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Uncertainty principle in relativistic quantum mechanics

Physics Asked on July 22, 2021

In Walter Greiner book about relativistic quantum mechanics, he writes the uncertainty relations for 4-position and 4-momentum in a neat way as:

$$[p^mu, x^nu] = ihbar eta^{munu}{bf 1}$$

with Minkowski sign convention $(+,-,-,-)$.
This gives manifestly all the uncertainty relations we want.
But here, time is just a coordinate, so how do we interpret the commutation relation between time and energy?

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