From: roberts@CMR.NCSL.NIST.GOV (John Roberts)
Newsgroups: sci.space
Subject: Re: Relativity
Date: 8 Sep 92 21:51:46 GMT
Organization: National Institute of Standards and Technology
	formerly National Bureau of Standards


-From: Alan_Barclay@mindlink.bc.ca (Alan Barclay)
-Subject: Re: Relativity
-Date: 7 Sep 92 04:40:24 GMT
-Organization: MIND LINK! - British Columbia, Canada

-#4300029 from John Roberts

-I always thought I had a good handle on the basics of relativity.
-Can you have a look at this for me, and tell me what you think?

-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.

-          ---->---->---->---->---->.9C
-              *A             *B

-                                                   __
-                 T = d/v     ->   T = 4ly/0.9C = 4.44 yrs
                                     ________________
-                 Tsubjective = T x \/ (1-(v*v/c*c))

-                              = 4.44 yrs x 0.44
-                              = 1.95 yrs

-                 Vsubj = d/Tsubj = 4ly/1.95yrs
-                                 = 2.05 ly/yr


-However, if he were to use instruments to determine his velocity
-relative to the frame of reference, his velocity would remain .9 C.

The astronaut knows from previous experience that the distance from A to B
in the frame of reference of A and B is 4 light years, so only in that sense 
he can say that the "effective" speed was greater than that of light. However,
by any measure he can make while traveling, the distance from A to B is less
than 4 light years, so it still works out to .9 c.

-From: davidme@qdpii.comp.qdpi.oz.au (David Meiklejohn)
-Date: 7 Sep 92 12:53:50 GMT
-Organization: Qld Dept Primary Industries

-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.

You divided by .9 instead of multiplying by it. The correct measured distance
is 1.74 light years. Otherwise, I agree.

-From: sk4i+@andrew.cmu.edu (Samuel John Kass)
-Subject: Re: Relativity
-Date: 7 Sep 92 15:15:49 GMT
-Organization: Sophomore, Math/Computer Science, Carnegie Mellon, Pittsburgh, PA

->>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.

-Could it?  I'm no expert either, but I thought that to get collapse,
-parts of the object had to be pulling against each other.  Since the
-ENTIRE spaceship is accelerating, from the frame of reference of the
-spaceship, wouldn't it be 'normal' mass?  Of course, from the frame of
-reference of a 'stationary' observer, the spaceship will have sqashed
-itself so flat that it should have fused anyway.  Since, by general
-relativity, there is no preferred frame of reference, why would the
-Earth, then, not collapse into a black hole, just because such a thing
-is possible.  (ie. Compared to the frame of reference of something else,
-the Earth has enough mass to collapse.)  For example, there may be an
-object in the universe travelling at such speeds that, to it, the Earth
-should have collapsed into a black hole.  But we're not a black hole. (I
-don't think.)

I think that's about right. The spaceship doesn't think that it's become
more massive. I don't know about interstellar gas and dust that the
spacecraft may encounter along its path - from its viewpoint, the
spacecraft should be perceived as more massive. Also, I don't know whether
increased mass/gravity would be perceived by an observer to the side.
I strongly suspect that to include gravitational effects, even with objects
of constant relative velocity, we have to go to general relativity, which 
makes things much harder for the amateur to figure out.

Another "paradox": suppose you run a train station, and a train of known
(rest) length is approaching the station at relativistic speed. You decide
that it would be a good prank to fire two paintballs at the train, a yellow 
one at the engine, and a blue one at the caboose. You want to fire the two 
paintballs at exactly the same time, so you set up the two paintball guns 
the (previously known) length of the train apart along the station, minus 
a smidgen, and use a calculation of the arrival time of the engine at the
yellow paintball gun to control both paintball guns. (You can put a high-speed
camera with a wide-angle lens midway between the two guns to verify that they
fire simultaneously.) (Note that accurately calculating the arrival time of
the engine isn't as easy as it looks, but it can be done.) Now the train 
zooms past the station and you fire the paintball guns. As the train speeds
away, you go to a telescope and look at the train for paint splotches
(compensating for the redshift, of course, so there's no confusion about
the colors). By the principles of special relativity, you find that you have 
hit the engine (yellow), but missed the caboose. Since the guns were fired at
exactly the same time, you conclude that the train was actually shorter
than you had been led to believe from its description. So far, so good, but
that's not all there is to the story.

Now suppose that the engineer on the train has a powerful telescope, and he
sees the paintball guns at the station, and figures out what you're up to,
so he decides that turnabout is fair play. He mounts two paintball guns on
the train, a green one at the front of the engine, and a red one at the
back of the caboose. Using techniques similar to your own, he calculates
exactly when the engine will pass the yellow paintball gun at the station,
and rigs a control halfway along the train to fire both of the train's
guns at that instant. The station whizzes by, and the guns fire. Looking
back, the engineer sees that the yellow paintball gun has been hit with the
green paint - a good shot. However, the red paintball has missed its target -
it hit way behind the blue paintball gun (i.e. further from the yellow
paintball gun than is the blue paintball gun). The engineer can draw the
logical conclusion that the train station was shorter than he thought is
was. 

Now it begins to look more confusing: from the viewpoint of the train, the
station is shorter, but from the viewpoint of the station, the train is
shorter, and both had their shots go wide (by the same amount, incidentally).
It seems like these two event would be mutually inconsistent. Fortunately,
the paradox can be resolved by an adjustment of the concept of simultaneity.
>From the viewpoint of the train engineer, his two shots were simultaneous,
meaning that an observer in the middle car of the train would see the flash
(or EMP, or whatever) of the two guns at exactly the same time. Similarly,
an observer standing on the platform at the station midway between the
two paintball guns there would see them fire at the same time. However, from
the viewpoint of the train, the station did *not* fire its guns simultaneously,
and vice versa. To the train engineer, it looks like the yellow gun fired
first, then the blue gun. From the viewpoint of the station, the red gun
fired first, then the green gun. Thus, nobody sees any inconsistencies. 
That's part of what I meant when I said in an earlier post that between
different frames of reference, simultaneity has no meaning (though you might
set up a single reference point at locations in the two frames that are
temporarily coincident in space).

Note that this is just a thought experiment - it's not entirely realistic,
and some of the details have been glossed over. For instance, having four
different colors of paintballs would be too expensive, and I bet green ones
are hard to get since they don't show up well on camouflage. There would
also be a few complications with the physics. :-)

For additional amusement, what do the wheels of the train look like:
 - from the viewpoint of a person at the station?
 - from the viewpoint of a person on the train?
 - from a camera mounted on a wheel?

John Roberts
roberts@cmr.ncsl.nist.gov

Newsgroups: sci.space