| Jeff Silverman
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01-07-2004 12:23 AM PT (US)
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Einstein says that only some things are relative, but other things are absolute. The speed of light is always 299,792,458 meters/second. It might not move in a "straight" line, but it always travels 299,792,458 meters/second.
For example, suppose I am traveling on a railroad flat car moving on a straight track at 80 Km/hr, and I throw a ball in the same direction as the train is moving at 40 Km/hr. An observer on the ground (perhaps using a radar gun similar to what police officers use) would measure the speed of the ball with respect to the ground as 120 Km/hr.
Now... suppose instead that the train is traveling at 180,000 Km/sec, or 3/5c, and I throw the ball at 240,000 Km/sec or 4/5c. If the problem took place in a "Newtonian" universe, then the observer on the ground would see the ball moving at 7/5c or 420,000 Km/sec. But in fact, both the train, the ball, and my arm are Lorentz contracted. The observer on the ground sees the ball moving at
Vobs = (Vtrain + Vball)/(1 + ( Vtrain * Vball)/(C**2))
or (3c/5 + 4c/5) / ( 1+ (3c/5 * 4c/5 )/c**2 = 7/5 / 37/25 = 35c/37
(One of the reasons why we use 3c/5, 4c/5 in these problems is that 3,4, and 5 form a Pythagorean triple. In some cases, that's helpful, but not in this one.
So the point of this discussion is that while some things are relative, not all things are relative; and one must be careful using the laws of physics as social metaphores.
Jeff
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