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What is the Twin Paradox?

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Question: What is the Twin Paradox?
The twin paradox is a thought experiment that demonstrates the curious manifestation of time dilation in modern physics, as it was introduced by Albert Einstein through the theory of relativity.
Answer: Consider two twins, named Biff and Cliff. On their twentieth birthday, Biff decides to get in a spaceship and take off into outer space, traveling at nearly the speed of light. He journeys around the cosmos at this speed for about 5 years, returning to the Earth when he is 25 years old.

Cliff, on the other hand, remains on the Earth. When Biff returns, it turns out that Cliff is 95 years old.

What Happened?

According to relativity, two frames of reference that move differently from each other experience time differently, a process known as time dilation. Because Biff was moving so rapidly, time was in effect moving slower for him. This can be calculated precisely using Lorentz transformations, which are a standard part of relativity.

Twin Paradox One

The first twin paradox isn't really a scientific paradox, but a logical one: How old is Biff?

Biff has experienced 25 years of life, but he was also born the same moment as Cliff, which was 90 years ago. So is he 25 years old or 90 years old?

In this case, the answer is "both" ... depending on which way you're measuring age. According to his driver's license, which measures Earth time (and is no doubt expired), he's 90. According to his body, he's 25. Neither age is "right" or "wrong," although the social security administration might take exception if he tries to claim benefits.

Twin Paradox Two

The second paradox is a bit more technical, and really comes to the heart of what physicists mean when they talk about relativity. The entire scenario is based on the idea that Biff was traveling very fast, so time slowed down for him.

The problem is that in relativity, only the relative motion is involved. So what if you considered things from Biff's point of view, then he stayed stationary the whole time, and it was Cliff who was moving away at rapid speeds. Shouldn't calculations performed in this way mean that Cliff is the one who ages more slowly? Doesn't relativity imply that these situations are symmetrical?

Now, if Biff and Cliff were on spaceships traveling at constant speeds in opposite directions, this argument would be perfectly true. The rules of special relativity, which govern constant speed (inertial) frames of reference, indicate that only the relative motion between the two is what matters. In fact, if you're moving at a constant speed, there's not even an experiment that you can perform within your frame of reference which would distinguish you from being at rest. (Even if you looked outside the ship and compared yourself to some other constant frame of reference, you could only determine that one of you is moving, but not which one.)

But there's one very important distinction here: Biff is accelerating during this process. Cliff is on the Earth, which for the purposes of this is basically "at rest" (even though in reality the Earth moves, rotates, and accelerates in various ways). Biff is on a spaceship which undergoes intensive acceleration to read near lightspeed. This means, according to general relativity, that there are actually physical experiments that could be performed by Biff which would reveal to him that he's accelerating ... and the same experiments would show Cliff that he's not accelerating (or at least accelerating much less than Biff is).

The key feature is that while Cliff is in one frame of reference the entire time, Biff is actually in two frames of reference - the one where he's traveling away from the Earth and the one where he's coming back to the Earth.

So Biff's situation and Cliff's situation are not actually symmetrical in our scenario. Biff is absolutely the one undergoing the more significant acceleration, and therefore he's the one who undergoes the least amount of time passage.

History of the Twin Paradox

This paradox (in a different form) was first presented in 1911 by Paul Langevin, in which the emphasis stressed the idea that the acceleration itself was the key element that caused the distinction. In Langevin's view, acceleration therefore had an absolute meaning. In 1913, though, Max von Laue demonstrated that the two frames of reference alone are enough to explain the distinction, without having to account for the acceleration itself.
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