Chapter 3.1 Measuring spaces in time

How can one spaceship be shorter and longer than the other? Is there a contradiction? The short answer is no. For a contradiction, opposite properties must belong to one thing at the same time, but this is not the case. The different spaceships have different times.

Consider how the lengths of moving bodies are measured. For concreteness, imagine that a Jaguar is on a road that is covered by alternating black and white squares like a chess-board. If the Jaguar is standing still, its length is easy to measure: just count the number of squares between the front and the back wheels. If the Jaguar is moving, however, the wheels are at different places at different times.

For a meaningful measurement, we must count the squares between the locations of the front and the back wheels at the same time.

The general point is, therefore, that length measurements depend on a definition of simultaneity. Suppose that there are two observers.

If they disagree about which events are simultaneous, they will disagree about where the wheels are “at the same time”. Thus they will disagree about the length of the car.

Einstein suggested a practical method for measuring the speed of moving objects: a clock must be set up in each square of the chess- board, and all the clocks must be synchronized to show the same time simultaneously. To measure the length of a speeding Jaguar, we simply agree to mark the location of its wheels at the same time, say, precisely at noon, and count the intervening squares.

But how should the clocks be synchronized? If we collect them all together, synchronize them, and then move them back to their squares, the movement will cause time dilation and destroy their synchronization. Just as Jack in Houston and Jill in her spaceship experienced different flows of time, the moving clocks will show divergent times.

Einstein suggested that each clock be left sitting in its own square, and that a light beam be used to synchronize them. Suppose a flash of light travels across the chess-board, and that light takes a billionth of a second to cross one square. Then, if the flash of light strikes one clock at noon, it should strike the next at noon plus a billionth of a second, the next at noon plus two billionths of a second, and so on. The clocks can be adjusted to show these times, and thus will be synchronized.

Since light always travels at the same speed, there are no distorting effects to disturb the clocks. The same sort of procedure can be used for making length measurements with a moving yardstick. Tiny clocks can be set up at regular intervals along the stick, and a ray of light travelling along the beam will synchronize them.

Einstein stressed that our intuition about measuring lengths cannot be trusted. Great care must be taken to measure the front and back locations of moving objects at the same time, and to use clocks synchronized with light beams.

Measurements of space depend on time.

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