From: ucap22w@ucl.ac.uk (Martin S T Watts)
Newsgroups: sci.physics
Subject: Re: energy, mass, and all that
Date: 20 Nov 92 16:19:00 GMT
Organization: Bloomsbury Computing Consortium


sichase@csa1.lbl.gov (SCOTT I CHASE) writes:

>In article <1992Nov19.145532.34225@bas-a.bcc.ac.uk>, ucap22w@ucl.ac.uk (Martin S T Watts) writes...
>> 
>>	"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. 

>No matter which definition of mass ("old" or "modern") you use, energy
>and mass are still interconvertible.  When an electron and positron 
>annihilate into a pair of photons, which are absorbed by a piece of lead, 
>you end up with hot lead. 

But the thermal energy of the hot lead is not exempt from E=mc^2. It has
mass too.

> You can extract work from the temperature 
>difference thus created.  The mass of the original pair (whether you 
>count just the rest mass, or the relativistic mass) has been converted 
>into work.  If this is not mass being converted to energy, what is it?

It's mass being conserved and it's energy being conserved. The mass is present
as that of the particle-antiparticle pair originally, then that of the photons
(often three in e+ e- annihilation actually), which I maintain *do* have mass,
and finally as that of the thermal energy of the lead. The energy is the
"rest mass" energy of the positron and electron, the electromagnetic energy
of the photons, and the thermal energy of the lead.

>>	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.

>That's just gibberish.  The equation you quote is not a physical relationship
>between two physical quantitites.  It is the definition of density. It
>has no physics content.  

Are mass and volume not two physical quantities? I'd have thought so.
It mightn't be a perfect analogy, but I wouldn't say it was gibberish. You
could argue that E=mc^2 was a definition of the speed of light.

>E^2 = m^2 + p^2 tells you how much total energy
>a system contains, i.e., how much work you can extract from it. 

Yes, but it still doesn't say that energy and mass are one and the same. And
take care to note that your m is the rest mass here, whereas p is a function
of the relativistic mass. I'm sure you realise this.

> It includes
>the physically necessary contribution from the mass, which, when converted
>into energy, allows more work to be done than can be accounted for by 
>just the kinetic energy of the original system components.

Again, the mass isn't convertible into energy and the way you describe it seems
to imply that this isn't just a matter of definition. The equation you cite is
just a splitting up of the total energy of a system in to rest mass energy and
kinetic energy. Both forms have mass. The mass of the total energy is easily
calculable:

Since E^2 = m(0)^2c^4  + p^2c^2

and  m=E/c^2   (m being the relativistic mass)

then  m^2 = m(0)^2  +  p^2/c^2

          = m(0)^2  +  m^2 (v^2/c^2)

whereupon  m^2 = m(0)^2 / (1 - (v^2/c^2))

as is well known.

>A question for Martin:

>If energy and matter are not interconvertible, where does all the energy
>of an atomic bomb blast come from?  

I'm afraid someone got in ahead of me, but the energy was simply present
originally as the binding energy of a nucleus. No new energy is created.
Neither is any mass destroyed, since the mass of the binding energy becomes
the mass of the kinetic energy of the fission fragments (assuming we're talking
about fission).

This is where I think this definition of mass as rest mass becomes confusing,
because people automatically think of "relativistic mass" as referring to
mass acquired as a consequence of kinetic energy, whereas it's really the mass
that we know, through SR, *all* forms of energy to possess.

I was always taught at school, and as an undergraduate too, that the energy
was released in fission as a consequence of the mass of the fragments being
less than that of the original nucleus. The rest mass of the fragments
certainly is less than the rest mass of the parent nucleus, but this
description encourages the conclusion that mass is destroyed, which I don't
think is a useful way of looking at things. I still don't see what's so
confusing about defining mass to be that quantity which is *always* conserved
in an inertial frame of reference - surely that's a more appealing description
and one which is more closely related to original definitions of mass.

Martin.
Newsgroups: sci.physics