🚀 go-pugleaf

This is the second discussion of "rest mass" vs. "relativistic mass"
that I've seen in sci.physics, though I'm sure there have been others
in the past.  There's a position held by a number of folks which one
might sum up as:

	The idea of 'relativistic mass' is bad, don't use it.
	Its only purpose seems to be to confuse innocent physics
	students.  It isn't ever necessary and can be completely
	dispensed with.

I had questions about the feasibility of this position the last time
the topic was discussed that no one answered.  This time around Leigh
Palmer brought up good objections which were never clearly addressed
either.  I'm starting to think that these objections can't be addressed
and that proponents of "rest mass only, relativistic mass is out" just
haven't looked closely at the problems this position causes when you
work with macroscopic objects.

To avoid misunderstanding (and to save innocent straw men from being
beaten) let me make it clear that the problem comes from dealing with
macroscopic objects.  If you're only working with particle physics then
I'd agree that you can dispense altogether with the notion of relativistic
mass.  In fact I think it's fine that particle physicists universally use
"mass" to mean the intrinsic rest mass of a particle.  Since it should be
possible *in principle* to reduce all of physics (all of science?) to
particle physics (in principle!) then some might conclude that relativistic
mass can be completely dispensed with.

No!  Here's a statement of my position that relativistic mass can't be
dispensed with when dealing with the mass of macroscopic objects (looking
again to spare helpless straw men from beatings):

	It's perfectly reasonable to talk about the mass of a
	macroscopic object.  The inertial mass of the object
	can be operationally defined in terms of the force
	that has to be applied to the object to produce a given
	rate of acceleration.  Methods exist which allow you to
	measure the mass of an object, so defined, with great
	precision.  It has umpteen applications and it would
	be silly to try and dispense with this notion of the
	mass of a macroscopic object.  Yet you can't make this
	notion of mass work in *full generality* without using
	the notion of relativistic mass.  More precisely, if
	you reject relativistic mass then the amount of mass
	you have on hand is subjective and completely dependent
	upon how you think the objects on hand should be viewed.

David Knapp wrote in reply to Leigh's objections:

>   This caricature of the "currently fashionable definition of mass"
> is pretty twisted.  Surely you can't be claiming that the use of
> "rest mass" as "mass" implies that one must use the sum of
> constituent masses to obtain the mass of an object?

To which I say, not quite but you're almost correct David.  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.

Continuing from David Knapp's reply:

> If you are, then
> how do you think particle physicists define the proton mass?  As the
> sum of the masses of the constituent quarks?  Not likely.

Perfect example.  The proton: a nice simple system where everyone (me
too!) naturally views the constituent quarks as being bound together.
They're bound so tight that there's no danger of anyone being interested
in the sum of the (rest) masses of the individual quarks.  Right?

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!
Sure, you look at a proton and everyone has the *same viewpoint*, so
you can wave hands and call your notion of mass well-defined.  But
try to talk about the mass of something a little more complex than
a proton.  As soon as it isn't clear anymore just what is bound to
what then you are going to have a real hard time deciding just how
much mass you really have on hand in a given situation.

By the way, this is completely different from the situation for those
of us who talk freely about relativistic mass.  There the mass of an
object depends upon it's velocity relative to you, but relative velocity
is objective; it has a simple definition and can be measured.  How do you
"measure" whether it's correct to view several objects as bound together
in a system or as separate entities?  It's just a subjective viewpoint in
general, and has the potential of becoming arbitrarily complex to judge.

I'll agree that using the sum of the constituent (rest) masses of a
system gives you a very silly definition of "mass".  But I'd challenge
anyone to give a better definition of the "mass" of a macroscopic object,
with no reference to relativistic mass, and then explain how to apply
their definition in the following pretty simple situation:

	You have a very strong box with walls that are very
	elastic.  Inside you have two very elastic cannon balls
	held together by a latch.  Between the cannon balls is
	a very very strong compressed spring.  (Too strong to be
	possible for a real spring.)  You can't see inside the
	box and *don't have to* in order to measure its rest mass;
	just apply a force to the box and measure the resulting
	acceleration.  Better definitions for the "rest mass" of
	this object are welcome, but lacking an alternative this
	is the definition used here.

	At some time T=0 a little mechanism within the box
	frees the latch that holds the two cannon balls together.
	This spring is *real* strong; the two cannon balls are
	propelled away from each other with a relative velocity
	of 0.99 lightspeed.  They proceed to bounce around inside
	the box, which is a very strong box and doesn't break.

	You can still measure the mass of this object after the
	latch has been freed, and you will find that it hasn't
	changed.  So open the box.  The cannon balls go flying
	off in opposite directions at equal speeds (roughly).

How much mass do you have now?  No references to that confusing notion
"relativistic mass" please!  Go find each cannon ball and see how much
it accelerates when you apply a standard force.  Measure the mass of the
empty box and the other parts left over (spring and latch).  Do we still
have a concept of mass which is additive?  If so add up the masses of the
objects you now have on hand.  You'll find that a whole lot of mass is
gone, it just "turned into" kinetic energy.

Just when did this conversion of mass into energy take place, and why?
When the box was opened?  Just after the first cannon ball left the
open lid?  Maybe a little later, when the balls are "far enough" away
from the box?  And why was the mass converted into energy?  I'd say the
only reason is that you shifted your perspective from seeing the box and
contents as a single object to seeing them as separate objects.  It
doesn't take much to make this kind of "mass" vanish.  You just change
your viewpoint!

Leigh Palmer mentioned temperature, another case that was muddled over
but never answered.  Measure the rest mass of an object, say a cool
block of iron.  Heat this object and measure its rest mass again.  We
all agree that it will now have a slightly larger rest mass, yes?  So
is this another case of a little bit of energy being "converted" into
mass?  How so?  Why has the additional kinetic energy of the constituent
iron atoms "turned into" rest mass?  Can anyone who thinks relativistic
mass is an idea to be avoided explain why kinetic energy in the form
of heat constitutes mass, but the kinetic energy of an electron in
a particle accelerator does not constitute mass?  At least not until
the electron hits a positron and a bunch of mass is "created".

If the particles created managed to "hang together", would that mean that
their kinetic energy would be mass too?  Just how tightly would they have
to hang together in order to have this conversion of energy into mass take
place?  As tight as the quarks in a proton?  As tight as the electrons
in a helium atom?  As tight as the atoms in a block of hot iron?  As
tight as two cannon balls flying apart at 0.99C with a loose string
connecting them?

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.  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!

Mark Corscadden
markc@smsc.sony.com
work: (408)944-4086