Re: [Phys-l] Rest mass again?

[Derek McKenzie <derek_s_mckenzie@hotmail.com>]

I've been thinking about this subject quite a bit lately and I have issues with *both* the terms 'rest mass' and 'invariant mass'.

The term 'rest mass' seems to be quite misleading to me because although we may choose to view a lump of matter as 'at rest' in a particular frame, it is made up of many moving constituents in that same frame, and what one person calls 'rest mass' could equally well be called a sum of relativistic masses of its constituents. The term 'rest mass' then becomes one of perspective. I don't mean just a perspective of reference frame, but a perspective of model - that is, a choice as to whether you want to look at a solar system from a distance and consider it to be a single blob, or a bunch of moving stuff.

On the other hand, the term 'invariant mass' seems to me to conflict with a genuine geometric model of spacetime. In particular we must ask 'invariant with respect to what?'. Presumably, the invariance is with respect to a particular class of coordinate systems, but mass transcends these coordinate systems. If I take mass to be a property attached to a particle's worldline, there is no concept of invariance because there is no mention of transformations. To even mention invariance conjures up the reference-frame picture of relativity rather than the 4-d manifold picture.

I would be interested to know if my thinking is confused on either of these points, but at the moment I'm wondering if plain old vanilla 'mass' would be a better term.

Derek

> Date: Wed, 20 Oct 2010 13:12:04 -0400
> From: jsd@av8n.com
> To: phys-l@carnot.physics.buffalo.edu
> Subject: Re: [Phys-l] Rest mass again?
>
> On 10/20/2010 12:25 PM, Espinosa, James wrote:
>
> > For years, and even recently, the term "rest mass" has been used.
> > Well, I hope that everyone knows that the magnitude of a 3-vector is
> > invariant under Galilean transformations between coordinate systems
> > (or inertial frames).  Under Poincare transformations between
> > inertial frames (coordinate systems) the magnitude of a 4-vectpr is
> > invariant.  This means that the value does not change from one system
> > to the another.  The magnitude of the 4-momentum is the mass.  What
> > part of "invariant" do some physicists not get?
>
> I'm not sure that's the right question.
>
> Most physicists get this, and have gotten it for many decades.
> Textbooks for upper-division students and graduate students
> mostly get this right.  Recommended reference:
>     Gary Oas
>     ``On the abuse and use of relativistic mass''
>     http://arxiv.org/PS_cache/physics/pdf/0504/0504110v2.pdf
>
> The real question is, why do the folks who write introductory
> textbooks and "popularizations" of physics continue to get
> this wrong, generation after generation?
>
>   Part of the problem is that some of these authors started 
>   out as cartoonists and took up textbook-writing as a second 
>   career.  Their knowledge of modern physics is, shall we say,
>   sketchy.
>
> Constructive suggestion / reminder:  The place where the rubber
> meets the road is the famous formula E=mc^2.  It must be emphasized
> that mc^2 is the _rest energy_ not the total energy.
>
> The notion of rest energy is useful.
>
> Mass is invariant.  Calling it the "rest" mass is mostly harmless.
>
> The idea of non-invariant "relativistic mass" aka "velocity-dependent
> mass" is bad news for a number of reasons.  Ditto for "velocity-
> dependent rulers" and "velocity-dependent clocks".  See e.g.
>   http://www.av8n.com/physics/odometer.htm
> and references therein.
> _______________________________________________
> Forum for Physics Educators
> Phys-l@carnot.physics.buffalo.edu
> https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l