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Re: [Phys-l] geometry of spacetime (was: relativisitic mass ...)



Bob LaMontagne wrote:

"The problem I have with relativistic mass is that conceptual level texts use
it to explain why it is more difficult to accelerate an object when it is
traveling at high speeds. Unfortunately, they are implicitly using an F=ma
approach - which means that they are actually talking about the old
"longitudinal" mass (a 3/2 power) - not the relativistic mass (a 1/2 power
of 1-v^2/c^2). Invariant mass and the use of F=dp/dt avoids this."


I do not see why the necessity to distinguish between the longitudinal and
transverse masses should be considered as an argument against the relativistic
mass. To me it is the same as to say that because A is different from B there
should be no A. In fact, precisely in cases when the applied force F is along
or perpendicular to the velocity, the resulting acceleration a is parallel
to F, and the corresponding mass can be measured as the ratio F/a, which is
rigorously defined, appealing to intuitive view of mass as a measure of
"inertness" of the system, and gives its reasonable measure.


Then Mark Silvester wrote (as far as I understood, quoting Philip Freeman):

"Why do we wish to use invariant mass? The short answer is that it is more
elegant, and that using mass as an invariant allows us to see the other
invariants of relativity more directly. These are good things, but largely
a matter of taste.
So... why would we want to use relativistic mass ideas? Well, for one thing
it underscores that the "=" equals sign in E=mc^2 is an identity, not a
conversion. This is true for ALL forms of energy if we use the concept of
relativistic mass, but only true of all forms of energy EXCEPT kinetic if
we use invariant mass.
Basically invariant mass is the energy in an object which we cannot 'see'.
If you heat an object the internal energy increases, and so does its
'invariant mass'. BUT this energy is, if we look more closely, largely in
the motion of the atoms and we have unknowingly used relativistic mass (the
rest is in the fields, which we want to deny invariant mass to as well...).
Oops... so we will regroup and look that the invariant masses of the atoms,
now a different value than the invariant mass we had for the whole object.
But the energy of these in turn is largely 'hidden' energy in the motions
of the constituents of the atoms and the internal fields, and so on. Each
time we look more closely we discover that the "mass" is not mass at all,
but forms of energy which we are trying to exclude from the invariant mass".

I could not think of a better argument in favor of both - invariant and
also relativistic mass.


Moses Fayngold,
NJIT