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From: dxm@lanl.ARPA
Newsgroups: net.physics
Subject: Re: "speed of light" puzzle
Message-ID: <25676@lanl.ARPA>
Date: Fri, 10-May-85 12:46:37 EDT
Article-I.D.: lanl.25676
Posted: Fri May 10 12:46:37 1985
Date-Received: Mon, 10-Jun-85 05:57:17 EDT
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Organization: Los Alamos National Laboratory
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> I find it sad that people interested in physics (at least enough to
> read net.physics) don't have *some* basic ideas about relativity,
> as shown by the recent discussion about speed of light. Sigh.
> 
> Anyway, here is the puzzle:
> 
> I have a laser on a turntable in such a way that the beam falls on
> the moon during each revolution. If my laser rotates at omega
> rad/s and the moon is at distance D, the spot moves on the moon
> at speed V = omega*D. Since I can make omega as big as I want,
> V can be made very big, and certainly much more than C. (e.g.
> with D ~ 300,000km and omega = 10rad/s, a very gentle speed,
> V = 3,000,000km/s = 10*C)
> 
> How can anything move at 10*C without violating relativity ?

I suppose somebody should answer this "puzzle" for the sake of
completeness in the universe.  Nothing is moving faster than c here.
As anyone who took PHY 353 at UT Austin will tell you, the spot on the
moon can go as fast as it likes because it is not an entity except in
your mind.  The spot that exists over Tycho crater, say, is not the same
spot ( and here I mean same energy or aggregate of photons ) as the spot
several kilometers away a few seconds later.  Since there is no actual
motion involved here (except for the light going from laser to moon),
relativity isn't destroyed which is a great relief to us all. :-)

And now, a counter-puzzle: replace the above laser with a long ( *very*
long) rod.  It is easy to move it at the 10 rad/s speed mentioned above;
how fast is the rod moving out near the moon ?  Pseudo-hint: rigid body
mechanics ain't gonna help you here.  Make any assumptions you like
about the rod (mass distribution, moment of inertia, rigidity, etc), just 
don't replace it with a string (in which case the problem becomes "how long
does it take to roll up a very long string ?").
 

 Doug Miller     currently at         dxm@lanl
                                 ....!ihnp4!lanl!dxm
Los Alamos National Laboratory,  P.O.B 1663 MS J960,  Los Alamos, NM 87545
 
		 but soon to be at ...ihnp4!ut-ngp!bomber
				   bomber@ut-ngp.arpa
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