Re: David question four: the "beer paradox" (string theory?)
From: N:dlzc D:aol T:com \(dlzc\) (net_at_nospam.com)
Date: 12/11/04
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Date: Sat, 11 Dec 2004 13:22:25 -0700
Dear DavidBowman:
"DavidBowman" <dt041054@yahoo.com> wrote in message
news:1102785462.672904.101100@z14g2000cwz.googlegroups.com...
> If a massive galaxy is halfway between us and a distant bright galaxy,
> General Relativity correctly predicts that light from the bright galaxy
> will be bent towards us by the gravity of the massive galaxy (i.e., the
> massive galaxy is "lensing"). The path light takes is called a
> geodesic, and though it appears to be curved, it is actually the
> "straightest possible" line between us and the distant galaxy.
Actually, *all* particle/body paths that are not affected by forces are
geodesics. Light travels a null geodesic, which is somewhat special.
> Now, consider two spacecraft: each ship has a string wound up on a
> spool, with one end hanging out the window and tied to a telephone
> pole. The strings are reeealy long, and as a spaceship flies away,
> more and more string unwinds from the spool and is pulled out of the
> window. One spaceship flies to the distant galaxy following the path
> light takes
It can't. The ship is massive, no? Mass cannot travel a null geodesic.
>, and one flies directly through the dark massive galaxy.
>
> If they both go the same speed, the ship following the light-path
> geodesic will arrive first (i.e., in the shortest possible proper
> time), so the pilot hangs around, drinking beer and waiting for the
> second ship to arrive. When both ships have landed next to each other
> in the distant galaxy, the strings hanging out the windows are cut.
> Each pilot tugs on his string, which rings a bell dangling from the
> other end of each string. This tells a real strong guy waiting near the
> telephone pole to retrieve the strings by winding them up on two big
> spools, measuring the length of each string as he does so.
>
> Now: the string running through the massive galaxy is shorter because
> the geodesic detour path is longer -- arbitrarily longer. In fact,
> it's excess length is limited only by the mass of the intermediate
> galaxy. The detour could even be many times the "straight-line"
> distance through the intermediate galaxy.
>
> On the other hand, the string from the ship landing first is shorter
> because it spent less time unwinding. We know that because the pilot
> was sitting around drinking beer while the other pilot was still
> feeding string through his spaceship's window.
>
> The question to answer is: what brand of beer was he drinking?
>
> Just kidding.
> What I really want to know is: which string is actually shorter?
You've got a really muxed up situation. Strings that cannot physically
exist, signalling that will take aeons to occur, and no clear description
of terms. "Both ships travel the same speed." By who's measure is this
assured? Neither ship will agree that the other travels at the same speed.
David A. Smith
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