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Path: utzoo!utcsri!garfield!robertj
From: robertj@garfield.UUCP (Robert Janes)
Newsgroups: net.sf-lovers,net.physics
Subject: RE:FLT ( fundamental laws of physics )
Message-ID: <3295@garfield.UUCP>
Date: Wed, 17-Jul-85 15:37:44 EDT
Article-I.D.: garfield.3295
Posted: Wed Jul 17 15:37:44 1985
Date-Received: Wed, 17-Jul-85 17:27:13 EDT
Distribution: net
Organization: Memorial U. of Nfld. C.S. Dept., St. John's
Lines: 86


Just a few comments on an article posted to net.sf-lovers which may be of
interest to physics people on the net. The comments reflect my own
probably inadequate understanding of the subject but here goes anyways.

>Subject: RE: FLT
>From: jagardner@watmath.UUCP (Jim Gardner)
>Reply-To: jagardner@watmath.UUCP (Jim Gardner)
>Organization: U of Waterloo, Ontario
.
.

>A little relativity theory: we begin with the basic law of
>physics F=ma.

	This equation is a   >special case<  of the  the basic law
law of physics called Newton's Second Law. Newton original framed somewhat
in this fashion:

	" force is porportional to the change in the quantity of movement".

Quantity of movement is what we now call momentum and thus the basic law is
reformulated as:

	F = (dp)/(dt)

where p = momentum and t = time ( you run into certain problems when you
try to establish what you mean by time in high velocity situations )

In classical mechanics and in relativistic mechanics if we are careful
about what we mean by m we have:

	p = mv

apply ing the product rule we get

	F = m*dv/dt + v*dm/dt 

where if m is constant and we denote dv/dt by a we have

	F = ma.

Newton however made the assumption that m was independent of v which is
not in fact the case as was shown by Einstein. In fact mass ( as measured
by an observer not moving with the object ) does depend upon v as follows

	m = m0/sqrt( 1 - (v/c)**2)

Using this we see that m increases assymptotically as v->c.

Thus the basic law is still quite sound if properly applied!

Einstein did though as a consequence of his work on time, velocity and
electromagnetic bodies show that we had to refine our understanding of the
relationship between mass and velocity.


>Tachyons get around the problem by _starting_out_ going faster
>than the speed of light.  Since they're already past the boundary,
>you don't run into the infinite force problem, so they can happily
>do whatever they want.
				>Jim Gardner
				>University of Waterloo



	But then we have the following problem:

		if v>>c then 1-(v/c)**2 < 0
		hence sqrt( 1 -(v/c)**2) is imaginary !!

	What is imaginary mass and why is it necessarily more tangible and
	acceptable then infinite mass ? There is no scientific evidence for
	the existence of tachyons nor do any of the current models of
	physics require their existence so while they may exist there is no
	reason to believe they do save for ( at present ) wishfull
	thinking.

	I don't read net.physics so please send any critiques or
	corrections by mail. I would be interested in followups 
	relativity theory is a favorite area.

					cheers
					Robert Janes
					Memorial University of
					Newfoundland