Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Posting-Version: version B 2.10.2 9/18/84; site utastro.UUCP
Path: utzoo!watmath!clyde!burl!ulysses!mhuxr!mhuxn!ihnp4!qantel!lll-crg!dual!mordor!ut-sally!utastro!matt
From: matt@utastro.UUCP (Matt Wood)
Newsgroups: net.space
Subject: Re: Time Retardation
Message-ID: <73@utastro.UUCP>
Date: Fri, 15-Nov-85 17:31:52 EST
Article-I.D.: utastro.73
Posted: Fri Nov 15 17:31:52 1985
Date-Received: Sun, 24-Nov-85 07:27:06 EST
References: <8511111807.AA01976@s1-b.arpa> <399@sesame.UUCP>
Organization: U. Texas, Astronomy, Austin, TX
Lines: 63

> > 
> > 
> > The difference in the rate at which time passes for two different inertial
> > frames of reference is determined by the Lorentz Transformation:
> > 
> > 	     ---------
> > 	    /    v**2		v = Velocity of one frame with respect to
> > 	\  / 1 - ----			the other.
> > 	 \/      c**2		c = Speed of light.
> > 
> > As one approaches the speed of light, the rate that time passes in one
> > frame of reference (like a spaceship) as "observed" from the other
> > (say on Earth) approaches zero.
> 
> What happens if two ships leave with opposite vectors, and they both approach
> the speed of light relative to their initial frame.  The v above, relative to
> each other, would approach 2*c, giving a non-real answer.  Where am I goofing?
> (Or is it time to invest in a FTL ship?  :-) )
> 
> 
> -- 
> Opinions expressed are public domain, and do not belong to Lotus
> Development Corp.
> ----------------------------------------------------------------
> 
> Simcha-Yitzchak Lerner
> 
>               {genrad|ihnp4|ima}!wjh12!talcott!sesame!slerner
>                       {cbosgd|harvard}!talcott!sesame!slerner
>                        talcott!sesame!slerner@harvard.ARPA 

Velocity transformation isn't as simple.   Assume there's two
reference frames, K1 and K2, that K1 is at rest, and that K2
is moving at velocity v along the x-axis.  Your question then
is:  if I have a space ship in K1 moving in the -x direction
at nearly the speed of light, there's a ship in K2 at rest, and
K2 is moving in the +x direction (as seen from K1) at nearly
the speed of light (i.e., v = (nearly) c), then what is the
velocity of ship 1 as measured by ship 2.

Let u1 = the velocity of ship 1 as measured in K1.
We want to know the expression of 
u2 = the the velocity of ship 1 as measured in K2.
The equation is:

	u2 = (u1 + v) / (1 + (v*u1) / c**2 )

For v = u1 = 0.990000 c, we get

	u2 = 0.999949 c

You can see that in the limit, u2 = c.
If you want, see the book "Special Relativity" by Resnick.
It's written for an undergrad jr.-level course for science
majors, and is small, unintimidating, and clearly written.

"If this is SU UMa, then my great, great, great grandchild must be dead."

-- 
		Matt A. Wood 
		Astronomy Dept, University of Texas, Austin TX 78712  
		{allegra,ihnp4}!{ut-sally,noao}!utastro!matt	(UUCP)
		matt@astro.UTEXAS.EDU.				(Internet)