carnes@gargoyle.UChicago.UUCP (Richard Carnes) (11/24/84)
----- Here is a simple (or simple-minded) explanation of why c is the universal speed limit. It follows directly from the postulate that the speed of light is always observed to be c. This thought experiment also helps one to "visualize" the slowing down of time in a frame of reference in motion with respect to the observer. Imagine a spaceship with a "light clock", i.e., a ray of light bouncing back and forth vertically between two mirrors. Since the distance between the mirrors (h) and the speed of the ray (c) are both invariant for the crew, the time it takes the ray to traverse the distance (h/c) is invariant for them as well. As the ship moves past you from left to right you observe the ray traversing the following path, through a window in the ship: | * * * * * * * * * * * * h| * * * * * * * * * * * * * * * * * * * * * * * | * * * * * * * * * * * * * * * * * * * * * * * | * * * * * * * * * * * Since the light is now moving along the hypotenuse of a right triangle one of whose sides is h, it appears to you to be traversing a greater distance than h between bounces. But its observed velocity is still c; hence it appears to you to take longer than h/c to traverse the distance. The Lorentz transformation equation can be derived quite simply from the Pythagorean theorem. (This is left as an exercise for the student.) Now let us suppose, although it is impossible, that the ship's velocity is c. Now the ray of light appears to you to take the following path: *************************************************************************** I.e., it appears to be stationary within the spaceship. Why? Because if there were any vertical component to the ray's observed velocity, the resultant (diagonal) velocity that you observe would have to be greater than c, since the horizontal component is already c. But the observed velocity of light is always c; therefore it is impossible for you to observe any vertical motion of the ray, and hence the clock and time as well appear to have stopped within the ship. Now if we suppose that the ship's velocity is greater than c, any conceivable observation by you would contradict our hypotheses that the ray is bouncing between the mirrors and that the observed velocity of light is always c. Therefore the ship cannot exceed the speed of light. Richard Carnes ihnp4!gargoyle!carnes