Is the “Many Worlds” Interpretation of Quantum Mechanics Metaphysics Instead of Physics?

Introduction

The Many Worlds (MW) interpretation of quantum mechanics (QM) is an attempt to make sense of the fundamental postulates of QM. However, many consider MW to be metaphysics rather than physics and therefore disregard it as a serious theory of reality. This can have impacts such as a lack of funding towards further developing MW. There are two main obstacles barring MW from being physics: the first is MW’s compatibility with the physics, namely the Born rule, and the second is its nature as an interpretation. As well as demonstrating the ways in which MW is compatible with the physics, I will delve into these two issues to explore whether they really are obstacles at all, and so whether MW can be considered physics. I will conclude that due to it possessing aspects of both physics and metaphysics, and aspects that cannot be clearly demarcated into either camp, MW lies in the grey area between physics and metaphysics, and therefore I disagree with the claim that MW is metaphysics and not physics.

MW as a Physical Theory

QM has revolutionized the field of physics; historically seen as intrinsically probabilistic, it has incredible p redictive powers and describes the fundamental behaviour of the constituent particles of our reality. However, the standard formulation of QM faces many issues, one of which is that there is no explanation for why transition from its deterministic behaviour to indeterministic behaviour happens, a paradox known as the measurement problem. Another is that it gives no explanation for what exists in reality; it has no ontology . The consequence of this is that we do not have a full accepted theory of QM, but instead a “quantum recipe” (Maudlin, 2019, p.36). Attempts have been made at formulating a full theory of QM, seeking to provide a clearer interpretation than the Copenhagen interpretation as well as solving the measurement problem, which is why MW was developed. In this section I will first give a brief explanation of the background physics that MW depends on, before explaining what MW is. This is to demonstrate the ways in which MW uses the quantum recipe and thus can be considered a physical theory.

A state vector in QM is a vector that r epresents the state a quantum system is in, and which contains all the possible information about the system. A wavefunction is the state vector projected onto a particular basis, such as the position representation, and therefore exists in a 3N-dimensional space called configuration space. Due to the linearity of the Schrödinger equation, the equation which governs the dynamics of the wavefunction, a wavefunction can be made up of superpositions of different eigenstates, or possible states it can be in upon measurement. When a ‘measurement’ is made on a system, its wavefunction ‘collapses’ into an eigenstate of the observable being measured, and the superposition of different eigenstates disappears.

First developed by Everett (1957) as a theory of relative states, MW states that upon measurement, the wavefunction continues to evolve deterministically instead of collapsing, and despite the superposition of eigenstates disappearing each eigenstate still exists in its own non-interfering branch of reality. This means that every possible outcome for a quantum measurement actually exists, contrary to the standard picture in which only one outcome exists in one reality. The way in which MW reaches this conclusion is by first assuming that the wavefunction in QM is real and that the wavefunction together with the Schrödinger equation are complete; no other equations are needed to describe reality (Maudlin, 2019). In effect, MW uses and builds from the quantum recipe without adding any new physics to it, as the wavefunction is the ontology of the theory. This means that MW is consistent with aspects of QM which can be taken to show that MW is a physical theory; for a theory to make use of the physics to such an extent and depend on it so heavily demonstrates the elements of the theory that are in line with what many consider a physical theory to be.

Because the wavefunction is taken to be real, upon measurement when we see all but one of the eigenstates disappear, it makes sense to pose the question: where do they go? Since the remaining eigenstate gives us a very real state that the quantum system is in and which represents our reality, the other eigenstates must also give equally real states for some quantum systems. If they are real, they cannot simply disappear. Therefore, there must be some other worlds in which these other eigenstates really do represent the state of the quantum system, giving rise to the general idea behind MW theory: that every eigenstate for a wavefunction is really instantiated in some reality once the wavefunction has effectively collapsed due to decoherence. Each of these different realities are the different ‘worlds’ in MW. This idea arguably follows from the physics, and I agree that it is compelling, but only if you take the wavefunction to be real.

Decoherence as an explanation for how the worlds branch results in MW being a mathematically consistent theory. Decoherence is a process by which the constituent parts of the wavefunction become dynamically independent in configuration space, meaning that they no longer interact. Environment induced decoherence happens when the environment a quantum system is in interacts with the quantum system, becoming entangled with it and resulting in an irreversible loss of information from it. This loss of coherence from the quantum system gives an effective wavefunction collapse, resulting in the system transforming into a classical system while the wavefunction continues to evolve deterministically. The dynamical independence means that all parts aside from the one measured can be disregarded for the present system as they will typically no longer further affect it. This mathematically explains how there can be no interference between the different branches (Saunders, 2010) which is important because we do not see any effects in our world due to other worlds. It also explains why the branches split to begin with. The mathematical consistency of MW makes it even more compelling as a theory of reality, and further demonstrates how compatible MW is with the quantum recipe, further demonstrating how MW can be a physical theory.

Probability

There are many difficulties associated with MW, one of which is the issue MW has with probability. This is an important part of MW because at its core MW is a deterministic theory, and so because it deviates drastically from our standard understanding of what probability is, probability in MW needs explaining (Saunders, 2021). If MW does not satisfactorily explain probability, then it cannot be consistent with a physics in which probability is central, and therefore MW may be relegated to the status of a metaphysical theory. Furthermore, as Carroll states, “part of science is predicting what will be observed, even if only probabilistically” (Carroll, 2019, p.142), which suggests that for MW to be science it must be able to assign the correct probability values to possible outcomes. The probability predictions MW makes do not align with experimental outcomes or the Born rule, which means some people do not consider MW to be physics.

Our standard understanding of probability, which is based on the experiential belief of there only existing one world, relies on the notion of frequency of outcomes dictating their probability. For a statistical distribution of outcomes for an event, the most likely outcome is the one which happens the greatest number of times. For an electron in a superposition of spin up and spin down, a 0.6 probability of obtaining spin up means that spin up is obtained 60% of the time for any electron prepared in an identical initial state.

The reason probability does not seem to exist in MW is because, upon a branching of the wavefunction, every possible outcome is really instantiated, meaning that there is no probability for each one happening as they all really do. For the example outlined above, this means that the electron has spin up in one world and spin down in another; both outcomes actually happen. Additionally, the probabilities of each outcome you could get in each world should be equal, or symmetric, because each branch is equally real, so there seems to be no way to talk about asymmetric probabilities. This would mean that for the same case as outlined above, since both spin up and spin down have the same frequency of occurrence, they therefore have the same probability and so do not follow the Born rule, which is not what we would observe experimentally.

Wallace (2003) divides the problem of probability in MW into two aspects: the incoherence problem and the quantitative problem. The former is the problem around why talking in terms of probability is coherent in a reality in which all possible outcomes come to fruition, while the latter centres around why probability conforms to the Born rule, the probability postulate of the quantum recipe, instead of some other rule, such as having equal probabilities for each branch (Wallace, 2003).

Carroll outlines a possible solution to the incoherence problem: the idea of self-locating uncertainty (Carroll, 2019). The idea is that because it does not make sense to talk about which of the different possible worlds you will end up in - which one will be the ‘real you’ - since they all lay equal claim to being you, we must instead talk about probability for branches that have already branched. When decoherence and subsequent branching happens, an observer does not know which world they have branched into until they check, for example by checking a measurement apparatus to see which result has been obtained. This means that there is a short instant between the branching happening and the observer finding out which branch they are on. In this short interval, the observer has an uncertainty about which branch they are on. This generally agreed upon concept is what lets us talk about probability in MW. From this it is possible to talk about future probabilities, because we know your future self is also going to have uncertainty about which branch they are on for future branching (Carroll, 2019). A solution to the incoherence problem such as the self-locating uncertainty explanation is a move in the direction of empiricism for MW, because the quantum recipe is inherently probabilistic and so being able to talk about probability is important.

However, the quantitative problem remains and is a much tougher problem to solve. A possible solution relies on decision theory to derive the Born rule. This explanation for probability states that a rational agent in MW would act as if there were standard probabilities because of the value, or “expected utility” (Maudlin, 2019, p.182), they place on certain outcomes. This value would reflect the same weightings that the Born rule predicts , because the value comes from the squared amplitudes of each possible branch. The Everettian agent would act to maximise the utility of their choices, and therefore they would act in the same way as a standard agent.

The clearest issue with the decision theoretic approach is that the Everettian agent knows that every outcome will happen in some world, and so some future version of themselves will obtain each outcome. In that case, it still is not rational to value one outcome over the other. In a single world theory, an agent cares about the outcome because there will be only one successor, only one version of themselves, and so they want the preferable outcome for that one successor (Maudlin, 2019). There is no such justification for the Everettian agent. Furthermore, it is not clear why an Everettian agent would want to act in the same way or why they would think that MW would have no impact on how they regard choices and decision-making (Maudlin, 2019). This is an unresolved ambiguity in the decision theoretic approach.

Overall, the decision theoretic approach contains many ambiguities and is lacking in conceptual clarity. It is an incredibly metaphysical approach to understanding probability, as it offers a metaphysically different account of reality. This means that were one to adopt it, MW would consequently be a very metaphysical theory. I do not think that the decision theoretic approach is a satisfactory solution to the quantitative problem, due to its vague and confusing nature. Because of these unresolved and metaphysical in nature issues with probability, MW can be considered a metaphysical theory . Furthermore, because there is currently no satisfactory way for MW to be consistent with the Born rule, it contains less physics than the quantum recipe.

However, MW having perhaps less physics than the quantum recipe and having these metaphysical issues does not automatically bar it from being physics overall, as containing less physics could just mean that it is a worse physical theory than others. Just because MW has enormous metaphysical implications for how we understand probability does not mean that MW itself must be only a metaphysical theory. Although the probability problem in MW contributes greatly towards MW being seen as a more metaphysical theory, its physical aspects should not be automatically discounted.

Nature as an Interpretation

Whether MW is physics does not solely rely on how compatible it is with the physics. It is also dependent on whether you consider an interpretation to be physics or not.

Further difficulties with MW being accepted as a physical theory include the objection that MW is only an interpretation of the quantum recipe and does not add any new physics to it. Everett himself said that his relative state theory was more of a “metatheory to a theory ” (Everett, 1957, p.454), which can be likened to the idea of a metaphysical theory to a physical one. Because some physicists do not think we need an interpretation of QM, and that interpretations are metaphysics not physics, MW would therefore be considered metaphysics rather than physics.

Without an interpretation, however, the quantum recipe is not clearly explaining what really exists and what is happening in reality. It is not clear how something can be a physical theory if it does not attempt to tell us about the fundamentals of reality. Some hold that physics only predicts what will happen instead of explaining what exists in the universe and how exactly it works, a view I take to be overly simplistic and narrow. Many physicists do have the motivation of seeking to uncover universal truths, such as motivations behind finding a theory of everything. This is a take on physics that I find to be more satisfactory, because predictions for what will happen are a product of theories that explain reality and how it works. As Maudlin states, a physical theory needs to properly answer the question of “what there is” (Maudlin, 2019, p.xi), meaning that an interpretation such as MW which seeks to explain the nature of reality shares aspects with a physical theory, and therefore cannot be entirely excluded from being a physical theory on the basis of it being an interpretation.

Discussion and Conclusion

Offering theories about the nature of reality and which ontologies to assume, even when in relation to scientific theories, is something that can be attributed to metaphysics, as this is what metaphysics is concerned with. However, it is also the case that physics offers explanations for what exists in reality , and this is a common motivation for physicists. A typical view is that an explanation for reality which contains within it equations is more of a physical theory, whereas an explanation for reality which does not have any equations is more of a metaphysical theory. What then of MW, which does not itself contain any equations, but is still dependent upon them? It is not clear whether its nature as an interpretation is physics or metaphysics.

This question is assuming that we need to demarcate MW into either physics or metaphysics. Demarcation means setting sharp boundaries around what something is, and for something to be demarcated means choosing one strict category for that thing to go into. However, I have demonstrated throughout this essay that the aspects within MW are not so easily categorised; overall, it is difficult from the arguments outlined to conclusively maintain that MW is either physics or metaphysics. Moreover, true demarcation is not possible – though this is an issue beyond the scope of this essay.

Neither is it clear why we should define such strict categories and demarcate such theories to begin with. There seems to be no objective difference between physics and metaphysics in the sense that these categories only exist for our own practical purposes, so attempting to outline the differences in such a strict manner seems to be futile and pointless.

There are many more ways in which MW can be argued to be physics or metaphysics, such as discussions of MW solving the measurement problem, the metaphysics of personal identity in MW, and empirical falsifiability. There are valid reasons for why MW can be considered physics, as well as there being valid reasons for why it can be considered metaphysics. Neither its physical nor metaphysical aspects should be discounted in the pursuit of categorising it as either physics or metaphysics, because in reality it does not have to be exclusively one or the other.

I have explored in this essay how putting strict boundaries between physics and metaphysics does not always hold up and is not a coherent view. Demarcation is neither necessary nor possible; a theory such as MW does not need to fit neatly into either physics or metaphysics, nor can it. I therefore advocate for a more continuous approach to the boundary between physics and metaphysics, if not for all topics within them then at least for the case of MW. A potential idea is that physics and metaphysics lie on opposite ends of a spectrum. While MW may lie closer to being metaphysics, it still has elements of physics and is not completely at the metaphysics end of the spectrum.

References

Carroll, S.M. 2019. Something deeply hidden: quantum worlds and the emergence of spacetime. London: Oneworld.

Everett, H. 1957. ‘Relative State’ Formulation of Quantum Mechanics. Reviews of Modern Physics. 29(3), pp.454–462.

Maudlin, T. 2019. Philosophy of physics: quantum theory. Princeton, New Jersey: Princeton University Press.

Saunders, S. 2010. Many Worlds: an introduction.

Saunders, S. 2021. The Everett Interpretation: Probability.

Wallace, D. 2003. Everettian Rationality: defending Deutsch’s approach to probability in the Everett interpretation.