Perihelion drift in SR and in GR

[lalbatros]

I think that in Special Relativity, the drift of the perihelion can be calculated by cumulating elementary Lorentz transformations along the (Newtonian, unperturbed) trajectory. I read that the result of this calculation is much smaller than the experimental value.

It is also well known that general Relativity produces the exact result, within the error bars.

My questions are:

What happened and what can we learn from that ?

How and why did GR perform better ?

Furthermore, is that not somehow in contradiction with the Equivalence Principle ? Could we not imagine that the EP applied to this system would imply the same result for both SR and GR ?


Thanks a lot for your feedback,

Michel

PS: I would also be interrested by a reference about these calculations, I am a bit lazy !
Specially about calculating the drift as a perturbation of the Newtonian case.
Can that really be done by Lorentz tranformations?

 

[Chris Hillman]

I think that in Special Relativity, the drift of the perihelion can be calculated by cumulating elementary Lorentz transformations along the (Newtonian, unperturbed) trajectory. I read that the result of this calculation is much smaller than the experimental value.

It is also well known that general Relativity produces the exact result, within the error bars.

My questions are:

What happened and what can we learn from that ?

How and why did GR perform better ?

You would probably enjoy reading a book by Cuifolini and Wheeler, Gravitation and Inertia, which will probably further mystify you (it's not as clear as MTW), but the authors do try to answer in passing something like your questions above.

calculating the drift as a perturbation of the Newtonian case.
Can that really be done by Lorentz tranformations?

I am not sure I understand exactly what you have in mind ("cumulating elementary Lorentz transformations along the (Newtonian, unperturbed) trajectory" doesn't quite make sense as stated, as you will probably appreciate after a bit of thought), but the obvious guess is that you are thinking of some computation Einstein made in flat spacetime when he was working toward discovering gtr. E.g, one can imagine a static observer in Minkowski spacetime who holds a string and whizzes a stone around. One can imagine further that he carefully adjusts the force on the string to mimic an inverse-squared central force as closely as possible, and that the stone is following a quasi-elliptical orbit. One can then ask: should the pericenters slowly precess, as happens to a test particle in quasi-Keplerian motion around an isolated massive object in gtr? If I recall correctly, the answer is yes, and the precession turns out to be sometthing like half the rate predicted by gtr, but I'm too lazy to work the computation again right now, in order to check my memory.

is that not somehow in contradiction with the Equivalence Principle ? Could we not imagine that the EP applied to this system would imply the same result for both SR and GR ?

Sorry, I can't figure out what you might have in mind here, but I can say that gtr fully conforms to various versions of "the" equivalence principle, and that this theory is self-consistent. The EP certainly does not imply that the answer in the flat spacetime scenario I outlined above should agree with the gtr prediction for a test particle orbiting an isolated massive object, and I don't see why you might think otherwise.

Chris Hillman