Hello, I've had my first couple of lectures on general relativity. Actually, we started by talking about special relativity. We were taught the SR uses Minkowski spacetime and that the displacement (squared) between any two events is given as follows: ds^2 = (c^2)(dt^2) - dx^2 - dy^2 - dz^2 Now, please correct wherever you guys spot I got something wrong in my understanding: 1) The spatial coordinates have a minus sign because we want light to have a displacement of 0, and only light can have (c^2)(dt^2) equal to the sum of the spatial coordinates, and thus achieving a slope of 1 in a space vs time diagram. 2) What does the displacement ds actually mean? If light has a displacement of 0, then what does it mean? Does it not move through spacetime :S ? 3) The professor said that ds^2 is invariant under any coordinate change... can anyone explain why this is so? 4) The professor also rapidly wrote this equation towards the end of the lecture but I really didn't understand where it came from and what it means... could someone tell me more or less what it is? The equation is: ds^2 = g(ab) dx(a) dx(b) a and b are bottom indices of g, and then they're upper indices for both dx's, so that there is a summation over both (Einstein convention). I believe g(ab) is something which he called the metric tensor... but he didn't really explain it that much, maybe next lecture. However I want to understand how this equation connects with the other one. I would appreciate any help you guys can give me. Take care.