# Is the potential energy in a compressed spring a Lorentz invariant?

Libby Owens 2022-07-16 Answered
The total energy of an object comes from the time part of the four-momentum, and so isn't a Lorentz invariant. On the other hand, is the potential energy of a compressed spring a Lorentz invariant?
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Cheyanne Charles
The potential energy is not a Lorentz invariant, it is just a field energy for the spring parts, including the most significant contribution, the increased electronic energy from the compression of the electronic wavefunction, and it transforms along with the field momentum as a four-vector. In general, it isn't useful to separate energy into potential energy and kinetic energy in special relativity, the energy must have local flow, and is described by field energy, a stress-energy tensor, and it is due to a combination of local fields.
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Karsyn Beltran
It depends of what potential energy you are using. If you refer to a potential energy that depends only on position variables, $V=V\left(x\right)$, this is not Lorentz invariant. If you refer to potential energy that depends both on position and time variables, this can be Lorentz invariant.