From: bcr@cernapo.cern.ch (Bill Riemers)
Subject: Re: HELP! (was: Do starships collapse when flying near c?)
Organization: CERN, European Research Center for High Energy Physics
	<85f2qwd@rpi.edu>
Date: Fri, 11 Dec 1992 19:07:10 GMT

In article <85f2qwd@rpi.edu> ncc1701@madoka.its.rpi.edu (Mark O. Chadwick) writes:

> Shoot, you think you got it all figured out, and you see a post like this.
> Now I'm confused again.

> I thought the reason the speed of light was unattainable was
> because your mass increased as you approached c.  Therefore, you need
> more and more thrust to accellerate mass m' and eventually you
> need infinite thrust to acellerate infinite mass.

> Help!

Lets try an example:

Say we wanted to measure how much faster you can run than
your friend Bob.  So we have you both start at the same time
from the same starting line and time how long it takes you
to get 100m ahead of Bob.  Lets say it takes 100 seconds.
In this case you run 1m/s faster than Bob.  This is your
relative speed with respect to Bob.  According to Einstein
the only type of velocity we can measure is relative velocity.

So, now lets say we try the same experiment with you and 
Fred.  Admazingly enough, it turns out that you and Fred 
stay neck-to-neck no matter how long you run.  So your
relative velocity is 0 m/s.  In this case we say Fred
is at rest with respect to you.

Finially, we race you adgainst your nose.  Admazingly enough
you never seem to get ahead of your nose.  So likewise we
say your nose is at rest with respect to you.

Still with me?

Fred and Bob are nolonger runners, but starships.  You are
ridding in FRED.  Out the port window, you see BOB accellerating
away.  You measure how fast BOB is going by how long it takes
for the nose his ship to move 100km farther away from your ship.
As BOB moves faster, you also notice his ship is getting
heavier.  So, poor BOB doesn't have enough fuel to reach
the speed of light.  

However, this does not bother you.  Since the ship FRED
is a better ship, you should have no problems reaching
the speed of light dispite this mysterious increase in mass.
So, you turn on your engines.  After carefull measurements
you are surprised to discover that the mass of your ship
is not increasing.  (Maybe it was just a design flaw with
BOB.)  So, now you go down to the velocity measuring how
fast you are going.  To measure how fast BOB was going you
timmed how long it took for the separation between you and
the nose of BOB to increase by 100m.  Obviously you should
use the same method to determine how fast you are going.
To your horror you realize your nose isn't getting any
farther away.  You are at rest with respect to your nose.
No matter how high you turn-up the engines you will never
move with repect to your  nose.  So it looks like you'll
never reach the speed of light either.

I know this argument sounds like it is flawed, but it
is not.  Velocity really is completely relative.  The only
reason we don't notice this in everyday life, is because
it is much easier to measure everything with respect to
one referance frame rather than many.  So standardly we
measure velocity with respect to the Earth rather than
each-other.  It took a Genious like Albert Einstein to
point out that in such a system we will make a mistake
for objects moving very fast with repect to eachother.

                            Bill


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