Thanks for the reply (and the latex sample!). It is acting on a vector A:
\Gamma^{\tau}_{\alpha\nu} \frac{\partial A^{\alpha}}{\partial x^{\sigma}} -
\Gamma^{\tau}_{\alpha\sigma} \frac{\partial A^{\alpha}}{\partial x^{\nu}}
I've tried rewriting the partials as...
I would have to say mass does not create space. The 'curving' of spacetime is a description of the motion of an object near a gravitating body. It would follow a path given by the geodesic equation (which is a geodesic). I have never heard of space being a physical thing that can bend or distort...
No, time would not be infinite. It would be "normal" time (no time dilation). Just let r go to infinity in the equation and you will see that time is not changed.
Or more simply put:
{alpha nu, tau}*d/dx^sigma - {alpha sigma, tau}*d/dx^nu = 0
How can I show this is true? Is there some way of writing this with the nu and sigma switched in one of the terms?
Thanks.
I'm trying to work through getting the Riemann-Christoffel tensor using covariant differentiation and I don't see where two terms cancel. I have the correct result, plus these two terms:
d/dx^(sigma) *{alpha nu, tau}*A^(alpha)
and
d/dx^(nu) *{alpha sigma, tau}*A^(alpha)
Sorry, I couldn't...
I am not too familiar with the "Lorentz invariant", so I will have to do some reading on that... sounds kind of important. I'll look up "Formalism to deal with Reichenbach's special theory of relativity" as well. Thanks.
I usually think of space as a 3D grid of cubes having units of (1,1,1). Near a large mass it is like sticking a (2,2,2) cube into the small one. So each component has to bend for the ends to line up (make a D shape). The extra length of each component can't fit in and have to switch out with...
That makes sense why c must be used for the Electrodynamical part, but not (to me at least) the Kinematical part. Why couldn't you use, say, a baseball moving at v0 instead of the ray of light for the argument in "Simultaneity" and "Relativity of Lengths and Times"?
I am working through Einstein's "On the Electrodynamics of Moving Bodies", and I can't figure out why we are using c instead of a random constant velocity. It seems to me that c is an arbitrary value for the argument. I'm sure there is an explanation... I just can't think of it. Can anyone clear...