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From: jagardner@watmath.UUCP (Jim Gardner)
Newsgroups: net.sf-lovers,net.physics
Subject: Re: FLT ( fundamental laws of physics )
Message-ID: <15821@watmath.UUCP>
Date: Thu, 18-Jul-85 10:55:44 EDT
Article-I.D.: watmath.15821
Posted: Thu Jul 18 10:55:44 1985
Date-Received: Fri, 19-Jul-85 01:00:30 EDT
References: <3295@garfield.UUCP>
Reply-To: jagardner@watmath.UUCP (Jim Gardner)
Distribution: net
Organization: U of Waterloo, Ontario
Lines: 86
Xref: watmath net.sf-lovers:8723 net.physics:2887

[...]

A little while ago I posted an article talking about two interpretations
of a basic principle of special relativity that says the faster an object
is going, the more force you need to apply to make it accelerate.  I
don't want to get too far into physics in net.sf-lovers, but there is
an important law of philosophy of science here, so one more article to
clear things up.

In article <3295@garfield.UUCP> robertj@garfield.UUCP (Robert Janes) writes:
>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 gave many things to the physics world and one that is still
not adequately appreciated today is the concept of "operational
definitions".  Science was very close to relativity at the turn of
the century; the experimental results (like the Michaelson-Morley
experiment) were there; the mathematics was there; the recognition
of the problem was there.  Einstein gets the credit because he said,
"Let's look at the way people _measure_ time."  Once you look at the
_operation_ of taking various kinds of measurements, you see how such
operations lead to measuring time dilation, length contraction, and so
on.

Operationally, how does one measure mass?  One subjects an object to a known
force and sees how it accelerates, then one applies F=ma.  If the object
is more or less stationary in your own frame of reference, you can
for example put the object on a weigh scale.  The force of gravity
acts on the object, accelerating it downward a small distance before
the known force of the springs in the scale decelerate the object.
The distance that the object has moved (entirely a function of the
acceleration given by the two forces) is used to determine the object's
mass.

When an object is moving relative to your frame of reference, physicists
measure its mass the same way.  They subject the object to a known
force and see how much it accelerates.  For example, a particle in
a particle accelerator is subjected to a known electrical force and
various techniques are used to see how fast it ends up going.

Observations and special relativity both show that the particle behaves
_as_if_ its mass were greater than its rest mass (the formula given
above is correct).  However, the reason physicists get this result is
that they believe in F=ma (or its generalization F=dp/dt)!  They work
out the mass from the observed acceleration from the known force (or
sometimes the force observed to be necessary to obtain a given acceleration).

I'm certainly not proposing that we do away with F=ma or that it is
even incorrect.  All I'm pointing out is that the definition of mass
and the formula for calculating mass has F=ma built right into it.
Physicists decided that F=ma (a mathematical equation) was more important
to preserve than the concept that the mass of an object is fixed.
They changed the definition of mass rather than changing the equation.

Mr.Janes goes on to talk about tachyons and applies the mass equation
to them.
>	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?

I don't claim that tachyons exist.  But if they did exist, there is no
reason why the given formula for mass would apply.  It does not apply
to particles going at the speed of light, since the formula would involve
division by zero.  Nevertheless, there are many many "things" that move
at the speed of light (light being a prime example).  We can say that
the mass formula is not correct for "things" whose speed is >= the
speed of light; or we can say that mass is not a meaningful concept
for such things.  Either way, we cannot say that the given formula
argues against the existence of tachyons, since it argues against the
existence of light too, and we know that light exists.  The formula
does provide substantial argument that you won't reach light speeds
through acceleration from slower than light speeds, but it says nothing
about things that are already at light speeds or faster.

				Jim Gardner, University of Waterloo