Anomalous Addition

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/