From: matt@physics2.berkeley.edu (Matt Austern)
Newsgroups: sci.physics
Subject: Re: Converting the masses
Date: 28 Jul 92 00:05:09
Organization: Lawrence Berkeley Laboratory (Theoretical Physics Group)
	<131516@lll-winken.LLNL.GOV> <1992Jul28.004259.9052@smsc.sony.com>
Reply-To: matt@physics.berkeley.edu
NNTP-Posting-Host: physics2.berkeley.edu
In-reply-to: markc@smsc.sony.com's message of 28 Jul 1992 00:42:59 GMT

In article <1992Jul28.004259.9052@smsc.sony.com> markc@smsc.sony.com (Mark Corscadden) writes:

> question 2:  Are physicists in general who use "mass" to mean "rest mass"
> or "intrinsic mass" really all in agreement as to how the concept works?

Yes.  Assuming that it is possible to tell what the energy of a system
is, and that it is possible to tell what its momentum is, then the
concept is unambiguous: you go to the rest frame of that system (i.e.,
the frame in which its spatial momentum is zero).  The energy of that
system, in its rest frame, is what we call its mass.  By the way, I
have never heard anyone use the phrase "intrinsic mass"; this is not a
customary term.  

Oh, and note that if a system interacts with the outside world (i.e.,
if it exchanges energy with the outside world), then its mass can
change; there's nothing terribly surprising about that.  Of course, if
it interacts terribly strongly with the outside world, you might want
to rethink whether or not you really want to call it a "system" at
all.

> 	You have two cannon balls (again).  Each has a mass
> 	(always read "rest mass" or "intrinsic mass" here) of
> 	1 kg.  They are separated by one million kilometers,
> 	so for all practical purposes they are independent
> 	of each other.
> 
> 	They are moving directly away from each other at 0.995
> 	lightspeed.  Then the mass of this system, consisting of
> 	the two cannon balls together, is 20 kg.  It is not 2 kg.

> 	On the other hand, if the center of mass of this pair of
> 	cannon balls is moving at 0.9999 lightspeed in your frame
> 	of reference, then their mass is still 20 kg.  Their mass
> 	is an intrinsic property of the system and does not depend
> 	in any way upon how the two-cannon ball system is moving
> 	with respect to you.
> 
> Is that right?

Yes.  Or rather, I haven't checked the math; I'll take it on faith
that the 20 kg figure is correct.  Certainly, the invariant mass of
this system is larger than 2 kg.  

And, in fact, it isn't quite as unnatural as it might seem to talk
about these two cannonballs as a "system".  There is one very similar
case in which I would do that: you have an electron and a positron,
which are separated by a few meters, which aren't interacting with
each other, and which are flying away from each other.  If you think
that the electron and positron might come from the decay of some other
particle, it is very common to define, and work with, the invariant
mass of that electron-positron system.

A less abstract example, though: consider the deuteron, i.e., a bound
state of a proton and a neutron.  The mass of the deuteron (according
to the latest Particle Data Book) is 1875.613 MeV.  The mass of the
proton is 938.272 MeV, and the mass of the neutron is 939.566 MeV.
Again: the mass of the proton-neutron system (the deuteron) is not
equal to the mass of the proton plus the mass of the neutron.
--
Matthew Austern              I dreamt I was being followed by a roving band of
(510) 644-2618               of young Republicans, all wearing the same suit,
matt@physics.berkeley.edu    taunting me and shouting, "Politically correct
austern@theorm.lbl.gov       multiculturist scum!"... They were going to make
austern@lbl.bitnet	     me kiss Jesse Helms's picture when I woke up.
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