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# Re: [Phys-l] Rest mass again?

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.
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