From Eternity to Here Read Online Free PDF

Of course we can connect two points in space by paths with different lengths; one could be straight and one could be curved, and we would always find that the distance along the curved path was greater. But the difference in coordinates between the same two points is always the same, regardless of how we get from one point to another. That’s because, to drive home the obvious, the distance you travel is not the same as your change in coordinates. Consider a running back in football who zips back and forth while evading tacklers, and ends up advancing from the 30-yard line to the 80-yard line. (It should really be “the opponent’s 20-yard line,” but the point is clearer this way.) The change in coordinates is 50 yards, no matter how long or short was the total distance he ran.

    Figure 4: Yard lines serve as coordinates on a football field. A running back who advances the ball from the 30-yard line to the 80-yard line has changed coordinates by 50 yards, even though the distance traveled may have been much greater.
    The centerpiece of special relativity is the realization that time is like that . Our second definition, time is duration as measured by clocks, is analogous to the total length of a path through space; the clock itself is analogous to an odometer or some other instrument that measures the total distance traveled. This definition is simply not the same as the concept of a coordinate labeling different slices of spacetime (analogous to the yard lines on a football field). And this is not some kind of technical problem that we can “fix” by building better clocks or making better choices about how we travel through spacetime; it’s a feature of how the universe works, and we need to learn to live with it.
    As fascinating and profound as it is that time works in many ways similar to space, it will come as no surprise that there are crucial differences as well. Two of them are central elements of the theory of relativity. First, while there are three dimensions of space, there is only one of time; that brute fact has important consequences for physics, as you might guess. And second, while a straight line between two points in space describes the shortest distance, a straight trajectory between two events in spacetime describes the longest elapsed duration.
    But the most obvious, blatant, unmistakable difference between time and space is that time has a direction, and space doesn’t. Time points from the past toward the future, while (out there in space, far away from local disturbances like the Earth) all directions of space are created equal. We can invert directions in space without doing damage to how physics works, but all sorts of real processes can happen in one direction of time but not the other. It’s to this crucial difference that we now turn.
    3. Time is a medium through which we move
    The sociology experiment suggested at the beginning of this chapter, in which you ask strangers how they would define “time,” also serves as a useful tool for distinguishing physicists from non-physicists. Nine times out of ten, a physicist will say something related to one of the first two notions above—time is a coordinate, or time is a measure of duration. Equally often, a non-physicist will say something related to the third aspect we mentioned—time is something that flows from past to future. Time whooshes along, from “back then” to “now” and on toward “later.”
    Or, conversely, someone might say that we move through time, as if time were a substance through which we could pass. In the Afterword to his classic Zen and the Art of Motorcycle Maintenance , Robert Pirsig relates a particular twist on this metaphor. The ancient Greeks, according to Pirsig, “saw the future as something that came upon them from behind their backs, with the past receding away before their eyes.” 12 When you think about it, that seems a bit more honest than the conventional view that we march toward the future