Demystifying Special Relativity, Part 2

OK, so we know what the theory of Special Relativity says. Now I want to examine some of the consequences that arise. Please understand that Special Relativity and it's effects are not things that we normally feel on a day to day basis. This is because neither we nor anything that we (unless you're in some specialized profession) care about moves anywhere near the speed of light relative to anything that matters to us. This is what makes the ideas of Special Relativity seem so crazy sometimes. We need to stretch our common sense notions of space and time, in order to really get a grasp of the theory and its effects.

Time Dilation

Imagine a clock like the one shown below. It has a light source on the bottom, a mirror on top, and a detector on the bottom to detect the signal when the light comes back down. So the time for it to go up and down is the twice the height of the light clock divided by the speed of light, c.
Now imagine that the light clock is moving relative to you. You would see the light follow a triangular path, like that shown in the second picture in the series below.



Basic trigonometry and the Pythagorean theorem will inform you that the distance from the detector to the mirror and back in your reference frame is greater than that in the proper frame of the clock. Proper is just a word that means in the rest frame. So now we know that the distance traveled for the light to get back to the detector in a non-proper frame of the clock is larger than in the proper frame of the clock. We also know, from the laws of electromagnetism, that light travels at speed c, always. So, we have the same speed and a larger distance. Because time elapsed is inversely proportional to velocity and directly proportional to distance, as distance increases, time elapsed also increases.

The time elapsed in a reference frame moving with respect to an observer is longer than that elapsed in the proper frame of the observer. When something moves and an observer looks at the moving thing, he sees time go by slower in the moving thing.

Note: Everything seems normal to the moving guy. In the guy's proper frame everything is just like it would be if he was in any other uniform state of motion.
Note: The Light Clock used above is just an example. Time dilation is not some unique effect of the light clock, nor is it just an effect of clocks in general. Time dilation is a property of space-time, which is the framework of our universe.

In the next entry I'll discuss length(Lorentz) contraction and start discussing what space-time is.