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Fiction, © Copyright 2000, Jim Loy
May I see your driver's license, vehicle registration, and proof of insurance?
Uh, here's the license...
Could you remove it from your wallet, please?
Sure. Sure. Here you are. And here's the registration and insurance.
Do you know why I stopped you?
I suppose I may have violated some bizarre law which I know nothing about, not that ignorance is any excuse. Actually it is an excuse, although maybe not a valid excuse. It is more of an explanation, I suppose.
How about speeding? Ever heard of that bizarre law?
Hm, I didn't think I was speeding.
37 in a 25 zone.
I noticed that you were driving in the opposite direction, Officer. How could you tell how fast I was going?
The radar compensates somehow. I don't know the details. I got a manual that explains it.
But Einstein showed that if an object (my car, for instance) is moving at a given velocity (say 37 miles per hour), that it is equally valid to say that it is motionless and that its surroundings were moving (37 miles per hour in this case) in the opposite direction. So from my point of view I was not going 37 miles per hour, but was motionless, according to the law of special relativity.
Good try. You were still speeding according to the laws of the State of Montana.
OK, how about this? Einstein also showed that when two observers are moving at different velocities, they cannot agree upon when and where any event happened. That, in turn, means that you and I (who are two observers in this case) cannot agree upon my speed. Einstein showed that my speedometer would not agree with your radar gun. And my speed as shown by my speedometer would be just as valid as the speed as shown by your radar gun. In fact my speedometer would be more valid, since it involves a more direct measurement.
Is that so? And just what speed did your speedometer show?
I don't know. I didn't look.
So, we have to rely on my radar gun.
Not necessarily. We can easily calculate the speed that my speedometer showed, if we know how fast you were going in the opposite direction. How fast were you going?
25.
Well then, let's see. 25 + 37=62, which is our relative Newtonian velocity in miles per hour. Our relativistic velocity is that number times the square root of 1 - 28 squared over c squared (because 62 miles per hour is about 28 meters per second). Let's see, that's 1 - 768 / c squared (c being about 3 times 10 to the 8th), and that is .9999992775. 62 times that is 61.999955205, minus 25 is 36.999955205. That was my speed, 36.999955205.
So you weren't going 37? You were going 36.9999 and some more digits?
Yes, 36.999955205.
I'll buy that. And uh. How about that? Your fine is the same number of dollars as it was ten minutes ago.
Well, all right... Wait a minute. Did I mention that space is curved in a gravitational field, according to the law of general relativity?