Classical intuition suggests that the all processes should be described by real variables that change locally — at finite speed. However, this is violated by standard Copenhagen interpretation of quantum mechanics, which allows for arbitrary instant direct measurements and free choices. The violation can be tested exeprimentally. The simplest, idealized test is based on violation of Bell inequalities. However, no experiment has confirmed the violation because of loopholes. An open question is whether the violation happens still with more general measurements (and which?) and less ideal setups and how this is related to the loopholes.

Classical intuition suggests that the all reversible processes should lead to time symmetric observations. In quantum physics direct observations (measurements) are invasive so they are ovbiously not time symmetric. However, in the limit of zero measurement strength, the observations become noninvasive but, surprisingly, they are still not time symmetric. This subtle and fundamental issue is independent of thermodynamic irreversibility and high energy symmetries (charge-parity-time).

Naively the vacuum is empty, so the "emptiness" should look the same in every (inertial) reference frame. However, the quantum vacuum is not empty, it looks rather like boiling water (so called vacuum fluctuations). Contrary to common belief, to show that it still looks the same in every frame is highly nontrivial. My proof (correct but "perturbative") requires taking time as a complex path. Contrary to "experts'" claims, it has never been shown and "simple proofs" are wrong or incomplete.