Orbit precessions - General Relativity vs Newton

[Hornbein]

Just think of how disappointed Al would have been if the GR math gave exactly the same result as 1/r^2. Viva la precesion!

 

[pixel]

Actually, Newtonian physics accounted for about 90% of Mercury's precession. General Relativity provided the rest.

 

[bcrowell]

Actually, Newtonian physics accounted for about 90% of Mercury's precession. General Relativity provided the rest.

Yes, what we've been discussing is the non-Newtonian part.

 

[pervect]

I'm not quite clear on your reasoning here. Your first paragraph seems persuasive, but your second paragraph muddies the waters. It's not obvious to me that there should be values of $\beta$ and $\gamma$ that correspond to the Newtonian limit. PPN assumes a nondegenerate metric, whereas Newtonian gravity has a degenerate metric. As far as I know (basically just from reading the review article by Will), the standard way of recovering the Newtonian limit from PPN is not by picking values of $\beta$ and $\gamma$ but rather by taking the limit of small velocities and weak fields.

I think it's possible to show explicitly that there are no values of $\beta$ and $\gamma$ that define the Newtonian theory. Perihelion advance is a non-Newtonian effect that is proportional to $2+2\gamma-\beta$, while the Shapiro time delay (or the part of it that Will describes as "non-Newtonian") is proportional to $1+\gamma$. The Nordtvedt effect is proportional to $4\beta-\gamma-3$ (assuming zero values for $\xi$, alphas, and zetas). Setting all three of these to zero gives no solutions for the two parameters.

My reasoning, in a nutshell, is there are at least two things that affect perihelion shift. The first is spatial curvature, represented by the PPN parameter $\gamma$, the second is the non-linear behavior of the gravitational field, represented by the PPN parameter $\beta$. But these two things alone are not sufficient to explain the exact value of perihelion shift. So I suggest there is probably something else going on as well, a third effect of some sort. At this point I don't have a simple physical explanation for this third effect (I wish I had one). But I feel obligated to mention that the effect is still there, even though I lack a simple "physical" explanation for it.

This leaves me skeptical as to any purported "simple" explanation for a "single physical cause" for perihelion shift, as I see at least two, and those are not sufficient in and of themselves.

I don't claim that my argument is air-tight. That being said, I'm still skeptical of proposed "simple" explanations of perihelion shift.

I have seen analyses based on a formal similarity between some of the differential equations in Schwarzschild coordinates and a classsical analysis, but these in my opinion are a bit of a mathematical trick, the point is they're not physically motivated in a certain sense. What I mean by "physically motivated" is that if you take the best available weak-field approximation of gravity (PPN) and working out the consequences, you get complicated-looking results. The apparently simple looking results only happen if you draw a formal analogy between some equations that fall out of a strong field approach and note the formal similarities in the differential equations and interpret those formal similarities as if they were somehow "physical".

 

[haushofer]

Ok, I can see that point of view, up to a point - the degeneracy of the metric flows from the degeneracy of the Galilean algebra (over 4 dimensions). However, I have never seen the value of the action principle derivation of geodesic equation in relativity (as opposed to all other uses of action principles), because making it work for null geodesics is highly artificial.

You mean by introducing the einbein? This is offtopic here, but I just want to say that in terms of sigma-models this is not so artificial at all; if you want to extend the geodesic equation to strings, branes etc. I think the action principle is quite natural.

But this is maybe for another topic ;)

 

[eltodesukane]

Basically, he major cause of orbit precession is that gravity travels at the speed of light, so that Mercury is not attracted to where the sun is, but to where the sun was.

 

[A.T.]

Basically, he major cause of orbit precession is that gravity travels at the speed of light, so that Mercury is not attracted to where the sun is, but to where the sun was.

This is wrong. Discussed many times here.

 

[PAllen]

Basically, he major cause of orbit precession is that gravity travels at the speed of light, so that Mercury is not attracted to where the sun is, but to where the sun was.

That is false. If that were the way gravity worked, orbits would be wildly unstable, and this was known even by Newton (he was reluctant to propose instant action at a distance but did so when he analyzed that a propagation delay would fail to explain stable orbits).

Here is a reference to the whole issue of apparent instant action at a distance in GR:

http://arxiv.org/abs/gr-qc/9909087

 

[eltodesukane]

Basically, he major cause of orbit precession is that gravity travels at the speed of light, so that Mercury is not attracted to where the sun is, but to where the sun was.

Seems I was wrong, situation not so simple.
Thanks for the reference.
Steven Carlip, Aberration and the Speed of Gravity (arXiv:gr-qc/9909087v2)
http://arxiv.org/abs/gr-qc/9909087