Take the 2-minute tour ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.

I know what is rest energy $E_0=m_0 c^2$, total energy $E=\gamma E_0$, kinetic energy $E- E_0=(\gamma-1) E_0$, and momentum $p=\gamma m_0 c$. But what is potential energy in special relativity?

share|improve this question
2  
The same thing it is in Newtonian mechanics. The expressions you are working with are for a free particle. If you put it in a potential the energy has another contributions. –  dmckee Mar 4 '13 at 0:06
add comment

2 Answers

Special relativity doesn't alter the fact that interactions between particles "store energy" in the form of "potential energy," alhtough special relativity does alter the terms you listed, all of which have to do with the energies possessed by particles either by virtue of their motion, or their mass.

For example, in special relativity, electromagnetic interactions can be said to "store potential energy." When two charged particles interact via the Coulomb force for example, there is an interaction energy between them that deserves to be called potential energy just as much as in pre-relativity classical physics. In fact, classical electrodynamics exhibits Lorentz invariance and is in this sense a fully relativistic theory without alteration.

Any other form of energy that is called "potential energy" in a non-relativistic context probably also deserves this designation in a relativistic concept (I, at least, can't think of any counterexamples).

share|improve this answer
add comment

If the source does not move, it creates a static electromagnetic field for a probe charge and it has classical interpretation, kind of $V(\vec{r}_1-\vec{r}_2)$. If the source moves, its electromagnetic field becomes retarded, so the third Newton law may be violated. In that case there is no potential energy of interaction of particles $V(\vec{r}_1-\vec{r}_2)$, but there is an interaction of a particle with an "external" electromagnetic field $q_i \varphi(\vec{r}_i,t)$ that depends on time explicitly.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.