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The question arises from here. People wants to define kinetic energy and potential energy from EM tensor.

My question: How to define kinetic energy and potential energy from EM tensor in newtonian physics.

The EM tensor in newtonian physics is given by taking the limit $v\ll c$ in EM tensor of particle in flat space limit, which can be derived by introducing a 4D delta function.

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  • $\begingroup$ Why do this? What is the application of this definition? Also, if you want to talk about energy of the electromagnetic field, you will need to define finite region in space and integrate. $\endgroup$
    – Cryo
    Dec 30, 2020 at 13:25
  • $\begingroup$ @Cryo I don't want to talk about electromagnetic field. EM is short for energy-momentum. $\endgroup$
    – user142288
    Dec 30, 2020 at 14:42
  • $\begingroup$ :) my bad, sorry. Still don't understand the aim. Energy is useful because it is conserved under specific, but ubiquitous conditions. Kinetic energy in classical mechanics can be useful in simple problems, but I don't quite see the need for it as a standalone thing in complex problems. That's why I thought example would be nice $\endgroup$
    – Cryo
    Dec 30, 2020 at 14:59
  • $\begingroup$ @Cryo,in fact, the answer what I expect is "we can't not define kinetic/potential energy via energy-momentum tensor even in newtonian physics", so logically I cannot give you an example. $\endgroup$
    – user142288
    Dec 30, 2020 at 15:21

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