Special Relativity

Date: 11/1/96 at 2:0:47
From: Timothy J Parrotte
Subject: Einstein's Theory of Special Relativity

Please explain Einstein's Theory of Special Relativity to me.  
I understand that if a person is stationary, that person's time 
will be greater than a person who is in motion. Does this mean that 
time is different for everyone who moves when compared to a stationary 
clock? Wouldn't this also mean that all over the world everyone reads 
a different time, since the clock they read is moving with them?  

Here's an example I have been pondering: There are two people; a 
runner and a coach. Each has his or her own stopwatch. Both start it 
when the runner starts running and they stop it when the runner stops.  
Won't the runner have a different time than the coach's time? The 
runner's time will be less than the coach's time, right? If not, why?  
If this is true, what is a true measurement of time?

Date: 11/1/96 at 11:37:15
From: Doctor Allen
Subject: Re: Einstein's Theory of Special Relativity

To answer your questions, first realize that special relativity states 
that there is no such thing as a stationary person. In order for us to 
say something is not moving, we have to compare it to something else. 
For example, when you're in a car, the person sitting next to you is 
not moving as far as you're concerned, but appears to be moving to a 
person standing on the street. The person standing on the street is 
not moving as far as a person next to them is concerned, but both 
appear to be moving (in terms of rotation of the earth) to a person on 
the moon. The only way to say something is stationary would be to 
have one thing absolutely still that everything else could be compared 
to. Einstein's theory says there is no such thing. So the special 
theory actually says that clocks in motion relative to an observer 
will appear to run slower than a clock in the observer's hand. This 
means that time is different for two different people if they are 
moving relative to each other. In general, everyday motion, such as 
walking, driving, or even flying, is not fast enough to make the 
effects of special relativity noticable.   

For your coach and runner problem, you need to consider that special 
relativity states that things that are at the same time for one 
observer may not be at the same time for another observer. In other 
words, if the runner sees that she stops the stopwatch at the same 
time as the coach, the coach may not see it as happening at the same 
time. Since the two are in motion relative to each other, they cannot 
operate the stopwatch simultaneously. At the speeds we're talking 
about, the difference in perceived time between the two is so small 
that it is not measurable. At the speed of a runner (say 15 mph) 
for 5 minutes, the difference between the two would be roughly 
.00000000000000001 seconds! In other words, it would take over 
300 million years to make a difference of 1 second. So the answer is 
"yes" the times would be different, but the difference would be too 
small to measure.

-Doctor Allen,  The Math Forum
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