  In a recent paper, PNAS, 118, e1921529118 (2021), it was argued that while
the standard definition of conservation laws in quantum mechanics, which is of
a statistical character, is perfectly valid, it misses essential features of
nature and it can and must be revisited to address the issue of
conservation/non-conservation in individual cases. Specifically, in the above
paper an experiment was presented in which it can be proven that in some
individual cases energy is not conserved, despite being conserved
statistically. It was felt however that this is worrisome, and that something
must be wrong if there are individual instances in which conservation doesn't
hold, even though this is not required by the standard conservation law. Here
we revisit that experiment and show that although its results are correct,
there is a way to circumvent them and ensure individual case conservation in
that situation. The solution is however quite unusual, challenging one of the
basic assumptions of quantum mechanics, namely that any quantum state can be
prepared, and it involves a time-holistic, double non-conservation effect. Our
results bring new light on the role of the preparation stage of the initial
state of a particle and on the interplay of conservation laws and frames of
reference. We also conjecture that when such a full analysis of any
conservation experiment is performed, conservation is obeyed in every
individual case.
