Hi, I have a few things I don't quite understand in general relativity. In my course we have gone through a lot of mathematical stuff that I have blindly followed without really appreciating its significance and I feel bad about that. The first thing is, where did this idea of the curvature of spacetime come from? I know that the relativistic view of gravitation is based on the idea that the more massive an object is, the more it warps spacetime around it. I'm not sure where this idea came from though - as I understand it, Einstein started by forgetting about two massive bodies attracting each other by a force, and just said that the presence of a massive object affects the motion of other stuff (either massive or massless) around it. What made Einstein make the leap from that to a curved spacetime? How is this curvature actually measured? What is it about mass that causes spacetime curvature? Does an object moving in a curved spacetime have any perception of it? Also, when it comes to measuring distances (i should really say "intervals", right?) in a curved spacetime, do we still think of this as being measured with, say, a straight metre ruler, or does the metre ruler itself become curved to conform to the spacetime it is in? Does a metre in a curved spacetime still mean a metre in a flat one? When we measure the distance between two points in a curved spacetime, do we do the straight line distance as if the curvature wasnt there, or do we have to curve our metre ruler along the shortest distance between the points in this curved space (eg. surface of a sphere)? Clocks are another thing that get me. Say we are talking about two clocks, one in free fall and one fixed at some radius from a massive object. The one in free fall has no perception of a gravitational field, am I right? (If it was enclosed in a box, that box would freefall with it, and so it would not feel any resistive force.) It ticks "normally". But then say someone freefalling along with that clock sees another clock at some fixed radius from the large mass. That one does notice itself accelerating. The free falling clock-observer compares his clock to the fixed-radius one, and sees that in 1second, his clock hand has ticked further than the other clock. Well, what about that other clock - would an observer sitting on that fixed-radius clock be aware that his time was running slower? would he be sitting around getting bored thinking, bloody hell, this is taking ages? Also, spacetime expansion is my other problem, again about distances. Say I measure the distance to a star, I place down my metre ruler X number of times until I get from Earth to the star. Then I allow time to pass, the universe "expands". I repeat the measurement again. Do I measure that it takes (X + some more) metre rulers to get to the star, or has the length of my metre ruler expanded with the universe so that I still need X metre rulers to get there? A major thing that I didn't understand is the way that light supposedly slows down as a photon approaches the Schwarzschild radius of a massive object. How come this is allowed? Finally, the cosmological principle. "The universe looks the same to all observers". How can that be true? We could go to mars and set up a telescope, and we could identify all the same stars we can already see from Earth, but they would be from a new angle. How can two observers see the same thing? There could be an asteroid coming towards us, but an observer on a planet on the far side of that asteroid, we would see it moving away from us. How does the cosmological principle work there? Can you enlighten me on any of these issues? Thanks.