Gravity: What Moves a Stationary Body?

[PeroK]

Oh well, never mind. It sounds like a stupid question anyhow. What I should have said is can someone lead me through the process. But I'm sure you must be ready to tear your hair our with me so I'll thank you all and let the matter drop.

It's not a stupid question, but it is a big subject. You could start here:

https://en.wikipedia.org/wiki/Minkowski_space

 

[Ibix]

Oh well, never mind. It sounds like a stupid question anyhow. What I should have said is can someone lead me through the process. But I'm sure you must be ready to tear your hair our with me so I'll thank you all and let the matter drop.

It's either far too complicated to go into or I've more or less done it.

Basically, Einstein realized that Lorentz' ad hoc patch to Maxwell's equations could be used to derive a revision of basic kinematics that looks really like Newtonian physics as long as nothing is moving too fast (which is why we didn't notice until we began to look into electromagnetism - even a rifle bullet is too slow by this standard). Minkowski, as far as I know, simply recognised that Einstein's maths looked like Riemann's maths describing a (3+1) dimensional space, and said so. The idea turned out to have truly useful theoretical legs because Newtonian gravity cannot work in relativity (nothing can travel faster than light, but Newtonian gravity is supposed to be infinitely fast), and trying to make special relativity work in curved coordinates (rotating reference frames) led people (notably Einstein) to the idea that gravity might be modeled as a curved version of Minkowski's spacetime.

If you want a lot more detail than that you're going to need a book. I usually reccomend Taylor and Wheeler's Spacetime Physics to people wanting to learn special relativity, but you seem to be more interested in the historical development than the physics. I'd try PeroK's link. If not, somebody posted a reference on the history of relativity the last time I wrote all this out - unfortunately I recall neither the reference nor the poster. Hopefully they'll post again, and hopefully I'll make a note this time.

 

[bhobba]

And there are still arguments about how best to teach it and it can take years to get your head around it.

Most definitely. Ohanian in his book Gravitation and Space-Time does it by first noting a theorem by Wigner that says all fields must be Tensors. Electromagnetism is based on a field with a tensor Au. Ok what would be the next most simple field - why Φuv of course (excluding the simplest of all - a scalar). So build a theory based in a similar way to EM but out of Φuv instad Au. It's not hard - in the Lorentz gauge (∂uAu=0) we have ∂v∂v Au = Ju so we assume in a similar gauge (∂uΦuv=0 - called the Hilbert gauge) and ∂w∂w Φuv = Tuv where Tuv is called the stress-energy tensor. Analyse it, and wonder of wonders it behaves like a relativistic extension of Newtonian gravity - and, being sneaky, what we define as the stress energy tensor turns out to act like the stress-energy tensor of SR thus justifying the name. Because of this its called linearised gravity. Then we do a bit more analysis and find it makes space-time act like it has an infinitesimal curvature, and its gauge invariance is just infinitesimal coordinate transformations. Very strange. Then we naturally ask what if space-time is more than just infinitesimally curved and is invariant to all coordinate transformations not just infinitesimal ones (which of course would be natural for a geometrical view - the geometry of course should not depend on coordinate transformations). Then something equally as strange - perhaps even a miracle - happens - your hands are tied - you get Einsteins Field Equations. So in this approach space-time curvature emerges by assuming a flat space-time and following the math. It was the first serious GR book I read - then I read Wald which is at a more advanced level and very geometrical. Then I read the famous MTW which is a bit more intuitive.

Thanks
Bill