What Happened to Potential Energy in E=m[tex]c^2[tex]

[bhthiang]

I have been wondering why is potential energy not included in the calculation of total energy E=mc^2?<br /> I know that mc^2includes the rest energy and the kinetic energy. Suppose the particle or object is charged and is moving in a strong electric field, its potential energy will be sdgnificant wouldn't it?<br /> If we have to include the PE, how should we do it?<br /> Thanks

 

[quantumdude]

The energy-momentum relation that you see in a standard general physics textbook is:

E^2=(pc)^2+(mc^2)^2

It is typically advertised as the energy-momentum relation for a *free* particle (so V=0). If memory serves, Goldstein's "Classical Mechanics" treats relativistic mechanics with a potential, via the Lagrangian formalism.

 

[krab]

Properly,
(E-V)^2=(pc)^2+(mc^2)^2
where V is the potential energy and m, the rest mass, does NOT contain the kinetic energy.

 

[krab]

Properly,
(E-V)^2=(pc)^2+m^2c^4
where m is the rest mass and V the potential energy