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Many folks have the impression that relativity constitutes the hardest set of concepts in physics to understand, next maybe to quantum physics. Well, I won't make any claims about quantum physics, but relativity is actually one of the easiest set of concepts in physics to grasp, because the basic ideas are so direct and easy to visualize. A key fact used to construct relativity is that the speed of light in a vacuum is the same, seen by all observers moving at constant velocity with respect to one another and to the source of light. Let's take a famous consequence of relativity: processes moving relative to the observer take longer to occur than processes at rest with respect to the observer. This is true for any process in nature. Now, processes generally involve interactions between the material pieces of the system. On their best day, these interactions can only travel at the speed of light. So let's take an example that only involves "naked light," and is thus very simple to visualize. |
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Imagine a process in which a pulse of light bounces between two mirrors. If the speed of light is c and the distance between mirrors is L it is easy to see that this periodic process "ticks" in a time given by 2L/c. Now imagine an identical system moving relative to us. Clearly, the process takes much longer to happen, because the light, travelling at the same speed as before, must cover a larger distance and thus takes longer. If you remember the Pythagorean theorem, and Middle-School geometry, you might even be able to see that, if the ticking time in the clock's rest frame is T and the moving clock's speed is v, the time T0 it takes to "tick" is given by the expression under the sketch. If you don't see this, don't worry, the main thing is that you do see it takes longer. And the math agrees with your eyes, because since the square root factor is always less than one, T0 must be larger than T |
 
If you think you can handle the algebra, click here. |
Can you stand some numbers? Suppose a process takes 3 seconds when it happens with us standing at rest beside it. If now we view an identical process that is moving past us with v/c = 0.8, since the square of 0.8 is 0.64, and 1 - 0.64 = 0.36 and the square root of 0.36 is 0.6, we see that T0 = T/0.6 = 5T/3. Thus we see the process take 5 seconds, not 3 seconds. This result agrees with the everyday experience of nuclear and particle physicists. Particles or systems of particles which undergo processes taking a millionth of a second when observed at rest, take longer for the same processes by precisely the amounts predicted by this simple argument, when moving at speed v with respect to the detectors, lab equipment and experimenters.
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The most important thing to realize about all this is that it is your own personal process that marks time T, and anyone else's process that marks time T0. That is, there is no clock or process that is "right" and others that are "slow". The processes at rest with respect to you always take their "proper" time, while processes moving with respect to you are always slowed. If James has a clock, and Jules has an identical clock, then James's clock gives the correct time for James, while he observes Jules's clock running slow, while Jules observes James's clock running slow and his own keeping the correct time. This is easy to understand from the bouncing light example. Any number of identical bouncing light clocks can be imagined, moving at any number of different constant velocities. The one we choose to ride along with is giving the "right" time, while all the others run slow. |
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Check out this nifty applet showing a moving clock compared to two synchronized stationary clocks.