MWI and splitting before entanglement

Question

Recently I saw a conversation between Sean Carroll and Slavoj Zizek concerning the MWI.

One of the questions that drove Slavoj concerned with this question of Ontology vs. Epistemology, as the way Sean had described the current understanding of MWI is that we merely 'don't know' where we are on the wavefunction which seems to keep the openness of reality at the level of epistemology rather than ontology.

The question I have concerns entanglement with new information that an object encounters as it is coming in from outside the object's light cone. In my understanding when entanglement-measurement occurs, some pair (or more) objects in the wavefunction take on a correlated value, but then the price of this is that other values become randomized (so electrons take on opposite spins, but then the spin of each electron is not determined).

What I am wondering is as we pass from before the moment of entanglement with new information coming in from outside the lightcone to after that moment, some of the information will be consistent (or not consistent) with our current history - that information gets zipped with (or excluded from) the entanglement event, but all the sort of 'random' information that is really new... is it the case that the wavefunction of our object has a different space (or location on the wavefunction) for each of these random timelines before the encounter with new information - or is that space created at the moment of entanglement with the new information?

That is... is it the case that our original object is actually already always split into all of its future possible timelines in a way such that various points on its original wavefunction can be assigned to various final 'futures' - or is that split not possible in principle or in the mathematics from the beginning of the calculation (so that in reality many futures pass through the same original point on the wave function)?

Answer 1

Suppose there is a measurement device $M$ and a system $S$. The measurement system $M$ starts in a ready state $|0\rangle_M$. The system $S$ is in a state $$|\psi\rangle_S=\frac{1}{\sqrt{2}}(|0\rangle_S+|1\rangle_S).$$ Before they interact the state of the joint system is $|\psi\rangle_S|0\rangle_M$.

The measurement device is used to measure $S$ and the state after the measurement is $$\frac{1}{\sqrt{2}}(|0\rangle_S|0\rangle_M+|1\rangle_S|1\rangle_M).$$

You could write the state of $M$ before the measurement as $$\alpha|0\rangle_M+(1-\alpha)|0\rangle_M$$ for any number $\alpha$ so in some sense there are multiple instances of $M$ that can be divided into sets that are uncountably infinite. However, all of these instances are identical: there is no measurement, nor any other kind of physical interaction, that can distinguish between them. After the measurement there are two distinguishable versions of $M$, but there is no fact of the matter about which of the instances of $M$ before the measurement became each version of $M$.

For more on the MWI see David Deutsch's books "The Fabric of Reality" and "The Beginning of Infinity" and the following papers:

https://arxiv.org/abs/2205.00568

https://arxiv.org/abs/quant-ph/0104033

https://arxiv.org/abs/2008.02328

https://arxiv.org/abs/0707.2832