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.
Bob at PC
-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu
[mailto:phys-l-bounces@carnot.physics.buffalo.edu] On Behalf Of Mark
Sylvester
Sent: Tuesday, February 21, 2006 6:44 AM
To: PHYS-L Maillist
Subject: Re: [Phys-l] geometry of spacetime (was: relativisitic mass ...)
Thanks for the excellent links posted earlier in this thread. I posted them
on the IB online curriculum centre physics forum, where the following post,
by Philip Freeman, was among several responses. Posted here with permission:
copy-paste begins***********************************************
"...as a relativist (and one who is moderately familiar with the geometric
models as well as GR) I am STILL prepared to come to the defence of
relativistic mass. Basically my argument would be the following:
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.
Ultimately, if certain current theories of mass and particle composition
are true, there may be NOTHING THERE to have invariant mass.
What we call the invariant mass is, in fact, dependent on the state of our
knowledge of the system.
In summary: you can go with relativistic mass -- in which case some
symmetries are cluttered up and you have a mass parameter that varies with
the observer. Or you can go with invariant mass in which case the
symmetries are clean and the parameter does not vary... but it is knowledge
dependent.
The general topic of the article as I understand it is that relativistic
mass is taught as is for pedagogical reasons. That the concept leads to
misconceptions if not taught clearly. Therefore it is not pedagogically
valid, and thus should not be taught. I think the "not taught clearly" is
an important rider... but in any case nothing in the argument addresses
what should be the central question, which is not "what is pedagogically
sound" or "what is popular or fashionable" but "what gives us the best
understanding of reality (whatever that means)?". The answer to that last
question, it seems to me, is simply "it depends"!
As a former prof of mine used to quote... "You pays your money and you
takes your choice".
PF
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