1) Whether or not QM conflicts with classical notions of
causality is very sensitive to just how you codify the
classical notion.
1a) QM does not require (or allow, so far as we know)
the non-causal transmission of _information_.
1b) QM does require _correlations_ at spacelike separations.
Lots of theory (starting with Bell) rules out a wide
class of hidden-variable theories and other attempts at
common-sense explanations for these correlations. Lots
of experiments (starting with Aspect et al.) confirm
that these correlations are present. I'm not saying it is
100% certain that no classical mechanism for establishing
such correlations can be found ... but everyone who has
attempted to find one has failed (sometimes without
realizing how badly they have failed).
Most people consider these correlations to be "spooky".
I'm not sure they should be called "lawless". We have a
pretty clear idea of what happens, even if we don't have a
ball-and-stick model of how it happens.
2a) Most QM predictions uphold the correspondence principle.
The classical behavior emerges in the appropriate limit, just
as geometric optics emerges as a limiting case of physical
optics.
2b) On the other hand, there are some aspects of QM that are
completely and unalterably non-classical.
For example: consider the spin of the electron. Classical
particles can be spinless, while electrons cannot, and there
is no middle ground.
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