Re: [Phys-L] The Physics Teacher and relativistic mass

[John Denker <jsd@av8n.com>]

On 07/27/2016 12:59 AM, Savinainen Antti wrote:
> Lev Okun who wrote critically about relativistic mass (if you are
> interested, google using "lev +okun + concept +mass").

This may save a few seconds of googling:
  L.B. Okun,
  "The mass versus relativistic and rest masses"
  Am. J. Phys. _77_ 430 (May 2009)
  http://scitation.aip.org/content/aapt/journal/ajp/77/5/10.1119/1.3056168
  http://www.stat.physik.uni-potsdam.de/~pikovsky/teaching/stud_seminar/einstein_okun.pdf
    Amusing earlier draft:
    http://isites.harvard.edu/fs/docs/icb.topic1214842.files/11lev-okun-on-mass.pdf

  Abstract:

> > The concept of relativistic mass, which increases with velocity, appears only in the
> > framework of a language which is not compatible with the standard language of relativity
> > theory and therefore impedes the understanding and learning the theory by beginners. The
> > same refers to the term rest mass.
> >
> > *To get rid of relativistic mass and rest mass it is appropriate to replace the famous
> > equation E=mc^2 by the true Einstein’s equation E_0 = mc^2, where E_0 is the rest energy.

There is some discussion of the history as well as the physics.

See also references therein.

=================================

Here's an important pedagogical point mentioned by Okun:
   When introducing the idea of spacetime, it makes sense to start with
   two-dimensional vectors, e.g. vectors in the (t, x) plane.

Therefore it is misleading to talk about «four-vectors».  Instead they
could be called /spacetime vectors/ or perhaps /Minkowski vectors/.
There is a great deal that can be done using (t, x).  The extension to
(t, x, y) or (t, x, y, z) can wait until later.

================================

I would emphasize that it is not a new idea to consider mc^2 to be
the rest energy (not the total energy).  Einstein was well aware of
this from the earliest days.

It is not even a new idea in the world of textbooks.  Misner, Thorne,
Wheeler _Gravitation_ was published more than 50 years ago (1973).
Its primary topic is general relativity, but for obvious reasons it
begins with special relativity.  It relies exclusively on the idea
that proper time is "the" time, proper length is "the" length, and
invariant mass is "the" mass.

I will grudgingly concede that in an ivory-tower classroom situation,
it is possible to /select/ a set of problems for which the notion of
velocity-dependent mass gets the right answer.  In this artificial
situation the question of velocity-dependent mass versus invariant
mass becomes a matter of opinion to some extent.  However, the larger
point remains: If you want to integrate the notion of mass with the
rest of physics, and with general relativity in particular, then the
spacetime approach (including invariant mass) is the only reasonable
option.