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From: emh@bonnie.UUCP (Ed Hummel)
Newsgroups: net.physics
Subject: Re: Definition of mass in relativistic mechanics
Message-ID: <581@bonnie.UUCP>
Date: Sun, 13-Oct-85 18:42:20 EDT
Article-I.D.: bonnie.581
Posted: Sun Oct 13 18:42:20 1985
Date-Received: Mon, 14-Oct-85 06:32:33 EDT
References: <576@bonnie.UUCP> <1997@brl-tgr.ARPA>
Organization: AT&T Bell Laboratories, Whippany NJ
Lines: 95


>> 	I have a question about semantics.  The concept of mass in
>> relativity is substantially different from the Newtonian view.  Yet, for
>> convenience, the word has been kept.  Most texts (even recent ones)
>> and all the early papers use the result (definition):
>> 		mass = gamma * (rest mass).
>> This  is consistent with keeping the Newtonian formula for momentum.
>> 	Most of the professional physicists that I know, do not use the
>> word "mass" according to the above definition, but use it to mean "rest
>> mass".  The preferred usage seems to be to redefine momentum:
>> 	momentum = gamma * mass * velocity.
>> Where mass is understood to be "rest mass".  Of course, the same goes
>> for energy:
>> 	E=m*c**2	->	E=gamma*m*c**2.
>
>Of course this is physically equivalent to the other approach.
>
	They are mathematically equivalent.  The question is about
"semantics".

>> I would like to hear opinions about:
>> 	What usage is more common?
>
>Both.  Most considerations of "mass" occur in cases where there is no
>difference in numerical value, since the matter is (nearly) stationary.
>
I obviously was referring to usage in the context of relativistic
mechanics.  Particle and nuclear physicists as well as cosmologists and
astronomers often use mass in situations were gamma is reasonably
larger than one.  Do any of them ever mean the traditional definition
of gamma*(rest mass)?

>> 	Are there good reasons for preferring one definition over the other?
>
>Yes.  Rest mass is invariant with respect to motion, whereas gamma-mass
>is dependent on the state of motion (coordinate system).  Momentum and
>energy together form a 4-vector, which has a (generalized) invariant
>meaning independent of coordinate system.  So rest mass, momentum, and
>energy all name physically meaningful characteristics whereas gamma-mass
>refers to something with an inherent dependence on convention

If this is such a good reason then why did the founding fathers of relativity,
(who were very aware of the invariance of the magnitude of the 4-momentum)
insist upon using the mass=gamma*(rest mass) definition?

>Physics largely consists of looking for invariant
>relationships among properties independent of any observer.  Gamma-mass
>is not a useful property for this endeavor.  Any attempt to express
>gamma-mass in an invariant manner leads to just using rest mass anyway.

	Take temperature, for example.  It is a well defined concept.  It is
not an invariant.  Why should there be a confusion regarding the definition
of "mass"?

>> 	What exactly is the role of "inertia" in relativistic mechanics?
>I don't think "inertia" has a formal technical meaning.  It could
>be taken to be just what "mass" measures, which doesn't get one
>anywhere.

Defining inertia as "what mass measures" is obviously circular.
Using the definition of inertia as "a property of matter such that a body
at rest tends to remain at rest and a body in motion tends etc...."
seems formal enough.  Certainly physicists have an understanding of what
is meant by inertia.  I am asking for viewpoints about the role of
inertia in relativistic mechanics.  At one time Einstein thought the
relativity of inertia was so important a notion that he listed it
(in the form of Mach's principle) on equal footing with the principle
of equivalence as a requirement for any good theory of gravitation.
[Annalen der Physik 55,241(1918); Naturw. 8,1010(1920); and Annalen der Physik
69,436(1922)]

>An "inertial frame" is a set of space-time coordinates
>in which the "law of inertia" (Newton's first law) appears to hold;
>laws of physics look somewhat simpler in such coordinate systems.
>Attempting to generalize physical laws to hold in (nearly) arbitrary
>coordinate systems leads into the realm of general relativity and
>unified field theory.
>
> Doug Gwyn

What do General Relativity and "unified field theories" tell us
about the role of inertia?  Tell me more.
----------------------------------------------------

I can give you a long list of Physics textbooks copyrighted in the last ten
years which define mass as gamma*(rest mass).  It seems to be the "official"
definition of mass in the relativistic context.  Ask a physicist why
matter can't be accelerated beyond the speed of light?  Most will
tell you that mass increases with velocity and it becomes "infinite"
at the speed of light, etc.  Then why do particle physicists (and others)
say mass to mean "rest mass".  Is it just sloppy usage?  I think
not.  Is it past time for a redefinition?

--------------
Ed Hummel