, but that is just an excuse. I promised to say I am wrong when I am wrong, and brother was I wrong. Profuse apologies to all.

 

[MikeGomez]

Until Gravitons have actually been found, it might be as well not to use them in discussions about well established gravity matters.

there is no self-consistent quantization of Gravity. That means, we have no reason to assume there is such a thing as a graviton.

Excellent, no gravitons.

our best non-classical description of gravity is GR, which doesn't have such a thing as gravitational field.

Wait a minute. Then what is meant by Einstein field equations of Einstein’s General Theory of Relativity?

From the Wikipedia article on the stress energy tensor.

"The stress–energy tensor is the source of the gravitational field in the Einstein field equations of general relativity, just as mass density is the source of such a field in Newtonian gravity."

 

[Nugatory]

Wait a minute. Then what is meant by Einstein field equations of Einstein’s General Theory of Relativity?

From the Wikipedia article on the stress energy tensor.

"The stress–energy tensor is the source of the gravitational field in the Einstein field equations of general relativity, just as mass density is the source of such a field in Newtonian gravity."

That's wikipedia being a bit sloppy. It's not really "just as"; and MTW's position (that there are multiple mathematical objects involved in the description of gravitational effects, no one of which is so uniquely important as to be called "the" gravitational field) is generally clearer.

 

[A.T.]

MTW's position (that there are multiple mathematical objects involved in the description of gravitational effects, no one of which is so uniquely important as to be called "the" gravitational field) is generally clearer.

Wouldn't the metric describing space-time geometry qualify as "the gravitational field of GR"?

 

[Dale]

Wouldn't the metric describing space-time geometry qualify as "the gravitational field of GR"?

Well, the metric doesn't really reduce to the Newtonian gravity field AFAIK.

I tend to think of the Christoffel symbols as being the most closely related to the Newtonian gravity field.

 

[K^2]

I tend to think of the Christoffel symbols as being the most closely related to the Newtonian gravity field.

But still, not really. Because I can take polar representation of Minkowski metric, which is flat and has no gravity, of course, modify it to be rotating at some angular velocity Ω, and now the Christoffel symbols represent centrifugal and Coriolis effects.

So Christoffel symbols are really whatever fictitious forces you happen to have. If you have curved space-time, then that includes gravity. But it still doesn't reduce to just gravity.

 

[Dale]

So Christoffel symbols are really whatever fictitious forces you happen to have. If you have curved space-time, then that includes gravity. But it still doesn't reduce to just gravity.

Yes, but I personally think that including other fictitious forces in gravity is more or less justified by the equivalence principle. However, since there isn't general agreement on the topic and since my justification is admittedly pretty sketchy I certainly don't push my viewpoint.

 

[MikeGomez]

That's wikipedia being a bit sloppy. It's not really "just as"; and MTW's position (that there are multiple mathematical objects involved in the description of gravitational effects, no one of which is so uniquely important as to be called "the" gravitational field) is generally clearer.

I agree with what you with what you are saying; that what has been called the gravitational field is not exactly the same sense as the electromagnetic, weak, and strong fields.

I have learned now, thanks to this forum, that there is no mediator of the "gravitational field", but still, doesn’t it seem useful to have a term for describing the intensity of gravitation? Would it be acceptable to speak of a “gravitational field” when referring to the values as given by the stress-energy tensor equations?

 

[BruceW]

Nugatory has explained it very well. When wikipedia says: "The stress–energy tensor is the source of the gravitational field in the Einstein field equations of general relativity, just as mass density is the source of such a field in Newtonian gravity." This is only a loose analogy. The two relationships are not meant to be taken as literally identical.

Edit: Also, on this page: http://en.wikipedia.org/wiki/Einstein_field_equations They give a derivation of Newton's law of gravity from Einstein's field equations, under several limiting assumptions. So from looking at this derivation, you can see in what sense the stress-energy tensor in general relativity and the mass density in Newtonian gravity are similar.

 

[MikeGomez]

Yes, but I personally think that including other fictitious forces in gravity is more or less justified by the equivalence principle. However, since there isn't general agreement on the topic and since my justification is admittedly pretty sketchy I certainly don't push my viewpoint.

Hmm, I don't know much about Christofel symbols, but I was under the impression that fictitious forces in gravity are justified by the equivalence principle.

You say there isn't general agreement on this, so it would be interesting if you could please provide some references to those arguments.

 

[Dale]

Hmm, I don't know much about Christofel symbols, but I was under the impression that fictitious forces in gravity are justified by the equivalence principle.

If you have a curvilinear coordinate system and you parallel transport a vector then its components will change, not due to any change in the vector itself, but due to the curving of the coordinates. The Christoffel symbols capture that effect.

You say there isn't general agreement on this, so it would be interesting if you could please provide some references to those arguments.

I think that MTW gives a good overview in "Gravitation". You should start around p 460-470 or so. Here is an online source: http://arxiv.org/abs/physics/0204044

 

[MikeGomez]

Thanks Dale.