One of the great upsides of the generally miserable or horrific pandemic is that more recordings of fascinating intellectual discussions are being made available to wider audiences. Recently I watched a set of talks hosted by an outfit called the “Harvard Foundations of Physics Workshop Series”, grouped together under the name “Mini-Workshop on the Many Worlds of Everettian Quantum Theory”. I am interested in this topic, but I have no more than amateurish competency. In what follows I’m going to offer what I think I understand; but if I get stuff wrong, just blame me, of course, and none of the presenters in this workshop.
Sean Carroll was one of the featured speakers, as his recent book Something Deeply Hidden champions the “many worlds” interpretation of quantum mechanics. The basic idea of the many worlds interpretation (hereafter, MWI) is that when we have some sort of quantum situation in which a system is in a superposition of many different states (think of the Schrödinger’s Cat example), at some point that system “decoheres” in such a way that each of those states becomes a real, actual state of the system in one world or some other world. This world-splitting includes any observers who are entangled with these quantum systems – they too branch into separate selves, living in separate worlds, each as real as the next. This happens many, many times every second, in case you haven’t noticed.
It is a brave view, and Carroll compellingly argues that it is in some ways the most basic, straight-ahead interpretation of quantum mechanics. Every other “more sensible” interpretation requires adding extra-theoretical elements to the theory, just so that we can feel more comfortable with it. But the simplest, no-frills, most straight-ahead version of quantum mechanics is just MWI (or what Carroll calls “Mad-Dog Everettianism”). This particular mini-workshop was aiming at whether we really can live with the many worlds interpretation – in other words, whether we really can make it square with seemingly obvious parts of our own experience, as well as deeply ingrained presuppositions of science.
A basic objection to raise against MWI is whether it can make sense of probabilities. Here is the problem. In some typical sort of quantum experiment, we can assess the probabilities of the outcomes. Let’s say there is a 90% chance that A will result, and a 10% chance that B will result. But according to the MWI, every outcome happens in some world or other, and all of these worlds are equally real. So what do “90%” and “10%” mean?
Initially we might say that the percentages express the chance that the initial world will evolve into one world or another world. At first we are in world 1, and then we do the experiment, and there is a 90% chance we will end up in world 2, and a 10% chance we will end up in world 3. But here is the problem: who is the “we”? The observers in world 2 are every much as continuously identical with the observers in the original world 1 as the observers in world 3 are. There is no pride of place in the multiverse. “We” end up in both worlds, fully and completely. So, once again: what do “90%” and “10%” mean?
Carroll’s own answer is that the 90% and 10% should be understood as the epistemic probabilities of self-location, after the experiment has taken place. That’s a mouthful, so here is what it means. Let’s say we have done the experiment, but have not yet checked to see whether A or B has been the result. (We haven’t opened the box.) We pause and ask ourselves, “What world are we in?” If we are rational, says Carroll, we ought to be 90% sure we are in world A, and 10% sure we are in world B. The percentages track what our levels of confidence ought to be, not our chances of surviving the splitting of worlds in one world versus another. We might run the experiment a few times to assure ourselves we are assigning the right probabilities to these outcomes, and over time, we will be assured. That’s been our experience over the last century, anyway.
The Easier Objection
It is at this point that philosopher David Albert raises an objection. Suppose we repeat this experiment many times over, with the worlds splitting every time. In the end there will be a large population of observers who have found themselves to be in worlds where A happens 90% of the time and B happens 10% of the time. Good for them (and for us). But these aren’t all the worlds there are. There will also be worlds where A happens all the time; worlds where B happens all the time; worlds where A and B happen with equal frequency; and all the possibilities in between. These observers are not going to come to the conclusion, based on their empirical evidence, that A should happen 90% of the time, and B should happen 10% of the time. They will get quantum mechanics quite wrong – or at the very least they will be quite astonished at how often “improbable” events happen in their world.
Carroll’s response is, basically, that it stinks to be them. They live in bad luck worlds that fail to confirm the true physics of the world. But that’s just the way the quantum cookie crumbles.
At this point Albert complains that this runs afoul of a deeply-entrenched scientific ideal, namely that the laws of nature are the regularities all observers should come to discover with enough time, patience, and rationality. Science represents the truths different observers converge upon, precisely because they are all governed by the same laws of nature. The MWI makes it absolutely certain that some observers, in some worlds, will never converge upon the true laws of nature, and not because they haven’t enough time, patience, or rationality. They just haven’t enough good luck to live in a world in which their experience reflects the true order of things.
Carroll’s reply to this is that, as science goes along, we should expect to have our minds changed, even about deeply-entrenched ideals of science. Perhaps we once thought that the probabilities in quantum mechanics reflected how likely certain events would take place in the world. But now, with MWI, we are realizing that probabilities measure something else; and perhaps along with that we are also realizing that reality really stinks for some scientists out there in the multiverse (or, as Carroll points out, it stinks even for some scientists in our universe, if it is so big to include a sufficient number of quantum scientists on other planets doing similar experiments).
The Harder Objection
But David Albert raises a deeper objection as well, which requires more care and effort to explain. According to Carroll, as we have seen, percentages reflect how much confidence observers should have regarding which world they are in. “There is a 90% chance that A will happen” really means “If I were in a world in which this experiment had just taken place, I should be 90% sure that A was the result.” Albert’s objection is, basically, why the universe should care about what percentages human beings would assign to being in this or that situation after doing an experiment.
There are lots of ways for human beings to assign probabilities. They could roll percentile dice. They could throw darts. They could take the temperature of the nearest wombat, divide by 2, and subtract from 100. Or they could follow the Born rule, which is the official quantum mechanics method for assigning probabilities. Experts agree that this is the best way to go.
So why is the Born rule the best way to go? We might initially say that it’s because it’s the rule that nature itself follows as it figures out what should happen next. That is a natural thing to say, but it is precisely not what an MWI theorist can say. Probabilities, remember, do not track genuine chance, since all chances get taken up in some world or other. Instead, probabilities track how much confidence observers should have about which world they are in.
And why should observers have one level of confidence rather than another? Again, why should they follow the Born rule, as opposed to any other rule? We might try this second answer: observers who have done this sort of experiment a whole bunch of times just happen to have found empirically that following the Born rule is more successful than any other known method of assigning probabilities to outcomes. Other observers in other worlds have no doubt come up with other rules that match their experience more closely, and still other observers have been pulling out their hair trying to find some pattern in the mess they are experiencing. But in our world the Born rule has worked extremely well.
In other words, in the unimaginably vast multiverse, there have to be some possible worlds in which the Born rule holds; just as there have to be worlds where the Shmorn rule holds, and the Blorn rule, and the Florn rule, and on and on. Every rule holds in some world or other, and in some worlds there is no rule that can be discerned at all. We just happen to find ourselves in a Born rule world.
But hold on. The Born rule is not supposed to be just one assignment of probabilities running alongside many other possible assignments of probabilities. It is supposed to be the right one, or the one we ought to follow if we want to be rational in making our predictions about what we shall see when we open the box. (Indeed, the Born rule is the right one to follow, or the rational one to follow, for all observers on all branches, even if some unlucky observers on some branches can be forgiven for not thinking so.) But now, in trying to make sense of all this, we are finding that there is an endless variety in rules that rational, empirically-minded observers will end up adopting in their different worlds, and each one of them can loudly brag about itself: “So far, so good.” The fact that the Born rule can brag about this success in our world does not make it the rational rule to follow in other worlds.
It gets worse. For why should we think that the Born rule is a good one to adopt even just within the confines of our world? Maybe our world is one that will suddenly turn anti-Bornian tomorrow at noon (we know, after all, that such worlds exist; and absolutely none of our evidence tells us that we are not in one of those worlds). All sorts of skeptical scenarios threaten to undermine our confidence in our predictions – and these threats should be taken seriously so long as our predictions are based on a principle that is assumed to be only an accidental regularity. To set aside such bothersome scenarios, we need to have some reason to believe that Born is no accident – that it actually does govern how things turn out, in all worlds that share our laws of nature. But this is an assurance that MWI cannot possibly give. (Or at least, so far as my amateur understanding can see!)
A Humean Observation
Overall, I am struck by the Humean sensibility of MWI. The most austere version of Hume’s account of the human situation is that nature chugs along following its rules (or maybe sometimes following no rules, who knows) in some fashion that is utterly opaque to us. When patterns and regularities emerge, we quickly get used to them, and we expect nature to continue to follow them. But nature is not obligated to follow our expectations; there is nothing in our experience or reason that tells us we are justified in expecting nature to keep doing the same sort of thing. So we plod along and hope for the best.
If MWI is true, then many observers across the many worlds are living Humean nightmares. Their worlds rudely surprise them with violations of the most common regularities. Other observers are quickly getting used to weird regularities never to be seen in our world. In our world – so far, anyway – we are not experiencing those rude surprises, and nature seems to follow the patterns we expect to see followed. That’s nice, if a little boring. And we think we have a theory that both explains our experience and explains the misfortunes of our colleagues in other worlds. What our colleagues believe, and what they think about us, God only knows.
But then again, maybe we are in a slightly nightmarish Humean world after all. There is quantum mechanics, after all. As odd as it may sound, if MWI is true, then some of our counterparts in other worlds never discovered quantum mechanics, and have been able to explain all events in terms of classical mechanics. We would say they were wrong – though it would be harder to say whether their experience has been lucky or unlucky. As it happens, in our world, we see nature do funny things in the quantum arena, and that complicates our science of nature, and gives rise to the complications mentioned in this essay, along with so many others. Maybe, if MWI is true, it might have been nicer for us never to have had to have come up with MWI in the first place?
(Thanks to Richard Harvey for comments on an earlier draft, though any remaining mistakes are entirely my own.)