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Re: Mass: Corrections,etc.



1) I collected my thoughts on "how to define mass" at
http://www.av8n.com/physics/mass.htm

Comments????

2) Hugh Logan wrote:

One might ask if the now largely abandonned formulation of relativity
which uses "relativistic mass,"
m=gamma*m_0 where m_0 is rest mass, doesn't provide a more intuitive
representation of inertia thought of as a resistance to a change in
motion. It would seem that a particle moving at a speed of
0.99*c would be more difficult to accelerate than one at or nearly at
rest corresponding to its greater (relativistic) mass.

Indeed one might ask ... but IMHO the answer is no. The
"gamma m_0" formulation paints a picture that I find misleading.

By way of analogy: consider an object constrained to move in
a circle. If the object is near top-dead-center, and I push
down on it -- force parallel to radius -- then object seems
to have a great "resistance to a change in motion." But this
must not be attributed to a change in mass.

Similarly, consider a relativistic object. I push on it with
a force F (measured in my frame) for a time t (measured in my
frame). The pusher has lost momentum p = F t. By conservation
of momentum, I am pretty darn sure that this momentum has been
transferred to the pushee (the object).

Now the thing that is really, really conserved is the four-vector
momentum,
p := m u
where m is the invariant mass, and u is the four-vector velocity,
u := (d x / d tau)
where tau is the proper time. So we know the change in p and
the change in the four-velocity u = p/m.

The final step is to figure out how fast the object travels
across the laboratory floor. For this we need the three-velocity
v := (d x / d t)
where t is the time as measured in the laboratory frame. This
differs from u by a factor of (d t / d tau), i.e. gamma.

So to my way of looking at it, the particle is (of course)
hard to accelerate. There is a factor of gamma in the
acceleration-resistance ... but this has got nothing to do with
the mass. The mass stays the same; (d t / d tau) changes.

This situation is profoundly analogous to the top-dead-center
situation, since boosts are analogous to rotations.

> I think one
can extract the same useful formulas ... from
either, and it hardly matters, as far as practical results are
concerned,

Undoubtedly, one could reformulate all of relativity using
"m" := gamma m_0, instead of m := invariant mass. This would
simplify some expressions and complicate others. To paraphrase
Richard Nixon, we could do that, but it would be a bad idea.
Even from a green-field point of view, the disadvantages appear
to outweigh the advantages. On top of that, it would have the
further disadvantage of being inconsistent with conventional
terminology and notation.