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Re: Inertia or the "amount of substance"



On Sun, 14 Nov 1999, Ludwik Kowalski wrote:

.... But, let me add a comment to yours when you stated
that the m of "E=mc^2" is only of kinetic origin: What about
the rest mass? When you move relative to two masses, which
are at rest one with respect to the other, their masses include
kinetic as well as other energies: gravitational, chemical,
thermal energy,...Hence, not kinetic origin alone.

Good comment. To refresh my memory I looked into Special
Relativity. It begins with frames of reference, length contraction,
the twins paradox, etc. This is kinematics, right? At some point
a distinction between m_zero and m appears, both are inertial
[...]
After that point "a declaration" is made that the second term is
the "total energy" of an object. Gravitational potential energy
is not analyzed anywhere, the identity of two masses (inertial
and gravitational) is silently assumed. Perhaps those who
teach special relativity will correct me. My understanding is
that the inertial mass is the one which appears in 0.5*m*v^2
while the gravitational mass is the one that appears in m*g*h.

I did say 'gravitational'...so I also had to look for some reference :)

You are right that no gravity is involved in all these derivations. Of
course, because this is SR, only inertial frames come into play. This is
also why those 'm' appearing there are called 'inertial'. Does this means
it only includes 'kinetic energy'? My answer is no. As far as I
understand, SR doesn't sheds light on the nature of mo (the mass as seen
from the comoving ref. system). Einstein himself refers to this in his
book on Relativity as that "the inertial mass of a system of bodies can
even be regarded as a measure of its energy".
There you can find the following example. Consider a body, mo, which
absorbs a photon of energy Eo without increasing its velocity. the
increase in mass will be given by
mo + Eo/c^2 (comoving reference syst.)
So you heat the body and both, you and me (moving relative to you and
your mass mo) will see an increase in its mass. Once again, mass seems not
to be only of kinetic origin. What seems clear at this point is at least
that mass cannot be the 'amount of substance', unless by 'substance' you
include all type of energy. Ultimately, if you invoke GR, mass is just the
source of space-time; instead of mass, you can call it energy, one just
has to fill the stress-energy tensor with some 'stuff', isn't?

Conversely, if you/me have a mean by which we can convert all the mass
mo/m into radiation, the amount of energy obtained would include 'all' the
energy of that piece of matter: I would include here the gravitational
potential energy which the mass has relative to you.
At this point I may be stressing too far the former quote. This was what
led me to include the word 'gravitational' in my last posting. But I would
also appreciate any comment by the experts on this list.

Regards,
Miguel A. Santos
msantos@etse.urv.es