Do you age more quickly at the pole than than equator due to relativity?

Dear Cecil:

Since people living close to the poles are moving much more slowly than people living at the equator, isn't it true that a person near the pole will age faster than someone at the equator due to the effects of the theory of relativity?

Cecil replies:

Ordinarily I don’t have time for this kind of thing, but I couldn’t find a magazine in the john this morning. As near as I can figure, people age the same at the pole and at the equator, mainly because of relativistic effects that cancel each other out.

Here’s how it works:

(1) Due to the rotation of the earth, people at the equator are moving at about 1,000 miles an hour, while those at the poles are more or less stationary.

(2) Special relativity tells us that for any inertial (i.e., nonaccelerating) observer, moving objects seem to age more slowly.

(3) Objects at the equator of a rotating sphere are not inertial, since they undergo continual acceleration toward the center of the earth. If they didn’t, they would fly off on a straight line into space. (Think about it.)

(4) Ergo, a person at the pole may legitimately consider that a person at the equator is aging more slowly, but not vice versa. (This may seem like an odd way of putting it, but the theoretical physicists out there will know what I mean.) However:

(5) The earth bulges at the equator due to centrifugal force.

(6) The pull of gravity decreases the farther you get from the center of the earth.

(7) General (as opposed to special) relativity tells us the farther you are from the point of max gravity (i.e., the center of the earth), the more quickly you age. Thus you age faster on a mountaintop than in a valley (which serves all those rich croutons in Beverly Hills right).

(8) Therefore, since people at the equator are farther from the center of the earth, they age faster.

(9) The special relativistic effect in #4 exactly cancels the general relativistic effect in #8. In other words, people at the pole and at the equator age at the same rate. Exactly what you would have guessed if you had an IQ of 1! But at least we’re right for the right reason.

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