Question

So, the uncertainty principle states that one can not measure momentum and position with accuracy simultaneously. However, we know from relativity that simultaneously is something frame dependent in nature, so how can we reconcile these two in relativistic quantum mechanics or even QFT?

I know that in QFT we define observables in different points in spacetime such that their Lie bracket is zero, but I'm not really sure how to go from this to an answer.

Answer 1

Observables in QFT are defined at different points in spacetime so that their measurements do not interfere with each other, allowing for the application of the uncertainty principle.

Step-by-step explanation:

In relativistic quantum mechanics and quantum field theory (QFT), the uncertainty principle is still applicable. Observables in QFT are defined at different points in spacetime so that their measurements do not interfere with each other, allowing for the application of the uncertainty principle.

However, it is important to note that the notion of simultaneity in relativity is frame-dependent. To reconcile these two concepts, observables in QFT are defined at different points in spacetime such that their Lie bracket is zero, which means their measurements do not interfere with each other. This allows for the consistent application of the uncertainty principle.