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Similar to the position-momentum uncertainty principle, there is a time-energy uncertainty of the form

$$\Delta E \Delta t \geq\frac{\hbar}{2}\enspace .$$

However, since time is not an observable, the derivation and interpretation of this inequality is somehow different compared to other uncertainty principles. Depending on the context of the derivation, the constant on the right might also be different.

In basic physics and quantum physics literature, I've seen this inequality as an "explanation" for vacuum fluctuations: Energy conservation can be violated by creating particles and antiparticles, as long as the time until they're annihilated is short enough to satisfy above inequality.

I wonder if there is any truth to that "explanation". The time-energy uncertainty can be derived from purely non-relativistic quantum mechanics which features a constant number of particles. Only with the introduction of quantum field theory the particle number becomes variable.

So is it pure coincidence (and an example of simplifying-too-much literature) that this inequality somehow also works to talk about vacuum fluctuations, or is there more to it?