Date: 02/17/99 at 04:30:06 From: Greg Subject: Anomalous Addition I heard from someone that a physicist by the name of Richard Feynman proved that 2 + 2 is sometimes not equal to 4. Can you clarify what this is? If it is true, when does it occur and why?
Date: 02/17/99 at 09:57:04 From: Doctor Mitteldorf Subject: Re: Anomalous Addition "2 + 2 is sometimes not equal to 4" Physicists will often say things like this, but of course they do not mean it literally. Literally, you know very well how to add 2 and 2, and you will always have the right answer. But here is an example of the kind of thing that sounds like a violation of the laws of simple addition. Suppose a train is going by at 20 km per hour, and there is a boy running through the aisles of the train at 20 km per hour. You are standing on the platform next to the train, and you mark where the boy is, and click your stopwatch. You can mark where he is a few seconds later, click your stopwatch again, and divide the distance he moved by the time distance to determine how fast he is going. Of course, you will find he is going at 40 km per hour, because 20+20 = 40, and his speed is just added to the train's speed. It is almost inconceivable that it could be otherwise. It seems like just simple addition. But the rules of relativity that Einstein derived in 1905 tell us it is not quite true. In fact, if the train had been going at 200,000 km per second instead, and if the boy had been running at 200,000 km per sec, then when you measured his speed you would not get 400,000 km/sec but 277,000 km/sec. When speeds get close to the speed of light, they do not behave the way you think they do. The sum of 200,000 and 200,000 is still exactly 400,000 but adding is not the appropriate way to combine these two speeds, even though it seems "obvious" that it should be. - Doctor Mitteldorf, The Math Forum http://mathforum.org/dr.math/
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