The article Why the Many-Worlds Interpretation Has Many Problems does an okay job of introducing MWI, but then its criticisms of the idea are terribly weak and misleading. I'm going to go over parts of the article and talk about what's wrong with it.

My own view is that the problems with the MWI are overwhelming — not because they show it must be wrong, but because they render it incoherent. It simply cannot be articulated meaningfully.

I’ll attempt to summarize the problems, but first, let’s dispense with a wrong objection. Some criticize the MWI on aesthetic grounds: People object to all those countless other universes, multiplying by the trillion every nanosecond, because it just doesn’t seem proper. Other copies of me? Other world histories? Worlds where I never existed? Honestly, whatever next! This objection is rightly dismissed by saying that an affront to one’s sense of propriety is no grounds for rejecting a theory. Who are we to say how the world should behave?

Reasonable so far but then this happens:

A stronger objection to the proliferation of worlds is not so much all this extra stuff you’re making, but the insouciance with which it is made. Roland Omnès says the idea that every little quantum “measurement” spawns a world “gives an undue importance to the little differences generated by quantum events, as if each of them were vital to the universe.” This, he says, is contrary to what we generally learn from physics: that most of the fine details make no difference at all to what happens at larger scales.

This is just another version of "the MWI universe seems too big".

The author goes wrong by calling the splits "undue importance". Splits just aren't a big-scale important thing in the MWI universe. They're only big-scale to us perpetually inside a small slice of the MWI universe. This criticism is like a 2D being saying a 3D world couldn't possibly make sense, because it places "undue importance" on your Z coordinate (moving one step in Z gives you a whole new XY plane full of possibly different objects).

I think the author is still operating on the idea that the split worlds are discrete countable things rather than operating as continuous values.

Occam's razor should be applied to judge a theory based on the number of rules it has, not on the number of entities in the world it predicts. MWI shouldn't be judged on the scale of the multiverse it predicts; otherwise, we should be much more skeptical of theories that predict that there are trillions of galaxies, etc.

But one of the most serious difficulties with the MWI is what it does to the notion of self. What can it mean to say that splittings generate copies of me? In what sense are those other copies “me?”

Yes, "self" is kind of alien under MWI, but it's not contradictory. Its weirdness doesn't rule out MWI! It's on us to figure out its weirdness. "Self" is more of an emergent concept in MWI rather than being a simple aspect of the world as it is in classical theories.

The author explained that it's a bad criticism to call out MWI just for being weird, and then made multiple criticisms like that. The article explains that MWI sounds like a TV sci-fi concept, and subtly encourages us to judge it for that. It's like an article talking about climate change by ridiculing it because people connect it to post-apocalypse movies. Sure, maybe there's a weird attractor to the idea that's worth judging, but that doesn't change the rest of the idea's actual merits. (It's possible that the actual merits are at least some part of the reason why it's popular in fiction! We can't treat its popularity in fiction as entirely unrelated.)

David Wallace, one of the most ingenious Everettians, has argued that purely in linguistic terms the notion of “I” can make sense only if identity/consciousness/mind is confined to a single branch of the quantum multiverse. Since it is not clear how that can possibly happen, Wallace might then have inadvertently demonstrated that the MWI is not after all proposing a conceit of “multiple selves.” On the contrary, it is dismantling the whole notion of selfhood. It is denying any real meaning of “you.”

Why does the author say "Since it is not clear how that can possibly happen"? There's a very definite answer: we only experience a single branch of the quantum multiverse because alternate branches mostly don't interact. The rest of the article hinges on refusing this sensible definition of "I".

What can you do with this power to generate worlds and selves? You could become a billionaire by playing quantum Russian roulette. Your quantum splitter is activated while you sleep, and if the dial says Up then you’re given a billion dollars when you wake. If it shows Down then you are put to death painlessly in your sleep. Few people, I think, would accept these odds on a coin toss. But a committed Everettian should have no hesitation about doing so using the quantum splitter. For you can be certain, in this view, that you’ll wake up to be presented with the cash. Of course, only one of “you” wakes up at all; the others have been killed. But those other yous knew nothing of their demise. Sure, you might worry about the grief afflicted on family and friends in those other worlds. But that aside, the rational choice is to play the game. What could possibly go wrong?

The "quantum suicide" routine decreases the measure of worlds where you live, and measure controls the chance you experience something. Unlike how the author presents it, it's not a given that MWI implies that the quantum suicide routine is useful. Killing yourself in some timelines doesn't do anything to increase the measure of other timelines. All the timelines resulting from buying a lottery ticket happen regardless of what you do in some of them after getting the lottery ticket.

Some Everettians have tried to articulate a meaning nonetheless. They argue that, despite the certainty of all outcomes, it is rational for any observer to consider the subjective probability for a particular outcome to be proportional to the amplitude of that world’s wave function — or what Vaidman calls the “measure of existence” of that world.

It’s a misleading term, since there’s no sense in which any of the many worlds exists less.

Measure is the way some worlds exist less. It might be a sloppy metaphor, but there's no argument here but flat-out denial.

What this boils down to is the interpretation of probabilities in the MWI. If all outcomes occur with 100-percent probability, where does that leave the probabilistic character of quantum mechanics? And how can two (or for that matter, a thousand) mutually exclusive outcomes all have 100-percent probability?

The type of "probability" where all outcomes definitely happen in isn't the type of probability that we personally experience! The author is switching the meanings of words between times they use the words, and then thinking it's a contradiction that the different meanings they used for the same word don't match up.

We experience one timeline and not the lives of all of our alternate selves, much in the same way we experience only our own life and not the lives of others.

Attempts to explain the appearance of probability within the MWI come down to saying that quantum probabilities are just what quantum mechanics looks like when consciousness is restricted to only one world.

Yes, exactly this.

As we saw, there is in fact no meaningful way to explain or justify such a restriction.

What? When was this shown? There's no reasoning here. Their previous arguments didn't actually find a contradiction in MWI but just said it's confusing to them.

This is like someone saying math is nonsense because it talks about numbers that are too big to be humanly conceivable, then goes through the steps of showing 10 * 10 = 100, and then ends with "but as we saw, this is nonsense because 100 is a too alien result to be real".

Imagine that our observer, Alice, is playing a quantum version of a simple coin-toss gambling game — nothing as drastic or emotive as quantum Russian roulette — that hinges on measurement of the spin state of an atom prepared in a 50:50 superposition of up and down. If the measurement elicits up, she doubles her money. If it’s down, she loses it all.

If the MWI is correct, the game seems pointless — for Alice will, with certainty, both win and lose. And there’s no point her saying, “Yes, but which world will I end up in?” Both of the two Alices that exist once the measurement is made are in some sense present in the “her” before the toss.

Alice doesn't care about the gods-eye view of the world that shows all results happening with some chance. Alice cares about subjective probability and therefore the measure or the proportions of the resulting worlds. Being a consciousness that only experiences one timeline causes us to make choices to try to cause more resulting timelines (or higher proportion of measure) have good results than bad results, because it increases the subjective probability of experiencing the good results.

If the game had better than 50% chances of winning, then Alice would want to play the game many times to become rich with great probability. If the game had a 50% chance or less of winning, then Alice would not want to play the game, because choosing to play it would increase the chance of losing money.

From the gods-eye view of the world, it looks like Alice is trying to arrange things so she's well off in the majority of resulting timelines. From the gods-eye view of the world from the outside, this might seem arbitrary, but so are all of Alice's desires (staying alive, eating food, etc) unless you consider her perspective.

But what if Alice were to say, “The experience I will have is that I will wake up in a room containing a chest that has a 100-percent chance of being empty”? The Everettian must accept this statement as a true and rational belief too, for the initial “I” here must apply to both Alices in the future.

No! An Everettian wouldn't accept that statement. The author is back to flipping between different meanings of probability again.

We experience only a single timeline in the same way we experience only our own life and not others. If you define "I" to refer to all of your selves, then you're going to get nonsense results just as if you defined "I" to refer to all people. You could reframe any of these examples that have results happening with some probability (results that are happening differently to different timelines) as situations with results that are happening to different people and be just as confused: if you have a setup where one person is going to open an empty box and another person is going to open a box with something in it, then sure, if you define "I" to include both people's perspectives, then with 100% chance "I" will open a box with something in it and 100% chance "I" will open an empty box, but that's only a good argument against defining "I" that way, not against the physical possibility of that situation.

In other words, Alice Before can’t use quantum mechanics to predict what will happen to her in a way that can be articulated — because there is no logical way to talk about “her” at any moment except the conscious present (which, in a frantically splitting universe, doesn’t exist).

This is basically Loki's Wager. Just because her different selves are separated by a fuzzy shifting boundary rather than being sharply discrete doesn't make them not exist.

The author goes on a weird diatribe below.

What the MWI really denies is the existence of facts at all. It replaces them with an experience of pseudo-facts (we think that this happened, even though that happened too). In so doing, it eliminates any coherent notion of what we can experience, or have experienced, or are experiencing right now. We might reasonably wonder if there is any value — any meaning — in what remains, and whether the sacrifice has been worth it.

[...]

It says that our unique experience as individuals is not simply a bit imperfect, a bit unreliable and fuzzy, but is a complete illusion. If we really pursue that idea, rather than pretending that it gives us quantum siblings, we find ourselves unable to say anything about anything that can be considered a meaningful truth. We are not just suspended in language; we have denied language any agency. The MWI — if taken seriously — is unthinkable.

What quantum theory seems to insist is that at the fundamental level the world cannot supply clear “yes/no” empirical answers to all the questions that seem at face value as though they should have one. The calm acceptance of that fact by the Copenhagen interpretation seems to some, and with good reason, to be far too unsatisfactory and complacent. The MWI is an exuberant attempt to rescue the “yes/no” by admitting both of them at once. But in the end, if you say everything is true, you have said nothing.

This is nonsense: there can be different yes/no empirical answers on different branches. The concept of empiricism is still useful.

The whole article hinges on defining "I" in a nonsense way relative to the quantum multiverse and then showing that definition is nonsense. There's no paradoxes if you don't try to define "I" that way.


I write all this not so much because I think belief in the Many-Worlds Interpretation is directly useful (it makes the same predictions as most other interpretations; the other "worlds" can't be meaningfully interacted with), but because I think MWI is a very interesting idea demonstrating the possibility that reality works utterly counter to our preconceptions. It's a great exercise to understand the idea and see how it's even possible that we could figure out that reality may work how MWI describes.

After writing this post, I searched online for other discussions of the article, and found some good ones that readers may be interested in:

If you want to learn more about MWI, then LessWrong's Quantum Mechanics sequence is an excellent introduction from a philosophy of science angle that I recommend!