by Lee Smolin
This is not a bet about the universe, because it is certain that the universe contains observers who live on both kinds of branches. It is instead a bet on where we are in the universe. There is no right answer to this question, because, if Everett is right, there are both kinds of observers, and some of us will be one kind, some the other.
Nonetheless, Deutsch proposes that it is more rational to bet we are on a benevolent branch. The argument is technical and employs a branch of probability theory called decision theory. Deutsch’s result then assumes certain axioms of decision theory, which specify what it means to make a rational decision.
Some experts have criticized this approach; some defend and develop it, while still other experts offer alternative arguments to the same conclusion. Given that I am not a specialist in this area, I am not going to speculate on which experts are right.
But notice what this kind of argument doesn’t—indeed cannot—do. It cannot offer us evidence that the Everett hypothesis is true, because Deutsch and his colleagues begin by assuming that the hypothesis is correct. Their arguments also assume the axioms of decision theory. If you don’t accept them you do not prove that the probabilities are related to the magnitudes. All the argument could show is that, assuming the axioms of decision theory, it is consistent with the Everett hypothesis to place bets, and make other kinds of decisions, as if Born’s rule were true.
Notice that, even given the assumption that Everett is true, the observers modeled as part of an Everett world do not know that they live in an Everett world. There is no reason they should, and if they nonetheless did, they would not be models of us, as observers in a universe whose full set of principles remain to be discovered. For them as for us, the Everett hypothesis must be one of several competing hypotheses as to the nature of the beables of the quantum universe.
Let us then consider the situation of observers inside an Everettian universe. There are two cases, depending on which kind of branch we live on. Suppose we are fortunate and live on a benevolent branch, so that our bets based on Born’s rule pay out. Well then, by definition, we do no better, and no worse, than people who believe in other formulations and interpretations of quantum mechanics and so also place bets based on Born’s rule. What the other approaches lack is a justification based on decision theory. On the other hand, pilot wave theory and collapse models have no need of such justification, because they rely on completely objective notions of probability arising from our ignorance of the details of the individual experiment.
Thus, on its own terms, in which it cannot address what is true, but can only offer advice about how best to place bets, Deutsch’s argument implies that it is no more rational for observers inside an Everettian world to believe in Everett than it is for them to believe in Bohr or de Broglie, Bohm or any other interpretation. So, in the best case, even assuming that Everett is right, observers in an Everettian world cannot muster any evidence to believe Everett’s hypotheses over the alternative hypotheses.
What about the versions of ourselves that live on malevolent branches? Their bets based on Born’s rule don’t pay off because the frequencies they measure disagree with those predicted by Born’s rule. So how does it look from the point of view of these unlucky observers? Remember that for them, the usual formulation of quantum mechanics (say, as presented in von Neumann’s book) must be a hypothesis, and Everett’s hypothesis is a different, competing, hypothesis.
Observers on a malevolent branch conclude that the first hypothesis is simply false because Born’s rule does not predict the results they observe. The second hypothesis, Everett’s, is not falsified, because that predicts that some observers will see Born’s rule fail. But it’s worse than that. Given any results of repeated measurements, Everett’s story predicts that some observers, living on a malevolent branch, will see exactly those results. So Everett’s hypothesis cannot be falsified by testing any probabilistic prediction based on Born’s rule, as there is no outcome of a repeated measurement that is inconsistent with an Everettian universe.
So it seems that the bulk of experimental predictions that could falsify ordinary quantum mechanics—those that compare theoretical probabilities to experimentally observed frequencies—would not count as falsifying Everettian quantum mechanics. While not completely unfalsifiable—because the theory makes other kinds of predictions, which do not involve probabilities—Everettian quantum mechanics seems to be far less vulnerable to falsification than ordinary quantum mechanics.
That, in itself, is a good reason to prefer an alternative approach. A theory that is less falsifiable is by definition less explanatory.
On the other hand, if we accept the assumptions of Deutsch and the other Oxfordians, then we must disregard the point of view of the malevolent branches, because those branches are very improbable. In this case there is work that shows that once one neglects the malevolent branches, the theory is testable.
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THE OXFORDIANS EMPHASIZE that if you assume the axioms of decision theory are correct, then you are allowed to deduce that it is rational to reason as if the magnitudes are related to the probabilities. It follows that it is rational to reason as if we have a very small probability of ending up on a malevolent branch, so that possibility can be ignored.
They might further claim that something like this is always the case when we reason probabilistically. We could always be unlucky and have a coin toss result in heads a thousand times in a row. But there is a difference. In a finite life, in a single finite world, we can rest assured that such things almost never happen. But in strong contrast, Everettian quantum mechanics asserts that correspondingly malevolent branches not only exist—they are as numerous as benevolent branches. While Deutsch’s argument tells us about subjective betting probabilities taken by observers inside the Everett world, it remains the case that the overall theory is deterministic and that each of the branches definitely exists.
It seems, at least as best I’ve been able to understand, that the attempts by Deutsch and others* to rescue the project of making sense of the Everett hypothesis by means only of subjective probabilities for observers in an Everett universe, introduced via decision theory, do not convincingly succeed. Arguments based on subjective notions of probability alone fail to explain why we can neglect the malevolent branches—for, if Everett is right, they are objectively real.
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SOMETHING NEW IS NEEDED. To save the day, Simon Saunders has proposed to cut the Gordian knot by positing that the magnitudes of the branches give objective probabilities (rather than betting probabilities) of an observer finding themselves on a decohered branch, in agreement with Born’s rule. His argument for this is that the magnitudes of the branches do indeed turn out to have many of the properties we would want objective probabilities to enjoy. Indeed, his claim is that they have these properties as a consequence of Rule 1—hence this is a discovery of a consequence of the laws by which quantum states evolve. It is not an additional postulate, as Rule 2 is. If his proposal succeeds, it would be a genuine derivation of Rule 2 and the Born rule from the theory based purely on Rule 1.
This gets us out of the problems raised by the malevolent branches, because, assuming Saunders is right, it is not very probable to find ourselves on one of them. But Saunders claims it would accomplish more than that: it would be a genuine derivation of how objective probabilities arise in nature, and it would explain why we must align our subjective betting odds with the objective probabilities.
My understanding is that the experts in Oxford are at present divided as to whether Saunders’s proposal succeeds. One issue is that the branch magnitudes have some but not all properties of objective probabilities. So we must leave this discussion here; after more than sixty years of study, it is still unresolved whether sense can be made of Everett’s startling idea.
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&
nbsp; RECOGNIZING THAT THE PROJECT of making sense of Everett’s hypothesis remains a work in progress, I can offer a series of remarks.
My overall understanding is that the Everett hypothesis, if successful, would explain vastly too much, and also much too little. Too much, because we have to believe that the whole world we used to think of as real is just one branch within a vastly larger reality. And too little, because a great deal is left out of this picture of reality. What is most characteristic about experienced reality is that every process we observe has a definite outcome. What is also most impressive about quantum theory is its ability, using Rule 2, to make precise predictions of the observed frequencies of those definite outcomes. What I want from realism is a detailed explanation for how those probabilities arise as relative frequencies, by averaging over a set of repeated runs of the experiment.
The reality that we realists seek is the world as it is, or would be, in our absence. Subjective probabilities that guide decision makers to place bets are not part of that world, since they would not exist if we did not. The question is not whether decision makers are real, for we are certainly real. Nor is the question whether we could, if we were interested, seek a scientific account of what constitutes rational decision making. The question is instead whether we can realize the ambition of physics to describe light and atoms in a way that is completely independent of whether we exist or not.
Let me emphasize that the jury is still out as to whether the Oxford approach succeeds, on its own terms, in making sense of the Many Worlds Interpretation. The Everett hypothesis may yet be shown to be inconsistent or incoherent. Or it may turn out to be the only realist approach to quantum mechanics, in which Rule 1 alone suffices to frame the theory. For me, either outcome would just strengthen the argument that we need a new theory.
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WHEN EMPIRICAL TESTS of theories fail, we still have to make decisions about which theory to work on. As a number of philosophers and historians have stressed, before definitive evidence is in, there is no avoiding bringing in factors that may seem nonscientific when evaluating which research program and theory is deserving of our time and attention. This is especially the case because these are in part individual decisions, and when empirical criteria have yet to be decisive, it is in the interests of the scientific community as a whole to encourage the widest diversity of approaches consistent with the evidence in hand at the moment. As Paul Feyerabend explains in his book Against Method, it is competition among diverse viewpoints and research programs that drives the progress of science, especially through critical periods when the evidence is not sufficient to decide which approach will ultimately yield the best explanations.
Evaluating a research program based on non-empirical factors is partly a matter of individual taste and judgment.* After a lot of effort to understand the thinking of its proponents, here is how the case for the Everett program seems to me. I expect, indeed I know, that others who have thought it through do not agree. I am not afraid to confess that no issue in quantum foundations has been more challenging and more painful to me personally than the issue of Everett, where I find myself in disagreement with friends and colleagues for whom over the years I have grown to have great respect.
We know that the original form of the Many Worlds Interpretation fails as a realist approach because it runs into two big problems, which are the preferred splitting problem and the problem that the theory is deterministic and has no probabilities. After a great deal of effort to develop a more sophisticated version based on decoherence and subjective probabilities, experts continue to disagree over technical issues. But even if they do succeed, what would be established is that the axioms of decision theory require that observers living in an Everett world bet as if Born’s rule were true. That does not, however, give us a reason to believe that we live in an Everettian universe. Nor am I aware of any empirically based argument that would require us to prefer Everett over other approaches. Despite some provocative claims to the contrary, there is no experimental outcome that cannot be explained at least as well by the other realist approaches. There are claims that Everett alone can explain phenomena such as the speed-up of quantum computing, but these are contradicted by the fact that the alternative realist programs, such as pilot wave theory, provide accounts of these experiments which are at least equally explanatory.
One argument for Everett begins with the assertion that there are only three realistic formulations of quantum theory, and that the other two, pilot wave theory and collapse theory, have tensions with relativity and hence have trouble incorporating quantum field theory. This argument then implies that, assuming it can be made sense of, Everett must be correct. I disagree, and take this as strong motivation to seek to invent other realist approaches, as I describe in the closing chapters of this book.
That is where the scientific case leaves off; let’s then turn to non-empirical factors. The philosopher Imre Lakatos recommended investing in research programs that are progressive, by which he meant that they are rapidly developing and have the potential to lead to a breakthrough. A progressive research program is also one that is open to future developments and surprises, in contrast to programs which assume the basic principles and phenomena are understood. Progressive criteria favor realistic approaches to quantum foundations over the anti-realist approaches because the latter confine us to developing new ways of talking about quantum phenomena which are assumed to be already known, while the former understand that quantum mechanics is incomplete and hence aim to discover new phenomena and new principles in which to situate them.
Within the realist approaches, I believe there is a case to be made that Everett’s hypothesis is the least progressive—although there are arguments on both sides. An enormous effort has gone into developing Everett quantum mechanics, much of it technical and extremely clever, but most of that work has gone to addressing problems that arise only in the Many Worlds Interpretation, but do not trouble the other approaches. I might suggest that the Everett program is, of the realist approaches, the least open to the possibility that future discoveries will lead us to modify the principles and the mathematical formalism of quantum mechanics.
On the other side, it should be pointed out that the Everett theory stimulated much work on decoherence, which was important generally for our understanding of quantum physics. It also inspired, and continues to provoke, much progress in quantum computing. The Many Worlds Interpretation played a role in the pioneering work of David Deutsch. Yet we must also credit pilot wave theory and collapse models for the experimental proposals they have stimulated regarding, for example, out-of-equilibrium physics in the early universe. So it seems that an argument about which realist approach is more progressive comes out about even.
The odd thing about the Oxford approach is that, while it tells us nothing about the world we experience that we didn’t already know, or couldn’t have deduced within other versions of quantum theory, it has a lot to say about all the worlds we don’t and can’t experience, and especially about the near copies of ourselves which populate them. Given that they are presumably just as alive and just as conscious as we are, I find myself wondering if we—or those of us who believe in Everett enough to contemplate it as a serious possibility—should care about our copies, and whether we have any responsibilities toward them.
I admit that to inquire into the quality of lives of our copies on other branches may seem a bit academic. But one thing we academics are trained to do is to work out the logical consequences of hypotheses and assumptions. And the most provocative and, to me, distasteful consequence of Everett is that we must believe that each of us has an infinite number of copies, each every bit as alive and conscious as we are. This sounds more like science fiction than science, but it does seem a straightforward consequence of Everett’s hypothesis. Since this is science and not faith, we don’t have the option of taking a “liberal” interpretation of Evere
tt in which we choose to believe certain aspects, such as the existence of a wave function of the universe, while ignoring others.
It then seems to me that Everett raises two kinds of ethical quandaries. First, it condemns a vast number of living and conscious beings to suffering which cannot be mitigated by efforts we make. Beyond that, I would worry that the fact that many of our most talented and accomplished scientists believe we live in that unhappy universe is inimical for the long-term public good, because, by erasing the distinction between possibility and actuality, it diminishes the motivation to work to improve our world.
Couldn’t we say the same about the increase in entropy mandated by the second law of thermodynamics, which is ultimately the cause of the death of most living creatures? The difference is that we know the second law is true. We have no choice whether to believe it, whereas there are alternative formulations of quantum theory which do not impose on us the existence of copies. It is also very legitimate to criticize the scientists and philosophers who drew unnecessarily pessimistic conclusions based on an incomplete picture that neglected the positive effects of self-organization in far-from-equilibrium systems.
The whole notion of an observer “living” on a malevolent branch can be objected to on the grounds that none of the biochemistry that life depends on would function well in a world in which Born’s rule regularly failed. To be more precise, we might rate malevolent branches by the proportion of events in which Born’s rule failed to hold. We could then catalogue branches by the severity of such failures. Living in a mildly malevolent branch would be like being subject to a low dose of ionizing radiation, with similar consequences of decreased health.