From: dk@imager (Dave Knapp)
Newsgroups: sci.physics
Subject: Re: Converting the masses
Date: 28 Jul 92 06:34:35 GMT
Organization: Laboratory for Experimental Astrophysics

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

> The general recommendation was that relativistic mass is an idea
> who's time has come and gone and that you should use the word
> "mass" to mean "rest mass" or the intrinsic mass of a particle or
> a system.

   Here's where I have a problem with what you are saying, Mark: you
are, in effect, saying that a system has some "intrisic mass" as if
it is some property of a system that cannot be changed.   That is not
what my perspective is at all: for example, the N(1440)P11+ particle
has the same quarks as a proton, but it is in an excited state.  So
a given collection of 3 quarks doesn't have an "intrisic mass."

> Here's a brief description of part of what I thought people were
> saying.  I still think this is the position that's being held by
> "rest mass only" people like David Knapp, but since it's *their*
> position only they can say whether or not I am expressing it
> correctly:

[parts of example deleted...]

> We say that the mass of the cannon ball is 1 kg, period.  The mass
> of a cannon ball is an intrinsic property which doesn't depend
> upon your frame of reference.

   Partly yes, partly no.  As was pointed out earlier, the mass of
the cannon ball depends (for example) upon its temperature.  On the
other hand, the mass doesn't depend on the reference frame.

> If it is moving at 0.99 lightspeed in your reference frame, then
> we say that you have a 1 kg cannon ball which happens to possess a
> very large amount of kinetic energy in your frame of reference.
> This kinetic energy is not mass, its energy!

   Right.  I'll buy off on this part, and the rest of your example.

> I think that you *can* give a clear unambiguous meaning to the
> concept of the one and only intrinsic rest mass of a given system,
> based upon nothing more than identifying the objects which
> comprise the system.  However I'm still puzzled because (as far as
> I can tell) it requires you, among other things, to treat the
> kinetic energy of the parts of the system, measured relative to
> the system as a whole, as mass.  I'm puzzled because at first I
> though that treating kinetic energy as mass was not kosher,
> period.

   I can certainly understand your confusion here.  However, I think
that the problem is identical in the case of subatomic particles; in
the example above of an excited proton, the quarks have more energy
associated with them, which gives the particle more mass.

I'll quote your next example in detail, because I have a point to
make about it:

> 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, that's right.  I think you are getting confused because it is
artificial to treat the "system" you have described as a single
object: why would you want to consider this system as a single mass? 
What purpose does that serve?  Because of the size of the system,
it's not useful to think about interactions with the system as a
whole, so the mass is useless in that context.  If you want to
calculate the gravity of the system, it is also not very useful, once
again because of the size of the system.  I suppose that from a large
enough distance, the gravitational interaction of your system would
look like a point mass of 20 kg; but closer to the system, one would
have to make a more detailed calculation of the energy-momentum
tensor.  In other words, the essential quantities for your system are
the energy and momentum, not the mass.

   My point here is that in order to arrive at an example that makes
my definition of mass unclear, you have been forced to use an example
in which: 1.) the definition of "system" is fuzzy, 2.) the usefulness
of the concept of "mass" for the system is questionable, and 3.) the
concept of "relativistic mass" would not evade the problems.

    -- Dave

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  * David Knapp        dk@imager.llnl.gov       (510) 422-1023  *
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