Pete, perhaps you could clear up a question I've had.

I'll do my best!

I've done some work in quantum mechanics and a little in (special) relativistic quantum mechanics.

The only relativistic quantum mechanics I've had touch with is towards the end of Liboff's

**Quantum Mechanics**. So I don't feel qualified to comment there. Relativist mass obviously has no place in non-relativistic quantum mechanics. But I say that one should go with what they find easier to use. I know experts who teach rel-mass but who don't use in a great deal in their scientific publications. They tell me that they find it useful to think of, say, light having mass. I recommend not assuming that what one uses is practice is not what they use on the path to getting there. Texts on the Philosophy of Science point this kind of thing out. I'll scan that portion of my undergrad text in to a PDF file and make it available for you to read if you're interested.

Could you comment on where relativistic mass sees use in physics? Where do calculations get simplified by its use?

Moslty its not about calculations. Did you read my paper on the concept of mass in relativity? In the abstract I wrote

Although I argue for the usage of relativistic mass I do not argue that proper mass is not an important tool in relativistic dynamics.

So I'm not really disagreeing with you for the most part. The article explains much more than I can lay out here. For a compete answer please see and read

http://arxiv.org/abs/0709.0687I'll do my best in this post.

A lot of my paper discusses bulk systems with extended bodies instead of systems which are only systems of particles.

JP - Have you ever used special relativity in any other cases other than systems of particles? Consider this

**Measuring the active gravitational mass of a moving object,** D.W. Olson and R.C. Guarino, Am. J. Phys. 53(7), July 1985

If a heavy object with rest mass M moves past you with a velocity comparable to the speed of light, you will be attracted gravitationally towards its path as though it had an increased mass. If the relativistic in active gravitational mass is measured by the transverse (and longitudinal) velocities which such a moving mass induces in test particles initially at rest near its path, then we find, with this definition, that

M_rel = \gamma(1 + \beta)M. Therefore, in the ultrarelativistic limit, the active gravitational mass of a moving body, measured in this way, is not \gammaM but is 2\gammaM

As far as reasons people use rel-mass goes, I've aleady explained what I know in the paper I wrote and is located here and mentioned in this thread. It's online at

http://arxiv.org/abs/0709.0687I wrote a paper on this because it deserves a full treatment in all generality. Most people who ask the question you just did seem to have only systems of particles in mind and then only closed systems.

Special relativity is much richer than just using it in particle physics. Particle physicists seem therefore to never consider anything besides systems of particles.

The world is composed with continuos systems of matter. Such systems are described by the stress-energy-momentum tensor.

Take a look at

**Physical Principles of Cosmology** by Peebles. It shows the density of active and passive gravitational mass as well as inertial mass densities. They are

*not* the same! I.e. the density of active gravitational mass is different than the density of passive gravitational mass (this addresses a question someone was wondering about above). Inertial mass density is the same as the density of passive gravitational mass. Schutz rigorously derives the inertial mass density and shows that it's a function proper mass density and pressure.

Schutz's book touches on this in his text

**Gravity from the Ground Up** so if you have that text look uo those terms.

In general, SR can be applied to anything in an inertial frame of reference in flat spacetime. It covers systems which are fully described by the stress-energy-momentum tensor. In

**Gravitation** by Misner, Thorne and Wheeler, the authors use relativistic mass (which they simply call "mass") in their proof that the stress-energy-momentum tensor is symmetric. Schutz does the same thing in his GR text.

I considered a simple system which consists of a rod which was cooling down by radiating energy in the form of emitting photons/EM radiation. The question was to find the momentum of the rod using the relation P = \gamma*m*v. If one tried to use that relation from a frame moving with respect to the rod then they'd get an error. I was finally able to get this page online yesterday. Please see

http://home.comcast.net/~peter.m.brown/sr/invariant_mass.htmPlease scroll down to where it says

**An Incorrect Application of Invariant Mass**Here's another web page I wrote on this subject to demonstrate how physicists - Well known physicists I mnight add - use the concept.

http://home.comcast.net/~peter.m.brown/ref/relativistic_mass/relativistic_mass.htmHere is a list of articles I've read (at least most of them - I just can't recall which ones and iof I did read them all) on the concept of mass.

http://home.comcast.net/~peter.m.brown/ref/mass_articles/mass_articles.htmAlso take a look at the web pages at

http://home.comcast.net/~peter.m.brown/sr/sr.htmMany of them use rel-mass to derive many SR relationships. They can all be derived using proper mass. However I myself found it easier using relativitic mass. All of our brains work differently and, to me anyway, its irrational to assume that all people think alike and therefore some people will find it easier and some will find it harder. I'm one of the people who finds it easier.

Here is something Guth told meto my face - He finds it easier somtimes to think of light as having mass.

Thinking about physics is much much more than deriving equations. Have you ever heard of Wheeler's First Moral Principle? It states

*Never make a calculation until you know the answer.* Make an estimate before every calculation, try a simple physical argument (symmetry! invariance! conservation!) before every derivation, guess the answer to every paradox and puzzle. Courage: No one else needs to know what the guess is. Therefore make it quickly, by instinct. A wrong guess brings refreshment of suprise. In either case life as a spacetime expert, however long, is more fun!