From: ucap22w@ucl.ac.uk (Martin S T Watts)
Newsgroups: sci.physics
Subject: Re: energy, mass, and all that
Date: 19 Nov 92 14:55:32 GMT
Organization: Bloomsbury Computing Consortium


bweiner@ruhets.rutgers.edu (Benjamin Weiner) writes:

>Look, Martin, it seems that you do understand this.  Rest mass is not
>conserved in e+ e- -> photons.  Energy, or what you seem to be calling
>"mass", is conserved.  Some years ago, physicists called E/c^2 the mass,
>which preserves relations like p = mv.  However, it confuses people,
>so the community has moved back to calling E/c^2 the "relativistic mass,"
>and letting "mass" be the invariant m, aka the rest mass.  Personally I
>like to call E/c^2 the "energy" (modulo a c^2) and never introduce the
>"relativistic mass," because it's not a very useful idea.  We had
>several long discussions over this on the net, which you seem to have
>had the good luck to miss.  There is no need to assume that Scott is
>dense just because he is using a convention which almost everybody
>uses while you are using a convention which was standard for a short 
>time a few decades ago.

>OK, now are we in agreement?

To a large extent, yes. I'm not disputing that your *interpretation* of SR
is a perfectly good one in the sense that it doesn't achieve any erroneous
conclusions in practice. But SR was arrived at partially through assuming
that conservation of mass and energy separately hold, not by assuming them
to be one and the same thing. It's all very well for theoreticians to roll
the two into one for the sake of convenience but it begins to lose  sight of
the empirical roots of the concepts, which remain intact. Mass and energy are
associated, yes, but they are *not* one and the same thing, nor are they
convertible from one form to the other.

>  I see no reason to refer to an abstract
>of Bondi's for something so trivial.  

I mentioned Bondi's article merely in passing and hadn't expected it to create
any real dispute. I chose it because, although it doesn't say anything new,
it clarifies to a greater extent than I've read anywhere else the meaning of
E=mc^2.

>Essentially the nomenclature has
>changed over the years, as using "mass" to mean "m_0 * gamma" came into
>and then out of favor.  If you are thinking of the argument that 
>faster-moving particles have an increased gravitational field, stop!
>They do, but not in any easily expressible quasi-Newtonian sense.

There! You just did it. 

I wasn't actually aware of the changing conventions as regards what "mass" 
refers to, but it seems to me that it makes for considerably less confusion
to allow mass to remain that measure of inertia which is conserved in an 
inertial frame of reference. It is my impression that this is also Bondi's
conviction and he obviously felt strongly, when he wrote the article mentioned,
that the vagueness that surrounds terms such as "mass-energy equivalence" was
leading to mistaken interpretations of SR being taught to students. I think
it is primarily at lecturers that the article was aimed.

Since I'm now being accused of misrepresenting Bondi, I've gone to the trouble
of typing in some of the article. It is entitled ENERGY HAS MASS - A common
misunderstanding is re-examined, by Sir Hermann Bondi and C B Spurgin.
(Physics Bulletin _38_ (1987) p62.)

	"It has come to our notice (for example Warren, 1976) that there is
	quite widespread misunderstanding about the interpretation of
	Einstein's famous equation E=mc^2. It seems that this is often
	regarded as something rather like a monetary rate of exchange, such
	as L1.00=$1.45, and that mass and energy are thought to be
	interconvertible, each to the other. This is not so. Mass and 
	energy are not interconvertible. They are entirely different
	quantities and are no more interconvertible than are mass and
	volume, which also happen to be related by an equation, V=m*rho^-1.
	Mass and volume are different quantities and have different 
	dimensions. So have mass and energy. They feature differently in
	equations.

        "The extent and serious nature of this misunderstanding are indicated
	by the examples in the box, all from very reputable sources.

        "What Einstein did show in his special theory of relativity, as has
	been fully accepted by all physicists and tested to high precision
	in countless experiments, is that all energy, necessarily and
	inevitably has mass. Mass, of course, is the measure of inertia, and
	the point is that if a body gains energy E, its inertia is increased
	by an amount of mass equal to E/c^2  (where c is the speed of light)
	and conversely if it loses energy. The derivation of this result was
	based on the assumption that conservation laws must hold, equally, in
	all frames of reference, and it used the principles of conservation
	of momentum, of mass and of energy to arrive at E=mc^2."

Bondi goes on to list (in the box mentioned above) several cases of "Mass and
energy misrepresented":

'The connection of energy and inertial mass by the proportional constant c^2
implies the release of vast amounts of energy for the destruction of relatively
small quantities of matter and vice versa.' Muirhead H, 1973 'The Special
Theory of Relativity' (London: Macmillan) p58

'... and, in fact, the conversion of matter into energy is the source of the
power liberated in all the exothermic reactions of physics and chemistry.
   Since mass and energy are not independent entities the separate conservation
principles of energy and mass are properly a single one, the principle of 
conservation of mass energy. Mass *can* be created or destroyed, but when this
happens an equivalent amount of energy simultaneously vanishes or comes into
being, and vice versa. Mass and energy are different aspects of the same thing.'
Beiser A, 1973 'Concepts of Modern Physics' (Tokyo: McGraw-Hill Kogakusha) p36

'...Einstein's Theory of Relativity provides an explanation. According to this
theory, mass and energy are no longer to be considered as independent things;
instead, one can be converted into the other. Matter can, under certain
circumstances, be converted into energy, and - the other way round - energy
can be frozen into the form of matter... in this way the mass-energy relation
has become firmly established as a physical law: mass and energy must now be
considered  to be interchangeable forms of the same thing.' Freeman I M, 1974
'Physics Made Simple' (London: Heinemann) p241

'For many years the laws of conservation of mass and energy were viewed as 
valid but quite independent laws. Einstein however showed that mass and energy
can be converted into each other, so that these two laws are but two aspects
of a single, deeper law, the conservation of mass-energy.
   In nuclear reaction...the change in mass can be easily measured. In such
cases the interconvertibility of mass and energy must be fully taken into
account.' Halliday D and Resnick R 1981 'Fundamentals of Physics (2nd edn)'
(New York: John Wiley) p123

Other instances are quoted too. Bondi concludes his article with a section on
"Getting in right" where he begins:

	"The best way to appreciate Einstein's conclusion is to realise that
	energy has mass. The best way to express it is to say that the mass of
	energy E is m, given by m=E/c^2. Students should be taught that:
    
 		i) energy has mass;
	       ii) energy is always conserved;
 	      iii) mass is always conserved.

        They should be warned against believing erroneous statements that mass
	and energy are interconvertible, and they should be urged to avoid
	such terminology as the 'the equivalence of mass and energy'."

I'm perfectly aware that the above contains no world-shattering revelations,
although if I'd read it when at school it would have cleared up quite a few
reservations I had about, say, the way I was taught about nuclear fission.
It does demonstrate, though, that the rather nonchalant attitude in the
research community filters down to a lower level, and is only really a trivial
matter if you ignore the importance of educating non-specialists properly.

Martin.