Re: [Phys-l] Mass and Energy

["Fayngold, Moses" <fayngold@ADM.NJIT.EDU>]

John Denker wrote responding to my comment:

> "There is a proverb that says no matter what you are doing, you can
always do it wrong."

   Well, there is also a sad truth that no matter what you are saying, 
and how clearly it is said, your opponent may get it wrong. At least,
I expected anything but the way John misinterpreted my words 
(although I do admit possible linguistic subtleties I might have missed
in Halliday-Resnik statement or in the way I formulated my comments).
The way a student might understand Halliday-Resnik statement is:
We know that there is, for example, kinetic energy and potential energy;
call them Ek and Ep, respectively; they are two different (although mutually convertible) forms of energy. Now authoritative textbook says that there is "another form of energy" called mass. Call it Em (better than Ef in my previous comment), so that m = Em. Then, if all three forms are present in a system, we can write
                    E = Ek + Ep + Em = Ek + Ep + m.               (1)

If only the last one is present, we can write simply

                           E = m.                                 (2)
 
 Since I wrote explicitly that when I say mass I mean relativistic mass 
m = m(v), I thought it should be pretty clear that the first equation (following directly from Halliday-Resnik statement) is total nonsense. 
It might have sense if you mean that m is the invariant mass, but this is not specified in Haliday-Resnik statement in its general form.
  But even admitting the latter possibility, there is a system of units (far from ideal but consistent and still widely used) in which energy is measured in Joules and mass in kg. In this system, the first equation (sorry as I am, still following from Halliday-Resnik statement in its more narrow sense that mass is the invariant mass) is again wrong, since in this system Em = mc2, whereas, according to Halliday-Resnik, Em = m.
  Finaly, even if you choose units so that mass and energy are both in eV or both in kg, but m is invariant mass, then the second equation becomes also generally wrong. 
  At this point, I personally would not like to be a student of Haliday-Resnik.
    
  
> "If you measure force in pounds, mass in kg, and acceleration in
Gees, you're going to have trouble applying F=ma.  So don't do
it that way".

  No matter what you choose, if potential energy is a form of energy, 
it will always be in the same units as energy. If you choose Gees 
(it sounds good to me) then both - potential energy and total energy -
will be in Gees. No matter how hard you try you will not find a system
of units in which energy will be in Gees but potential energy will be in
Boos. In contrast, we know at least one system of units in which mass, 
while being nothing more than a "form of energy", is in units other than energy.
Does not it tell you anything?

> "If you want to write E=m, that works just fine if you measure mass
in energy units ... which is absolutely routine in particle physics.
I happen to remember the mass of the electron in MeV but not in kg;
if you want it in SI units I'd have to do the conversion.
   (Alternatively, you could measure energy in mass units, but that
    is not nearly so commonly done.)"

In high energy physics the energy of a particle is as rutinely measured in terms of its rest mass, as mass is measured in MeV.


Moses Fayngold
NJIT