Thanks to those who answered my question here Length contraction in special relativity but there is an issue I think that might arise from a uniform contraction that may affect the energy between two particles, if their energies depend on their separation. Take for example a neutral wire of electrons and protons where the protons are arranged in a perfect one dimensional lattice. If the electrons move at a constant velocity extremely close to the speed of light, then the distance between the protons as perceived in the electrons inertial frame will get closer and closer. So wouldn't the electric potential energy between the protons skyrocket? How do we make sense of this? How would the protons not repel each other at such distances? I think this would be an issue for any energy that is a function of distance.
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Energy is frame dependent, i.e. it depends on relative velocity. This is true in Newtonian physics just as much as in relativity. For example, the kinetic energy of a freight train moving at 100 km/h relative to the ground depends on the observer. For someone standing on the tracks, the relative velocity is 100 km/h and the train's kinetic energy is enormous. For the driver of the train, the velocity is 0 and the energy is also 0. The driver may touch the train without injury; not so the observer standing on the tracks!
Eric Smith
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