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From: tm2b+@andrew.cmu.edu (Todd L. Masco)
Newsgroups: sci.space
Subject: Re: Approaching c
Message-ID: <YXs1Dcy00WB8EINop7@andrew.cmu.edu>
Date: 27 Jan 89 07:02:00 GMT
Organization: Carnegie Mellon, Pittsburgh, PA
Lines: 57

CALVIN@JHUIGF.BITNET ("That's not lake Minnetonka...") writes:

> Anyway, here goes. It seems to me that the argument for the impossibility of
> attaining speeds faster than c is flawed. Logically, an argument is invalid
> if it, at some point, assumes that which it attempts to prove.
	...
> Damian Hammontree
> System Programmer

	 Okay, he's your basic problem.  You're looking at the problem
 as though relativity was attemptig to argue through logic;  It isn't
 _exactly_ trying to do that;  rather, it's trying to provide a model
 that expresses what happens in "reality" (quotes for the enjoyment of
 you quantum people).  

	 The following gives a fairly reasonable explanation for you,
 as a mathematics person:

	 Picture a typical graph of a hyperbole, say (x-c)(y-m) = (C).
 [First c = c, second C = some constant, m=rest mass of object].

	 Now, imagine that, instead of moving along the x axis (which
 we will now reveal to be 'velocity') when kinetic energy is added,
 imagine that it moves along the line of the _graph_.

	 Close enough to x=0, the graph seems to be a straight
 line.  No problem.  Newtonian mechanics works fine.

	 Once we get past, say x=c/10, we being to notice some amount
 of discrepency;  We're not quite going as fast as we should, time's
 getting a wee bit altered, and some of our kinetic energy seems to
 have, strangely enough, gone to our mass instead of our velocity.

	 Undaunted, we continue to accelerate the object, thinking,
 "hurm.  What a wonderful toy the universe is."

	 As we approach c, the graph has begun to approach the vertical
 asymptote.  More and more, our Kinetic energy (remember, KE=(mv^2)/2)
 is increasing the mass, rather than the velocity.  We can add KE to
 our heart's content;  The universe won't care, we'll continue to
 travel along that hyperbolic line, approaching v=c, but never quit
 obtaining it.

	 The above isn't exactly what happens.  But it's close enough
 to show the concept involved.  Note that the structure does NOT
 prohibit something moving faster than v=c;  It only states that at v=c
 we have a discontinuity, and anything travelling along one line can't
 reach the other by conventional means (hedge, hedge).

	 Is it clearer?  [I used to be a math major -- I got better]

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|Todd L. Masco        | ...and the dead are, but for a moment, motionless... |
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