Running Circles Around One Another

Are you sitting or lying down? Perhaps you’re moving around at a walking pace? I probably am. And yet, unless you live in the northeastern US or in southern South America, you and I are moving relative to each other at hundreds of miles per hour.

In Chapter 2 of the book “‘Waves in an Impossible Sea”, I remarked on the this fact. (See below for the relevant passage.) At first glance it might seem puzzling. After all, the distance between your town and my town is constant; it never changes. And yet our relative motion is comparable to or faster than a jet aircraft. How can both of these things be true?

And then there’s another question: if we’re all moving so fast relative to one another, why don’t we feel the motion?

The answer to the second question: It’s the principle of relativity at work. As for the first question: Such is life on a spinning Earth.

In the book, I tried to illustrate how this works using a picture (Figure 2.) But this is one of those cases where an animation is much clearer than a static image. On this new page, I’ve presented animations that I hope will clarify the issue, in case you’re having trouble visualizing it.

Here’s the relevant quote from the book’s Chapter 2, where the principle of relativity is first discussed.

We are oblivious to our own motion, and also to the relative motion between ourselves and our friends in other parts of the world. That relative motion isn’t slow. If people sitting in Boston were to measure carefully, they’d see people standing in Miami as moving at 215 miles (345 km) per hour; meanwhile, those in Miami would perceive their friends in Boston as moving at 215 miles per hour in the opposite direction.

But wait: The distance from Miami to Boston, 1,257 miles (2050 km), never changes, so how can there be relative motion between those two cities? It’s because Bostonians view Miami as moving in a daily circle, one that leaves the distance between the two cities always unchanged—and vice versa.