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What is the definition of potential energy in the theory of relativity?
Total energy, rest energy and kinetic energy were all defined, but not potential energy.
- Laurel Duncan (age 60)
Lakewood, CO, USA
There are two levels of relativity: Special and General. Special (SR) doesn't include the full effects of gravity while GR does.
In SR, potential energy is very similar to classical potential energy. There are potential energy densities proportional to the square of fields, e.g. the electrical and magnetic fields. These transform differently between different reference frames than they do classically, but that's true of all the energy terms. So the definitions are really not different in kind from the ones you are already familiar with. The conservation law applies to the sum of all the energy terms.
GR is a little trickier, and I'm not familiar enough with it to give a good answer. The two problems of which I'm aware are:
1. The conservation law (same energy at each time) is more complicated because there is such a broad collection of ways of slicing up spacetime into time-like slices.
2. The gravitational potential term is more complicated.
Here's a more serious discussion of those issues: http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html
(published on 09/17/2011)
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