My first two summaries were:
b. Spinning Space Buckets
2. Greene begins with a little flashback to James Clerk Maxwell, whose beautiful equations conquered electromagnetism in the 1800s.
The problem was that there was no evidence of such an ether. More importantly, the speed of light seemed to be the same no matter where it was found--coming from something stationary, coming from something moving. Normally, speeds add up. A person walking 3 mph on a train moving 50 mph is moving 53 mph in relation to the ground. But light on the ground is 3 x 108 and light on the train is 3 x 108 and light from a plane is 3 x 108.
3. This is of course where Einstein comes in in 1905. Light can be the universal speed limit if space and time contract relative to speed. So the train is just a wee bit smaller from the perspective of the ground as it moves, to compensate for the speed of a flashlight shined by someone riding on it. You're not contracted on it, but it contracts relative to the person observing on the ground. A plane contracts relative the person on the ground a smidge more, so that the light shining from its wings also comes out exactly at 3 x 108 mps, no matter who is looking from whatever frame of reference, moving or not.
"The combined speed of any object's motion through space and its motion through time is always precisely equal to the speed of light" (49).
4. There were some new insights for me into some of the more precise contours of Einstein's theory in this chapter. So not everything is relative in Einstein's theory. "Spacetime" as a whole is an absolute reference point. It can be sliced up differently, but it is the same loaf. Time is sliced up differently in some cases. Space is sliced up differently in some cases. But it is the same loaf of spacetime, which he concludes by the end of the chapter is a thing. (I didn't fully understand this last part of the chapter, but I feel like I'm making progress)
At one point of the chapter, Greene talks about how there is a totality to motion through spacetime. If something is more or less not moving in space, then all of its motion is through time. But if it has a velocity, then some of its motion through time is diverted to its motion through space and time moves more slowly. It's a fascinating idea (48).
5. The last part of the chapter turns to the question of acceleration. Einstein's special theory of relativity only applied to objects moving with a constant velocity. His general theory in 1915 turned to the question of gravity and acceleration.
The fundamental insight here was that gravity is really only a body following the contours of spacetime, which is warped by mass. So a planet bends spacetime, and gravity is basically our bodies wanting to follow the path of the warp. The ground stops us. Free fall is thus nothing different from weightlessness.
His field equations were the result: