I'm sorry James, but I must pick you up on that. Space isn't curved. See this Baez article: "Note: not the curvature of space, but of spacetime. The distinction is crucial". The two ways of looking at the same effect are inhomogeneous space ≡ curved spacetime, as per this paper. Sorry if that sounds nitpicky, but IMHO it is very important.I don't have a problem with this explanation of the deflection of light. It does, however, assume that space is flat and that the speed of light therefore varies. A different way to look at things is that space is curved and the speed of light remains constant. It's really just two ways of looking at the same effect.
You could. That's like looking at the bowling ball analogy from the top. But you can derive the bowling ball analogy from the equatorial-slice light clocks.For example, in the animation above, we can explain the apparent slowing of the wavefronts that pass closer to the sun as due to their having to their not travelling in the two dimensions of the screen any more, but dipping "down" perpendicularly to the plane of the computer screen then up again, as they pass near the sun. The dip is greater for the waves passing nearer to the sun than it is for waves passing further away. The added component of the light's velocity perpendicular to the plane of the screen accounts for its apparent slowing in the plane of the screen. Adding up the components, the light still has its usual, constant speed.
This is pretty much the "given" explanation provided by modern texts. What I'm essentially saying is this: that given explanation isn't in line with Einstein or the evidence. And it's wrong.James R said:This is a somewhat flawed, 3-dimensional analogy of what actually happens, of course. Because, in fact, that bending of the light perpendicularly to the plane of the screen doesn't really happen in that particular direction at all. The bending actually happens in the 4 dimensional spacetime around the sun, which is such that there's actually more space near the sun than there would be if spacetime was flat there. Light takes longer to travel through the space near the sun than it would if the spacetime there wasn't curved, and that accounts for the apparent slowing of the light (the Shapiro delay).
And an easy way to understand that is that it's merely a curvature in your plot of equatorial-slice light-clock rates. A curvature in your plot of the speed of light.James R said:The common ball-on-a-trampoline picture of curved spacetime near the sun or the Earth, which appears as your very first diagram in the opening post of this thread, gives an easy way to picture what is going on with the curvature, although it does that at the expense of dropping a spatial dimension from the picture.