Re: Mass and Potential Energy
- From: "Pete" <someone@xxxxxxxxxxx>
- Date: Wed, 27 Sep 2006 14:05:36 -0400
<actionintegral@xxxxxxxxx> wrote in message
news:1159368310.699087.109720@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
When one speaks of the relativistic mass of an object, should one
include the potential energy of the object?
If the object has internal degrees of freedom in which the proper mass can
vary (e.g. an atom can transition between states) then its possible for the
internal potential energy to change along with a corresponding change in
mass. If you're speaking about a charged particle in an EM field then it has
the same meaning as it does in electrodynamics since EM is relativistically
correct. I.e. the total energy E = K + E_o (K = kinetic energy, E_o = rest
energy) is related to relativistic energy T and potential energy V as
E = T + V
For a proof please see -
http://www.geocities.com/physics_world/sr/work_energy.htm
(Note: I screwed up Eq. 18 so ignore that. It will be corrected sometime in
the future.)
The role of E in 4-vectors is that E is proportional to the time component
of the time component of the canonical momentum 1-form. The potential, V is
the time component of the 4-potential A^u. T is the proportional to the time
component of the 4-momentum.
Note: My notation is not standard but is consitent with Goldstein's
mechanics text.
Pete
.
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