Travel Faster and Stay Younger

The famous "twin paradox" of relativity was born in 1911, after Paul Langevin restated Einstein's time dilation of traveling clocks. It can be paraphrased as follows: "Pam, Jim's twin sister, undertakes a long, very fast space journey and on her return to Earth, finds her twin brother quite a bit older than herself".

It is called a 'paradox' because skeptics argue that after the Pam has reached her cruising speed, she could consider herself as stationary and that it's Jim (on Earth) that rushes away from her at great speed. In such a case, Pam must be aging faster than Jim. This is not the case however, as has been verified experimentally in particle accelerators many times.

To solve the paradox, one must consider the fact that Pam was physically accelerated by her spaceship, while Jim stayed at rest. However, experiments have also shown that acceleration does not directly affect good atomic (or biological) clocks. It is only the time that Pam spends traveling at the high speed relative to Jim that determines how much younger than Jim she will eventually be.

Einstein's relativity theory demands that space and time should be considered together as an entity called space-time. When Pam and Jim are together and stationary on Earth, they both acquire the space-time movement of their location on Earth. Since they do not move relative to that location, their space-time movements are the same as their time movements (the rate at which they grow older).

This acquired rate of space-time movement remains constant for both twins. As soon as Pam moves away from Jim, the change in the rate of her space movement (SM) is "subtracted" from the rate of her time movement (TM) in order to keep her acquired rate of space-time movement (STM) constant. Actually, it is the squares of the rates that are added/subtracted, which can be stated like this:

STM squared = SM squared + TM squared = Constant. (1)

It is like using the Pythagoras theorem for finding the hypotenuse of a triangle, only in this case the hypotenuse remains constant and the other two legs of the triangle can change, but they must satisfy the theorem.

While Pam is moving relative to Jim, she retains her rate of space-time movement, meaning that her rate of time movement must come down. Since the values are squared, it does not matter in which direction the movement is; the effect is the same for her outbound trip and her inbound trip.

To give some practical values: let Pam travel away from Jim at 60% of the speed of light and turn around after 4 years on her clock. If she returns at the same speed, it is obvious that she would have aged 8 years on her trip. However, she would find Jim to be 10 years older than when she left him, and he will have the birthday cards to show that! This should please Pam…

Let's verify the values with equation (1) above: Jim has not moved through space, so for him: STM squared = 0 + 10 squared = 100. Since Pam has moved, we must know how far she has moved according to Jim. At 60% of the speed of light for 10 years, she must have done a total distance of 6 light-years, hence for Pam: STM squared = 6 squared + 8 squared = 100, satisfying the theory.

That's it, girls! As Pam has shown, travel keeps you young!