00:01
For this problem, we are asked to show that in special relativity, if v -alpha equals g -alpha beta v -beta, then d -v -alpha by d -x -lamda is going to be equal to g -alpha beta times d -v -beta by d -x -lamda.
00:19
So the first thing that i'll note here is that we have the use of einstein's summation notation here.
00:25
So, for instance, v -alpha equals g -alpha -beta v -beta isn't just a single equation.
00:31
Several equations where we go through whatever possible values of alpha there are, but it would be, for instance, v1 equals g11 v1, plus g12 v2, plus g13 v3, and so on, where g is our metric for the space.
00:52
And i'll note that in special relativity, we have that the metric for our space is the standard lorentz metric, aeta mu -new, which is a constant...