From: dk@imager (Dave Knapp)
Newsgroups: sci.physics
Subject: Re: Converting the masses
Date: 26 Jul 92 06:15:50 GMT
Organization: Laboratory for Experimental Astrophysics


In Article <1992Jul25.194550.1970@smsc.sony.com> markc@smsc.sony.com 
(Mark Corscadden) writes:

> The use of "rest mass" as "mass" implies that one must wave hands
> when dealing with constituent masses and the systems which they
> comprise.  In particle physics you get away with it by avoiding
> complex systems and sticking to simple systems for which it's
> "obvious" whether objects should be grouped together or not.

   I don't understand why all the fuss about defining "mass" as
"energy in an object's rest frame."  If an object (or system) doesn't
have a well-defined rest frame, then it can have no well-defined
mass, no matter WHAT definition you use!

> In reality you are using a notion of mass in which mass floats
> into and out of existence based on nothing but your perspective as
> to what should or should not be grouped together and considered as
> a whole!

   Give me a definition of mass that doesn't.  The statement above
strikes me as a tautology.  Of _course_ the mass of a system depends
on "what you include!"  I still don't get the problem.

> This notion of rest mass seems pretty ill-defined to me.  I defy
> anyone to give general rules for determining just what is and
> isn't rest mass and for determining just how much rest mass you
> have on hand in a given situation.

   The mass of an object is its energy (note I did not say MASS) in
its rest frame.

   There.  A general rule.  Note that this definition works perfectly
well for your "cannon balls in a box" example.  In that case, when
you open the box, you end up with an "object" that is expanding very
quickly; the energy involved in that expansion appears as mass if it
is measured in the system's rest frame.  In any case, why would one
be interested in the mass of such a system in the first place?  It
seems to me that for any system in which the definition of mass were
fuzzy, you'd be interested in the _energy_ of the system, anyway,
which is something perfectly well-defined.

> If you can't then you're committed to a notion of mass that shifts
> with your perspective.  And the whole point of throwing out
> relativistic mass was to avoid confusion!

   That you have a mass that shifts with perspective is precisely the
problem with "relativistic mass!"

   Look.  I'll grant you that there is a potential problem with mass
as I have defined it.  It is that, as defined, mass is not a simply
additive quantity: it is no longer possible to calculate the mass of 
an object (or system) as the sum of the masses of its constituent
parts.  Nuclear and particle physicists have no trouble with that,
as a simple look at the table of isotopes will convince you.  After
all, the mass of carbon-12 is _not_ equal the 6 times the mass of the
proton plus 6 times the mass of the neutron plus 6 times the mass of
the electron.

   Coupled to this is the inevitable result that mass is not
conserved, although energy is.  I suppose that, for chemists (for
example), the notion of mass conservation is useful enough that it
might be difficult to thrown out immediately.  However, chemists
regularly erroneously teach undergraduates that the mass of NaCl is
the mass of Na plus the mass of Cl, a false statement no matter which
of the two definitions of mass you use.  The fact that it is _almost_
true desn't make it so.

   Earlier someone (Leigh Palmer?) posted something about the
definition of "mass" for a neutron star.  I didn't respond because
the example so obviously did not address the point I was making.  Of
course you can divide the mass of a neutron star into the mass of its
constituent particles and the binding energy; but so what?  Is there
any context in which you would not use the energy in the neutron
star's rest frame as it dynamical and gravitational mass?  The only
purpose for the "baryonic mass" of a neutron star is to quantify the
number of neutrons it contains.  The example asys nothing about the
difference between "relativistic mass" and "invariant mass."  

   The reason I reacted so negatively to Leigh Palmer's original post
was that he (incorrectly) stated that particle and nuclear physicists
think that mass is additive, in precisely the way I above said it
ISN'T.  Thus, his argument was based upon a straw man.

  -- Dave
-- 
  *-------------------------------------------------------------*
  * David Knapp        dk@imager.llnl.gov       (510) 422-1023  *
  *            98.7% of all statistics are made up.             *
  *-------------------------------------------------------------*
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