A pendulum swings back and forth.

foucault

Gravity keeps the wire taut. An electromagnet near the pivot at the ceiling gives just the right push, just the right pull, to keep the pendulum swinging. Below the pendulum, the Earth turns.

But wait. Isn’t the pendulum attached to the Earth? Surely the ceiling, connected to the walls, connected to the floor, connected to the ground, all turn with the Earth. You and I turn with the Earth. What makes the pendulum so special?

Let’s try an experiment. A ball is connected to a string. You are the Earth, and the ball and string are your pendulum. Swing the pendulum gently back and forth. Now turn in a circle. You’ll see the pendulum staying in the same plane, swinging back and forth, back and forth despite your rotation.

So it is on the rotating Earth. The pendulum holds its plane as the Earth turns below.

This would be true if we lived on either of our planet’s poles. But the weather is not so good.

Now hold the pendulum horizontally, as if your belt were our planet’s Equator. This time as you turn, you see the pendulum turning with you. Of course, you can’t swing the pendulum this way, but you can see in your minds eye that were it to swing above the equator, it would turn with the Earth.

At my latitude of 40 degrees North, the pendulum acts like two pendulums, each independent of the other. One portion acts as if it is on the North pole, ignoring the Earth’s rotation. The other part behaves as if it is at the equator, tugged along by the Earth’s daily spin.

All this is well-understood, and mathematical models make these descriptions rigorous and exact. We can predict within fractions of seconds just how long a pendulum at any latitude will swing before seeming to return to its starting point on the constantly-spinning Earth.

But the deeper question remains. Why? Why should the pendulum preserve its original plane? The question actually has a more general form: Why should constant-speed straight-line motion be no different than standing still, but motion in any kind of curve, arc, or acceleration be detectable by things like pendulum precession?

einstein with pendulum

The answer is deep and surprising. The universe has a memory. It remembers the path of everything, not through three-dimensional space, but through four-dimensional space-time. The pendulum at the north pole continues to keep its plane because it remembers its former self. Even in a universe in which nothing existed except the pendulum and the gravitational field which keeps it taut, the pendulum would hold the plane established by its own past. Three-dimensional motion through space is relative. Four-dimensional motion through space-time is absolute. What a strange world we find ourselves in.

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