1. Article
  2. Intro to Time Dilation

Special relativity comes from two main premises:

1. The laws of physics are the same in all inertial reference frames
2. The speed of light (c) in a vacuum is measured to be the same in all inertial reference frames.

The second postulate is the one to focus on here. The classic thought experiment here is of the light clock which is two mirrors placed opposite each other. One "tick" of the clock is when light bounces off a mirror.

So the time taken for one tick is the distance traveled divided by the velocity, or, d/c. Now, let's set the clock moving relative to us at a constant speed of v. From our frame of reference the clock now ticks like this:

Where H is the hypotenuse of the triangle we would see. We can find the length of this using Pythagoras' theorem:

If we now plug this into our equation for t' and rearrange we find that:

But from before we know that t= d/c, so:

So as v increases, the clock appears to slow down relative to a stationary one. At the speed of light, the clock would stop

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  1. Pythagoras + Maxwell = Einstein
    Die Logik ist keine Lehre, sondern ein Spiegelbild der Welt. Die Logik ist transcendental. - Wittgenstein