- #1

pmb

**[SOLVED] Energy and Special Relativity**

For some reason the time component of the 4-momentum has the name "Energy." Many people even call it the "total energy." However the time component is the "free particle energy" and not the total energy. Total energy for a conservative system is, by definition, an integral of motion i.e. it is a constant. It has the value of the energy function. The energy function expressed in terms of canonical momentum, instead of the the derivatives of the postion variable, is the Hamiltonian. For a precise definition of "energy function" see

www.geocities.com/physics_world/relativistic_charge.htm

h is the "total energy" of the particle. It is h which is the conserved energy - not E.

Note: A conservative system is one in which the potential energy function V is time independant [I.e. V = V(r) not V(r,t)] and thus the Lagrangian is time independant and thus the partial derivative with respect to time is zero. Also note that the energy function is not always the energy so one has to be careful when calling the Hamiltonian "total energy". Goldstein has a nice example of this. Referance provided upon request (I'd have to look up the page # anbd have to know what edition one has)

Pete