I have a question. I'm reading The Elegant Universe and it's talking about the special and general theory of relativity. One of the things it mentions is that time and the three dimensions of space share the terminal velocity of an object, ie. If an object is traveling through space and therefore time, that the faster it travels through space the slower it travels through time and vice versa, since all objects travel through the four known dimensions at an maximum velocity, that velocity being spread out between its travel relative to the amount of measurable movement through each of the four dimensions. It also talks about this being relative to a stationary observer. But there seems to be a problem that I have not seen addressed and that is just how relative the notion of "stationary" is. Since we know that the earth spins on its axis, the solar system revolves around the sun, the galaxy rotates, and space itself is constantly expanding etc and so on, wouldn't a true measurement of the relativity of movement through spacetime only be possible at the exact center of all existence? At a place where all motion through space is truly nonexistent in relation to any other point in existence? And would it not have to be so precise that even the slightest deviation from that exact center skew the results of any experiment? And what would theoretically be present at such a place since the lack of all motion would tend by the theory of relativity to state that all motion of any object located at a place where no motion through space exists, 100% of its motion would be through time?
2 Answers
The relevant part of the book is the section titled Motion through Spacetime in chapter 2. I'll copy the paragraph, but it's a bit long so feel free to skip over it:
Einstein proclaimed that all objects in the universe are always traveling through spacetime at one fixed speed—that of light. This is a strange idea; we are used to the notion that objects travel at speeds considerably less than that of light. We have repeatedly emphasized this as the reason relativistic effects are so unfamiliar in the everyday world. All of this is true. We are presently talking about an object's combined speed through all four dimensions—three space and one time—and it is the object's speed in this generalized sense that is equal to that of light. To understand this more fully and to reveal its importance, we note that like the impractical single-speed car discussed above, this one fixed speed can be shared between the different dimensions—different space and time dimensions, that is. If an object is sitting still (relative to us) and consequently does not move through space at all, then in analogy to the first runs of the car, all of the object's motion is used to travel through one dimension—in this case, the time dimension. Moreover, all objects that are at rest relative to us and to each other move through time—they age—at exactly the same rate or speed. If an object does move through space, however, this means that some of the previous motion through time must be diverted. Like the car traveling at an angle, this sharing of motion implies that the object will travel more slowly through time than its stationary counterparts, since some of its motion is now being used to move through space. That is, its clock will tick more slowly if it moves through space. This is exactly what we found earlier. We now see that time slows down when an object moves relative to us because this diverts some of its motion through time into motion through space. The speed of an object through space is thus merely a reflection of how much of its motion through time is diverted.
Note that Greene says If an object is sitting still (relative to us), and it's the relative to us that is the key phrase. In this context stationary means stationary with respect to the observer making the measurements. There is no absolute meaning for stationary. Indeed, Greene spends much of the preceeding part of chapter 2 explaining that all motion is relative.
To really understand relativity (both flavours) you need to appreciate the importance of coordinate systems. If I want to measure positions, times, velocities, etc I need to establish a measurement system. I need to choose an origin, which is conventionally at my position, and I need to choose $x$, $y$, $z$ and time axes. This constitutes my coordinate systyem, and having done this I can use my rulers and clocks to measure the positions of events in spacetime and thereby measure velocities.
When we talk about time dilation or length contraction we don't mean anything funny is happening to my lengths $x$, $y$ and $z$ or my times $t$. What we mean is that if I measure my elapsed times $t_2 - t_1$ they won't necessarily be the same as the measurements made by a different observer using a different coordinate system.
When we talk about a stationary object we mean one that shares my coordinate system i.e. I and the object will agree on the coordinate system we use to make measurements. Obviously this means our measurements of time and space will be the same since we're using the same coordinates.
In special relativity a coordinate system fills all of spacetime i.e. my axes carry on it a straight line forever. In general relativity life is much more complicated because the curvature of spacetime means my coordinates are only good locally.
Everywhere in the observerable universe is affected by gravity and since you can't escape it, that means it is always pulling on you.
So every objecct in every place will be moving relative to everything else, so an absolute state of rest is impossible.
If you could edit your post to quote the part of the book where he says "stationary", you will probably find that he means relative to something, not absolutely in a state of complete rest.