
Here's my synopsis of Chapter 5. I'm still hoping that someone will help me out:
1. Everything travels through spacetime at speed
c, which is to say at the speed of light. However, light travels only in space, not in time. Everything else does some of its traveling in time. Therefore, we don't get from place to place as fast as light does. In fact, we move so slowly (that is, we use so much of our share of
c on traveling in time) that our experience of spacetime is quite different from light's experience -- or what light's experience would be if it were sentient.
2. We can think of distances between two points in space (Fayetteville and Shreveport) or two points in time (5:00 and 6:00). We can also think about two points in spacetime (waking up in bed and breakfast at the kitchen table). If the distance needs to have a direction, then we can think of it as an arrow, or a vector (studiously ignoring mosquitoes as disease vectors). Depending on what's important, we can describe distances in spacetime by as many as three numbers: length, height, width, and passage of time.
3. The spacetime distance between two points is always the same, mathematically speaking; it can be distributed differently, though. So if we consider the spacetime between my great-grandfather at Ellis Island and me, there's the distance in miles between us of 1314.68 or so; then he was at sea level so I'm higher; I don't know how width could be measured; and then there's the time difference of a century. Presumably, there could have been a great burst of light at Ellis Island at just that moment that the ship arrived from Antwerp and the spacetime between that and me now would be identical to the spacetime between Robert Allen Haden and me -- but it would be taken up entirely by space and not by time.
I have no idea what #3 would mean. "So much," as the authors say, "for vectors."
4. Billiard balls colliding will take off with the same amount of energy with which they collided, but in opposite directions -- except for friction, which spoils this story, so we leave it out. All the energy used in any undertaking is conserved: it doesn't get used up or anything. It's still there, just as the water we're now drinking is the same water the dinosaurs drank. Energy can be stored and used and moved around, but it doesn't diminish.
5. This hooks up with the idea of all the movement through spacetime adding up to
c. But it's better because it makes a nicer equation with
y.
What am I missing?