@adele would it be fair to say that the issue with EPR type experiments is the existence of a correlation between measurements that violates Reichenbach’s principle? A correlates with B but neither A causes B nor B causes A (they are spacelike separated) nor do they have a common cause (no hidden variables). Many worlds solves this by saying that what we observe is conditioned on a collider (us being observers in this world).

The many-worlds interpretation is deterministic (and local), and whether it's the correct interpretation or not, it predicts the same observed results as the Copenhagen interpretation of QM.

In this interpretation, you can simply take your wavefunction, apply the time evolution operator generated by the quantum hamiltonian, and then that's how the wavefunction will be after that amount of time.

So Pearl's causality should work unmodified in this setting. You modify the wavefunction as desired, turn the crank, and obtain the resulting wavefunction. An observer in this wavefunction will then observe different branches according to the Born rule. That should be fine since AIUI, Pearl causality can already handle counterfactual interventions that give probability distributions. Assuming that's the case (am not super familiar with the details of Pearl's causality), even things like the Elitzur-Vaidman bomb tester will have reasonable causal explanations in this setting.

Then returning to the Copenhagen interpretation, the result should still work since the Copenhagen interpretation gives mathematically identical predictions. So from this point of view, it might look like you need to pretend certain "ghost branches" exist for some of the calculations to work, which you could interpret as an extension of the original theory (guaranteed to be compatible with the Copenhagen rules of quantum mechanics since many-worlds gives the same mathematical predictions). Most of the time, you wouldn't have to worry about this since decoherence will quickly make the contributions from the other branches negligible.

@adele Can you point me to some in depth review/textbook/reference material on the many worlds interpretation? I always dismissed it as metaphysics until now but if it happens to somehow work better than other interpretations with Pearl’s causality I will give it a chance

Edit: you may be also interested in the sister market https://manifold.markets/mariopasquato/will-pearls-causality-have-importan?r=bWFyaW9wYXNxdWF0bw

@mariopasquato This is the in-depth review I usually reference: https://plato.stanford.edu/entries/qm-manyworlds/, written by Vaidman himself. Anything by Vaidman honestly: https://arxiv.org/search/quant-ph?searchtype=author&query=Vaidman,+L

Sean Carrol also has a book about it called Something Deeply Hidden which I have not read but is supposedly good (more pop-sci though).

But the basic idea is very simple: What if the wavefunction is simply real?