From: davidme@qdpii.comp.qdpi.oz.au (David Meiklejohn)
Subject: Re: Relativity
Organization: Qld Dept Primary Industries
Date: Mon, 7 Sep 1992 12:53:50 GMT

In article <14902@mindlink.bc.ca> Alan_Barclay@mindlink.bc.ca (Alan Barclay) writes:
>#4300029 from John Roberts
>
>I always thought I had a good handle on the basics of relativity.

Well, we all like to think we do, don't we?  :-)

>Can you have a look at this for me, and tell me what you think?

OK, I'm just a humble engineer, but let's see...

>A Thought experiment:
>
>Star A is four light years from star B.  A spaceship leaves earth
>and accelerates to .9 C and ceases acceleration when it passes
>Star A.  An observer inside the moving frame notes the length of
>subjective time passing.  When the ship passes star B, the observer
>inside the frame has only experienced 1.95 subjective years.  For him,
>he traversed four light years in only 1.95 years.  A subjective speed
>of 2.05 C.

 [ mathematics deleted ]

>However, if he were to use instruments to determine his velocity
>relative to the frame of reference, his velocity would remain .9 C.
>
>The only flaw I can see in this is if my observer's velocity somehow
>changes the timing of his observations of incidence with Star A or B.

No, his time measured is 1.95 years, as you say.  What you're missing is that
there is no favoured frame of reference, given that he's not accelerating.
Therefore, as far as our astronaut is concerned, he's stationary, and the
universe is rushing by at 0.9 c.  Now, when you move, the only relatavistic
effect isn't time dilation.  You gain mass, and your metrics contract in the
direction of motion.  This last effect means that the observer measures the
distance between the stars as 2.17 ly.  As far as he's concerned, he's taken
1.95 years to travel between two objects 2.17 ly apart, so he's measured his
speed as 0.9 c.

So, it all works out.

>A recent SF book used relativistic mass to produce black holes.
>i.e. accelerate a spaceship until it's massive enough to collapse
>into a singularity.  Something seems missing in this equation.
>Could it happen?

I don't see why not.  To continue to accelerate, the spaceship needs energy.
An increasing proportion of this energy is converted into mass, rather than
velocity, as c is approached.  The real question is, where did the energy
come from?  Assume that the spaceship used a perfect antimatter drive, so
that all of the mass of it's fuel is converted into energy and is used for
acceleration.  In effect, your just turning mass into mass as c is approached.
Nothing is gained, except maybe some compression, depending on how the ship
is arranged.  If that's the case, it would have to be close to gravitational
collapse before it started.

Maybe energy is fed from outside as it travels.  Sounds dubious to me.

>Not knowing the more complex math of relativity, I have no way of
>proving it to myself.  But I wonder if time dilation due to velocity
>(and the gravitation itself?) would put the singularity at the end of
>an asymptotic curve, like v=1.0C, completely unachievable.

I'm hardly an expert on black holes, but you don't need infinite density to
initiate collapse, which is what your v=c would imply.


-- 

David Meiklejohn                  | Internet : davidme@qdpii.comp.qdpi.oz.au
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