I am not sure I understand the idea properly.
Moreover, why are philosophers so interested in quantum mechanics? What philosophical implications could quantum mechanics have?
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Because Humean Supervenience is based in contingency. This implies that no two objects or states can differ without an in-equivalence of at least one quality or property. Quantum Mechanics negates this presumption, as most famously demonstrated in Schrödinger's cat, where two opposite states are simultaneously true until observed.
Imagine two identical worlds A and B, that both only consist in conducting the same indeterministic/random/quantum experiments 10 times. They only differ with respect to the probability measure that is associated with the experiment. However even though the probability measures are different, we could still obtain the same results in world A and world B, which would make the worlds identical in the humean sense . It is therefore possible that two worlds are identical according to the humean mosaic, however they differ in the underlying probability distributions. This cannot be according to Humean supervenience.