The frequently thought-provoking series Closer to Truth, created and hosted by Robert Lawrence Kuhn, recently released an interview clip with the Oxford physicist Chiara Marletto. Marletto is perhaps best known for her work with another Oxford physicist, David Deutsch, on constructor theory. The clip was posted under the title “Is the Many-Worlds Interpretation Correct?”
Journalists have a general rule for headlines called “Betteridge’s Law” that seems to apply in this case. This “law” holds that any headline asking a question should be answerable with the word no, since, if the answer were yes, the headline would have said as much. The law is offered partially in jest and it admits of exceptions, but as we shall see, if the many-worlds interpretation originated by Hugh Everett is understood realistically as it was intended to be, Betteridge hits the mark. The reasons why this is so are worth understanding, because they go much deeper than the usual objections, and they’re grounded definitively in a result known as Haag’s theorem, first proved by Rudolf Haag in 1955, a connection that the usual criticisms of Everettian quantum theory never mention.
In the Everettian interpretation, the quantum wavefunction never collapses but rather branches endlessly into parallel histories. Marletto makes her case in favor of this approach on the strength of one claimed virtue, universality. Quantum theory, she opines, “doesn’t come with a label saying here I cannot be applied.” In other words, if you take the formalism at face value and apply it to everything, starting with the subatomic realm and on up through observers like us to the universe as a whole, and you reject the artificial addition of collapse postulates or hidden variables of any kind that end or supplement the continuous dynamics, then you arrive at the many-worlds version of quantum mechanics as the pure essence of the theory. Observers get treated “democratically, all in the same way as qubits.” It is, she states, “the interpretation with the least amount of problems.” This praise is fainter than it sounds, rather like commending a ship as the one with the fewest catastrophic leaks.
Taking the Theory at Face Value
“Taking the theory at face value” is neither as simple nor as innocent as it sounds. The mathematics of quantum theory does not wear its ontology on its sleeve. The claim, based on its mathematics, that every branch of the wavefunction is a real material universe containing a real material copy of you simply does not follow. It is an extravagant metaphysical gloss on the formalism that postulates an innumerable proliferation of unobservable worlds to avoid the conclusion that measurement outcomes are in any way special.
Marletto herself is aware of the extravagance and recoils from it. When pressed by Kuhn on the issue of an endlessly dividing reality, she demurs, insisting that this “sci-fi” version of MWI is a misunderstanding and that no universes are multiplied, no particles are created, and no conservation laws are violated. Rather, “it’s simply that the state changes” through the entanglement of systems.
This response is fair game since it is the going position among sophisticated Everettians who, following David Wallace, treat worlds as emergent patterns within the one evolving quantum state, real in the way tigers and hurricanes are real emergent patterns in the world. But the analogy conceals the difficulty rather than resolving it. Tigers and hurricanes are patterns within an already actual world, whereas branches are supposed to be worlds. An emergent pattern inherits its actuality from the arena in which it emerges, and in the Everettian case the actuality of the branch is the very thing in question. If what MWI refers to as “branching” is really nothing more than an entanglement structure developing within a single quantum state, then the question of how a branch is actually a world constituting a concrete reality with you in it has not been answered; it has been dropped from the picture entirely. You can’t have it both ways. Either the branches are, in fact, substantial parallel realities and the ontological inflation is real, or they’re merely bookkeeping structures in a mathematical object and you’re keeping the label “many worlds” while jettisoning the worlds.
The important point to recognize is that you can retain everything beautiful about the formalism, most notably the unbroken unitary dynamics purged of ad hoc collapse mechanisms, by realizing that the universal wavefunction, so-called, is a complete map of possibilities rather than a mass-production mechanism for parallel realities. In fact, if you are a theist, it is natural to read it in terms of divine omniscience, that is, as exhaustive conceptual knowledge of every history that could be experienced, of which one history, ours, is actual. The mathematical elegance and parsimony the Everettians so desire are preserved in this reading, but the quantum multiverse is not.
No physics is being denied by construing the mathematics in this way, and it is worthwhile seeing just how much is being granted. It is clear that quantum superpositions are real. Macroscopic superpositions have been created in the laboratory with systems ranging from large organic molecules to superconducting rings carrying two opposed currents consisting of billions of electrons. Decoherence, furthermore, is a real physical process.
What needs attention here is what these phenomena actually show. Superpositions yield interference effects that no single component could produce by itself, which means the phenomenon cannot be dismissed as a mere indicator of epistemic ignorance. But it is also the case that in the experimental manipulation of superposed states we stand outside the superposition observing it, so in these cases, at least, its components are demonstrably real without being co-actual parallel realities in which different versions of ourselves observe different things. Nothing in the physics compels their promotion to concrete worlds elsewhere, either.
What we are seeing in such cases is something that materialism has no category to describe: possibilities that shape what happens without being actualized themselves. Examined through a quantum lens, physical objects cast modal shadows. The quantum wavefunction maps this possibility structure, decoherence traces its path into the single stable history of our experience, and the choice we are presented with is not whether the structure is real, but where it resides. The Everettian finds a place for it by actualizing all of it at a heavy price that we are about to evaluate; the theist houses it in the mind of God, and pays nothing but recognition of the One “in whom we live and move and have our being” (Acts 17:28).
The Problems That Went Unmentioned
Marletto offers her judgment that the MWI has “the least amount of problems” of any interpretation, then neglects to mention the problems it does have. They are not small. Let’s start with the branching process itself. Consistent with the mathematics of waves, the quantum state can be decomposed into a sum of component waves in infinitely many different ways, each way defining a set of “worlds” that is wholly dependent on the choice of its components. For example, decompose the wavefunction one way and Schrödinger’s cat bifurcates into a living-cat branch and a dead-cat branch; but decompose it differently in an equally legitimate mathematical way, and the branches are exotic superpositions that have no classical description at all. Mathematics is no guide here.
This, in its classic form, is the preferred basis problem — the very branching MWI supposes to be the deep structure of reality is, in fact, an arbitrary artifact of the choice of mathematical notation. Standard attempts to respond to this problem appeal to decoherence, which is the lightning-fast suppression of interference that results when quantum systems interact with their environments. The problem with this is that the division into branches provided by decoherence is only an approximate, for-all-practical-purposes, resolution, not a definitive one. Decoherence explains why some decompositions are dynamically privileged; it does not turn an approximate decomposition into an exact ontology, and worlds that exist only for all practical purposes are a strange and inadequate foundation for a fundamental ontology.
The situation regarding quantum probabilities is even worse. To illustrate this, suppose that a quantum event has two outcomes with probabilities of one-third and two-thirds. If MWI is correct, then both outcomes occur, so what sense can be made of the assertion that their probabilities are unequal? In fact, if everything that can happen quantum-mechanically does happen, in what sense is anything improbable at all?
The currently favored patch for this problem is due to David Deutsch and David Wallace. What they do is reinterpret the quantum probabilities as betting odds that a rational agent should adopt with respect to his or her branching future. This is a clever proposal, but there are compelling reasons to think it ultimately fails. As David Baker has argued, there is a vicious circularity in the repair. The branches must exist before the bets are placed, but these branches are created by decoherence, and the decoherence required has already helped itself to the probabilities the decision-theoretic analysis was supposed to supply.
Beyond this, as David Albert points out, the Deutsch-Wallace repair is answering the wrong question. The phenomenon that needs to be explained is the empirical frequencies of the outcomes we actually observe; it is not the phenomenon of how ideally rational agents with radically quixotic convictions about how the world is constituted would place their bets. Furthermore, we may add to this observation, with somewhat delicious irony, that since every outcome with nonzero amplitude occurs somewhere, the branching structure that MWI would impose on reality contains innumerable histories in which the statistics we observe do not conform to the Born rule. Since the Born rule is the quantum-mechanical algorithm that connects the wavefunction to experimental frequencies, any inhabitants of those histories, reasoning from the data available to them, would reject both the Born rule and quantum mechanics altogether.
The Everettian will reply that such histories carry minuscule Born weight. But in a one-world stochastic theory, anomalous histories are mere possibilities, at most one of which ever becomes actual; in the Everettian multiverse their occurrence is guaranteed. The reply therefore requires that epistemic significance attach to branch weight rather than branch existence, and establishing precisely that is the probability problem the Deutsch-Wallace program was supposed to solve. If Baker is right, it cannot solve it without circularity. Confirmation runs in a circle. Oops.
Finally, let’s not forget the matter of persons. Marletto’s suggestion that MWI treats observers “democratically as qubits” sounds enticingly egalitarian until one asks “What happens to me?” at a branching event. Aside from our earlier point that in the experimental manipulation of superposed states we stand outside the superposition observing it, so its components are not co-actual parallel realities in which different versions of ourselves observe different things, the fact remains that the first-person perspective each of us occupies is an unassailable datum before we do any physics at all. It is not the sort of thing that can be partitioned. Furthermore, if the branching structure contains continuers of you making incompatible decisions, so that choices that you make are unmade by you elsewhere, then moral responsibility, which requires you (and not quantum dynamics) to be the actualizing source of the choice that is made, is left without a basis.
The Elephant Theorem in the Room
While the difficulties just discussed are well known, if unmentioned by Marletto, the deepest problem is not widely known at all. The load-bearing inference MWI draws from universality encounters an obstruction inside physics itself, and the obstruction is a theorem, proved by Rudolf Haag in 1955 and then made even more precise by Hall and Wightman two years later. The theorem concerns the framework that undergirds the Standard Model of particle physics in which quantum theory is conjoined with special relativity to yield relativistic quantum field theory.
When we are dealing with finitely many degrees of freedom in ordinary quantum mechanics, the classic Stone-von Neumann theorem guarantees that, under standard regularity assumptions, the theory has essentially one Hilbert space representation in which it functions. Different formulations amount to nothing more than different notations that represent the same physics. When we move to quantum field theory (QFT), however, fields have infinitely many degrees of freedom — roughly, one for each point of space — and the guarantee of a unique representation collapses. There are infinitely many mathematically legitimate representations and they are inequivalent in the sense that the vacuum state from which the representation is built is not even a state in any other representation.
What Haag showed is that this is no mere mathematical curiosity; it is a catastrophe for the standard textbook formalism. The textbook scheme by which QFT depicts particles actually meeting and scattering — the “interaction picture” — supposes a single arena that contains both free and interacting fields, the two descriptions related by a unitary transformation. Haag’s theorem proves that there is no such arena. Taken at “face value,” that scheme describes fields in which nothing ever happens. Miraculously, the calculations work anyway, and in regulated and renormalized form they work magnificently, not least because the experiments we perform only ask local questions in bounded laboratories, a context that the global failure never touches.
The fact remains, however, that this success is purchased by quietly setting aside premises that cannot hold exactly in the interacting relativistic theory, and even after seventy years of effort, no nontrivial interacting QFT describing our four-dimensional world has ever been rigorously constructed. In fact, for the simplest candidate, approached through its standard lattice formulation, the mathematicians Aizenman and Duminil-Copin showed in 2021 that the exact interacting theory does not exist at all: take the continuum limit and the interaction completely disappears.
Now, consider the many-worlds picture: the Everettian asks us to be face-value realists about the “universal wavefunction,” the quantum state of life, the universe, and everything. In this picture, the state of everything must be a state of quantum fields. But Haag’s theorem tells us that no unique, dynamics-independent arena exists for there to be such a state.
What state are we even talking about, then, in the midst of uncountably many inequivalent representations? Abstract algebraic formulations can define states without first fixing a Hilbert space, but this concedes the point rather than evading it: on that approach the representation is recovered from a state on the algebra of observables, and the physically relevant state must itself be selected by the dynamics, so the ontology must be selected by physics that, for realistic interacting theories in four dimensions, no one has been able to construct.
Notice what’s going on here. We are encountering an analogue of the preferred basis problem one level down in a more virulent form. Earlier, within a single state space, what the branches were depended on an arbitrary decomposition of the state function, and Everettians could at least gesture, however ineffectively, at decoherence as a way of dealing with which decomposition to privilege. When we’re dealing with inequivalent representations, however, the arbitrariness concerns the very arena itself. All the candidate arenas are physically distinct rather than equivalent, and no decoherence exists to gesture at, since decoherence is only defined within a representation, and any interacting dynamics that might have selected a preferred representation is exactly what no one has been able to construct.
What Haag’s theorem tells us, therefore, is that the object about which many-worlds theorists claim to be face-value realists, so far as real-world physics is concerned, turns out to be a chimera. Contrary to Marletto’s assertion that quantum theory lacks a label delimiting its application, we see that it bears such a label after all — not one saying “Here quantum theory ceases to apply,” but one saying “Here the simple face-value reading ceases to be available.” Haag’s theorem wrote that label seventy years ago.
What Is Actually Universal
There is a lesson here that is far more interesting than a mere negative verdict on the many-worlds interpretation. We have granted that superpositions are real and have been observed macroscopically in the laboratory. We have granted that decoherence is genuinely suppressive of interference in producing the appearance of a stable classical-looking world. What we call a “physical object” by these lights thus turns out to be something much stranger than matter. It is a local structure of possibilities that have decohered into an appearance that is hyperrealistic — vivid enough to live in — but which has nothing substantial beneath it. This is just what QFT independently indicates. There are no fundamental particles in the classical sense of enduring material quanta — a chain of results culminating in a theorem of Greenberg and Licht shows that a field globally describable in Fock-particle terms can produce no scattering at all. To be describable as particles, in this global sense, is just to be free of anything happening at all (see also here). Alas, fields fare no better. The reality show in which we all participate has no material bearer.
What remains are the appearances, and all appearances are appearances to someone: an experiencer is a necessary condition for turning stabilized possibilities into perceived actualities. Decoherence, as far as it goes, explains why the world of our experience is orderly, but it does not explain why this history, rather than any other permitted by the wavefunction, is the one we actually experience. Nor can decoherence ground the regularity on which it depends. At bottom, nature behaves in ways we can count on, but it does so for no discernible physical reason.
This is no mere gap awaiting some clever equation to close it. If we follow the two explanatory demands — the first being the existence of experiencers, and the second being the existence of a ground for their experiences — to their logical and ontological conclusion, declining, with the tradition of sufficient reason, to treat this structure as a brute fact, we arrive at the inversion of materialism. The possibility structures of this world reside in a Mind, and the actual world of our experience is that Mind’s communication of one unified history to the finite minds who share it. The signature that reality bears is one of a world whose lawful order is grounded in mind rather than matter. Kuhn’s instinct in the interview that “maybe there’s something deeper” is exactly right. But what lies deeper is not more physics (and so on, ad infinitum); it is the Intelligence whose Gedankenwelt (thought-world) the mathematics has been describing all along.
To answer the video’s question — “Is the Many-Worlds Interpretation Correct?” — we find that Betteridge’s instincts were right. While an interpretation might survive many difficulties, it cannot survive the failure to provide the one thing it promises — and even after seventy years, “many worlds” has yet to produce even one.