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

Einstein described the time dilation of traveling clocks in 1905. The "twin paradox" was first noticed in 1911, when Paul Langevin restated time dilation in the now famous "paradox". Paraphrased, he wrote: "Pam, Jim's twin sister, undertakes a long and fast round-trip in space. On her return to Earth, she finds that her twin brother has aged quite a bit more 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. The solution to the paradox lurks in the fact that Pam has been accelerated for some parts of the trip, while Jim has not. 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.

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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?br /> 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!

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