Re: [Phys-l] Relativisitic mass vs Invariant mass

[John Denker <jsd@av8n.com>]

Laurent Hodges wrote:

> > I remember reading something by Einstein once (a paper? a chapter in a book?)
> > and noting he didn't write E = m c^2  but  E-sub-0 = m c^2, where m was clearly
> > what we call the rest mass.

I'm afraid I must retract and apologize for my previous response to this.
 -- Some things I said that were literally true were not relevant.
 -- Some things I said that were relevant were not true.

Again, let's look at the original article:
    Einstein (1905d)
    "Ist die Trägheit eines Körpers von seinem Energiegehalt abhängig?"
    http://www.zbp.univie.ac.at/einstein/einstein4.pdf
or the English translation:
    "Does the Inertia of a Body Depend Upon Its Energy Content?"
    http://www.fourmilab.ch/etexts/einstein/E_mc2/e_mc2.pdf

Uncle Al does not write (E_0) or (m_0) or even (m).  In the crucial sentence,
he uses only the full word for mass, and writes energy as a word and as a
symbol without a subscript:

> > >  Gibt en Körper die Energie L in Form von Strahlung ab,
> > >  so verkleinert sich seine Masse um L/V^2.

 ... where L denotes energy and V denotes the speed of light.  Capital V
is *not* the speed of the particle, nor (equivalently) the speed of the
rest frame relative to the lab frame;  he uses small v for that.

!!! I suspect I mistook V for v when I read this sentence last week.
!!! That's the only way I can explain how wrong my conclusions were ...
!!! ... that plus the fact that I didn't take the time to fully
!!! understand the argument leading up to that sentence.
!!! Also I was perhaps predisposed to see a non-invariant formulation
!!! of mass, since Einstein was definitely using non-invariant notions
!!! of time and length (time dilation and FitzGerald-Lorentz contraction).
!!! He didn't adopt the fully geometric view of spacetime until later.

Let's be clear:  The paper doesn't say whether "the mass" is the rest
mass or any other kind of mass;  both the words and the equations are
silent on this issue.

The argument is actually quite clever.  There is the particle, and there
are the photons.  The photons are of course ultra-relativistic, and have
no mass of any kind.  The kinetic energy of the particle, interestingly
enough, is calculated in the _nonrelativistic_ limit:

> > > Unter Vernachlässigung von Größen vierter und höherer Ordnung ...

i.e. neglecting quantities of fourth and higher order.  That forecloses
any chance to notice any dependence of mass on kinetic energy itself.


Bottom line:  This 1905 notion of mass is _consistent_ with the
notion of an invariant mass (invariant with respect to boosts) ...
but only consistent in the weak sense.  It is equally weakly
consistent with various other interpretations.  It doesn't state
(clearly or otherwise) the dependence -- or independence -- of mass
on velocity.

Also keep in mind that non-invariant mass is only one problem out
of three:  we also need to worry about non-invariant notions of
time and length.
  http://www.av8n.com/draft/odometer.pdf

I also emphasize that our teaching should not be dependent on what
this-or-that famous person did in 1905.  It shouldn't matter whether
he got it completely right or completely wrong -- or anything in
between.  We should use the best available concepts, not the most
ancient concepts.