Chapter 3.4 A fountain of youth?

The most famous of the problems prominent in the early controver- sies over relativity was the twin paradox. It is easy to state but exposes some very deep issues, and so hundreds of papers have been written about it over the decades. Now that the dust has settled, it is clear that the paradox does contain a profound lesson. It does not show that relativity is nonsense, but helps us sharpen our intuitions about life at the speed of light.

Suppose that Jack and Jill are twins. Jack still works in Houston for NASA, and Jill is an astronaut embarking on a long journey to some distant star. If her spaceship travels at nearly the speed of light, the clocks and other processes on board will slow because of time dilation. For Jill, the astronaut twin, the journeys out and back again will both be fairly brief. But on Jill’s return, stay-at-home Jack in Houston will be a grey grandparent, and many years “older” than his twin.

As the experiment with the atomic clocks showed, this is not a fairy tale. If long space journeys occur in the future with very fast spaceships, such discrepancies in age will become common. Many generations of workers may retire from mission control before a crew of youthful astronauts return from a single journey.

Why did early critics believe this was a paradox that disproved relativity? Because, they argued, the theory is symmetric. According to Einstein, the spaceship’s clocks are slower than those on Earth and the earth-bound clocks are slower than those on the spaceship. If both these are true, then why should only the twin in Houston be so old?

Whatever happens, shouldn’t the twins’ experiences be symmetric, that is, the same despite their different journeys?

These critics have made a mistake. There is a big difference between the twins: the astronaut twin accelerates. Remember that Einstein’s special theory of relativity is special because it applies only to rulers and clocks moving steadily in the same direction, that is, moving inertially. Jill climbs into a rocket that accelerates to leave Earth and our solar system. In the middle and again at the end of her trip, further accelerations are needed to land at home again. Since these accelerations are asymmetric and experienced only by one twin, there is no reason to expect that their ages will remain the same.

Asymmetric causes imply asymmetric effects.

Steady motion is not detectable by experiment. Thus when two bodies approach each other inertially, no experimental evidence will show whether one or the other or both are moving. Acceleration, however, is not inertial movement, and is easy to detect. Those who drink hot coffee in a suddenly braking car will soon have the experimental evidence in their laps. As a car moves inertially, the surface of the liquid remains flat; but with any acceleration – speeding up, slowing down or turning – the liquid will slurp over to one side of the cup. Acceleration has dramatic effects, and the difference in the twins’ ages is one of them.

Of course, the acceleration does not directly cause the asymmetry.

The acceleration determines the path of the astronaut twin, and it is this path that determines the age difference. The asymmetry of the acceleration causes an asymmetry in the motions of the twins, and this causes the asymmetry between their ages.

In retrospect, the twin paradox is so prominent in the literature on relativity because many believe that Einstein showed that “everything is relative”. But this is not true even for motions. Inertial motions are relative, but accelerations are physical.

Regardless of which set of inertial rulers and clocks is used, if the distance between two bodies changes with accelerating speeds, then experiments will quickly decide which body is moving. The lesson of the twin paradox is that, even in relativity theory, not everything is relative.

Speed reflects the distance covered during a duration of time; acceleration is a change in speed. It is surprising that accelera- tions have physical effects even though distances and durations are not physical properties.

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