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### Light and the Theory of Relativity

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Date: 10/15/97 at 22:02:45
From: Ashton Bennett
Subject: Theory of Relativity

Based on the theory of general relativity, where the faster something
goes, the slower time goes, how come light can go anywhere?

I read my encyclopedias, and checked out books from the library.
I am a second grader who has just started algebra and ninth grade
science in the gifted and talented program with my school.
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Date: 10/16/97 at 13:24:07
From: Doctor Tom
Subject: Re: Theory of Relativity

Except for light, nothing can go at the speed of light, so in a sense
it's meaningless to ask what a clock would do if it were travelling
at the speed of light.

But what happens is this. Time only slows down for the observer going
at that speed.

Take two perfect clocks on earth, and set them to the same time.
Now move one of them slowly to a planet on another star that's four
light-years away. In the meantime, continue to move the clock on earth
at the same slow speed so that its time is slowed by the same amount
as the clock you're carrying to the star, and stop it when the other
clock gets to that star.

So from the point of view of somebody sitting on earth, both those
clocks show exactly the same time.

Now assume somebody in a fast rocket goes racing past earth toward the
other star, and as he passes earth, he synchronizes his clock with the
one he sees on earth.  If he's going at half the speed of light, from
our point of view on earth, it'll take him eight years to get to the
other star, and the clock on that star will have thus advanced by
eight years, but the clock on the rocket ship when he passes the other
star will read significantly less than eight years.

The faster the rocket goes, the less time will go by on the rocket's
clock when it reaches the new star. If the rocket is going at
.99999999999999999999999999 times the speed of light (from our point
of view on earth), its clock may advance only a fraction of a second
for the entire trip.

If it were possible to carry a clock on a light beam that passed
earth, that clock would not advance at all when it was at the next
star. It seems weird and counterintuitive, but that's the way it is.

In fact, in a calculation similar to distance calculations we do, you
can calculate the "interval" in a relativistic sense between two
events, and it's possible for that interval to be zero for different
events. The arrival of the light beam at earth is one event and the
arrival at the other star is another event, and the interval between
the two is zero.

If x, y, z, and t are the differences in the coordinates in space and
time between two events in some inertial reference frame, the interval
between the events is:

square root(x^2 + y^2 + z^2 - (ct)^2)

where c is the speed of light. The interval will be the same for any
observer in any reference frame. For the guy racing past in a rocket
ship, the distances are shrunk, but the time is exactly shrunk to
match it.  For the guy "travelling on a light beam," both distance and
time are shrunk to zero.

This stuff is not obvious, and it'll take you a while to get an
intuitive feeling for what's going on.

-Doctor Tom,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
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Associated Topics:
High School Physics/Chemistry

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