Does Quantum Mechanics Suggest Violations of Conservation Laws?

[pivoxa15]

In QM only expectation values can be discussed due to the HUP. i.e energy conservation implies the change in the average value of energy with time is 0. So does that mean there are instances where fundalmental physical laws like the conservation of energy are violated? But we will never be able to measure these violated instances due to the HUP?

 

[Meir Achuz]

Generally all matrix elements of an operator can be measured, not just expectation values. If conservation of energy were violated, it could be observed, but it hasn't been.

 

[jostpuur]

pivoxa15, are you sure you know what you mean when you are talking about conserving or not conserving energy? The system doesn't necessarely have any precise energy, so I don't understand what it could mean, that the energy is not conserved then.

To my understanding, the conservation of expectation values is as far as the conservation laws go in quantum physics.

 

[smallphi]

To be precise the HUP is an inequality about the dispersions in measured expectation values of two operators. Time is not an operator in QM so the interpretation of the E-t HUP is not that clear as the position-momentum one.