High School Another question about Gravity -- Does the apple attract the Earth?

[PAllen]

When I posted a lot of sci.physics.reativity we had a lot of high powered people posting at one time - they gradually disappeared due to the cranks. But back then when I just found out about it and posted could I see a proof - only John Baez and Steve Calip knew about it - of those that posted there of course - and were not cranks. I suspect others did know it but not the proof - so kept quiet. I had to dig it up myself. John and Steve of course knew the proof but also knew I would learn more doing it myself. Of course they were right - that was a lesson I learned there and try to foster here - targeted at the appropriate level of course.

Thanks
Bill

As to how well known it is, both Synge’s 1960 book and MTW discuss it. Those are fairly early standard texts.

There are actually many variants of proof. The one you reference is related to work done by Einstein, Infeld, and Hoffman way back in 1938 - the first derivation of particle motion from the field equations. This early type of proof is not affected by the issue of energy conditions because it does not actually apply to matter at all - you assume the vacuum field equations throughout, and are really talking about the motion of BH as stand ins for test particles.

The more complicated problem is showing that matter, in an appropriate limit, follows timelike geodesics. It is this case for which it has turned out that dominant energy condition is both necessary and sufficient for timelike geodesic motion to follow from the field equations, for the limit of small bodies. This line of work starts from Geroch, and the most rigorous derivation is by Gralla and Wald (for a while, several years ago, Sam Gralla was active on these forums).

 

[bhobba]

As to how well known it is, both Synge’s 1960 book and MTW discuss it.

I lost my copy of MTW ages ago - but never really did an in depth study - I preferred Wald which I did study a lot of.

Might have to get a copy again. They do say if you really want to understand GR you need both MTW and Wald. I am going to check now if its in Wald and simply forgot (its been ages since I was into GR). Will get back.

Added Later:
Had a quick scan of Wald. You so and so - looks like I will have to get MTW - again

Thanks
Bill

 

[PAllen]

I lost my copy of MTW ages ago - but never really did an in depth study - I preferred Wald which I did study a lot of.

Might have to get a copy again. They do say if you really want to understand GR you need both MTW and Wald. I am going to check now if its in Wald and simply forgot (its been ages since I was into GR). Will get back.

Added Later:
Had a quick scan of Wald. You so and so - looks like I will have to get MTW - again

Thanks
Bill

Actually, they (Wald) do discuss it briefly, referencing literature, on page 73-4 of the edition I checked. However, they don’t present a full discussion as MTW do (a whole 10 page section, 20.6)

 

[bhobba]

Actually, they (Wald) do discuss it briefly, referencing literature, on page 73-4 of the edition I checked. However, they don’t present a full discussion as MTW do (a whole 10 page section, 20.6)

So it does - on those very pages - but as you say the detail is in references - sneaky.

Relented - got MTW - huge difference in the Kindle price and while its not the best for serious study - if I remember right MTW was so huge it wasn't physically an easy read either so got that one. Talk about HUGE - it took a while to even download.

Thanks
Bill