Summary: Perspective-based reasoning would reject the Many-Worlds Interpretation because it relies on self-locating probabilities to explain the randomness of quantum experiments.
It may seem off-topic to talk about quantum mechanics in anthropic reasoning. Yet that is actually quite a common occurrence. For example, Titelbaum’s Ten Reasons to Care About the Sleeping Beauty Problem suggested the two are closely related. Darren Bradley and Alastair Wilson debated on whether or not the thirder position naively confirms the Many-Worlds Interpretation. Physicists are also aware of this parallelism. For example, Charles Sebens and Sean Carroll discussed the Sleeping Beauty Problem while explaining Self-locating Uncertainty and the Origin of Probability in Everettian Quantum Mechanics.
Safe to say anthropic reasoning and quantum mechanics, especially the Many-Worlds Interpretation (MWI), have some underlying connections. In fact, it would be disingenuous of me to avoid this topic. Because my argument is categorically incompatible with the MWI. To put it plainly, perspective-based reasoning would reject Everettian quantum mechanics.
I think a disclaimer is needed here. I am not a physicist. Therefore, though I am confident about the argument presented, please read with a critical mindset. If you are unfamiliar with quantum mechanics and the debate of its interpretations, I highly recommend Sean Carroll’s Something Deeply Hidden. It is an easy-to-read book that IMO fairly presents various interpretations. It is especially relevant because the author favors the MWI and discussed it in detail.
Self-Locating Probability, Again
Because the MWI describes the world by the deterministic evolution of the universal wave function, it needs to explain the apparent randomness of quantum experiments’ outcomes. This is often justified by using self-locating probabilities. For example, after a quantum coin is tossed, it is certain both Heads and Tails actualizes in two different branches (worlds), yet before checking the result it is unknown to “me” which branch “I” am in. So even though the universe changes deterministically, observers would still perceive randomness from their perspectives. Basing on this explanation, supporters of MWI would start to derive the Born rule. It typically begins with assigning equal probabilities to highly symmetrical branches.
However, as discussed in Part 3, the self-locating probability is an invalid concept caused by not reasoning from a consistent perspective. Therefore, according to PBA, the MWI can neither explain the probability nor derive the Born rule.
Other Ways to Explain the Probability?
Readers familiar with this topic would know the nature of probability in MWI has been its Achilles’ heel for a long time. It is the most debated point between its supporters and critics. Unsurprisingly, there are other schools of thought explaining the randomness besides using self-locating probabilities. (e.g. using decision theory etc) So the question is, would there be an explanation that makes the MWI compatible with perspective-based reasoning?
Unfortunately, I am quite certain that is not possible. This boils down to the fact the MWI describes the world by the universal wave function. Traditional reasoning would simply treat this as an objective description. Yet perspective-based reasoning requires us to examine which perspective is this description made from. As the universal wave function encompasses all branches, it describes the world from an imaginary impartial observer’s perspective (or from a god’s eye view). From this perspective, the MWI suggests there is no inherent randomness or unknowables (in contrast to Bohmian Mechanics). So the probability has to be explained as illusions experienced by observers within a particular branch. This demands a perspective switch from the god’s eye view to someone’s first-person view. This switch would make the argument inconsistent according to perspective-based reasoning.
Which Interpretation Then?
I think it is worth saying the MWI is an otherwise appealing theory. It is parsimonious in terms of assumptions and has a clear logic structure. My disagreement with it is purely based on perspective reasoning, not because of the controversial existence of other worlds.
That said, the MWI is the only interpretation definitively incompatible with perspective-based reasoning (the only one I am aware of at least). However, that does not mean other interpretations are equally appealing when perspectives are considered. In my opinion, some interpretations are clearly superior to others according to PBA. I will discuss it in the following sections.