How the Many Worlds Interpretation Brings Common Sense to Paradoxical Quantum Experiments

How the Many Worlds Interpretation brings Common Sense to Paradoxical Quantum Experiments Kelvin J. McQueen and Lev Vaidman The many worlds interpretation of quantum mechanics (MWI) states that the world we live in is just one among many parallel worlds. It is widely believed that because of this commitment to parallel worlds, the MWI violates common sense. Some go so far as to reject the MWI on this basis. This is despite its myriad of advantages to physics (e.g. consistency with relativity theory, mathematical simplicity, realism, determinism, etc.). Here, we make the case that common sense in fact favors the MWI. We argue that causal explanations are commonsensical only when they are local causal explanations. We present several quantum mechanical experiments that seem to exhibit nonlocal “action at a distance”. Under the assumption that only one world exists, these experiments seem immune to local causal explanation. However, we show that the MWI, by taking all worlds together, can provide local causal explanations of the experiments. The MWI therefore restores common sense to physical explanation. 1. Introduction The purpose of explanation is to help us understand why things happen as they do. Typically, one explains an event by citing the causes of that event. For example, to explain why the window broke, one might cite the throwing of a stone. A particularly compelling and natural type of causal explanation is local causal explanation. In a local causal explanation there is spatiotemporal continuity between the cause and the explained effect. For example, the thrown stone explains the broken window in part because the stone traces out a continuous trajectory from the stone-thrower’s hand to the window. In opposition to local explanations are nonlocal explanations. Nonlocal explanations involve “action at a distance”. Nonlocal explanations are rare in everyday life. Familiar cases are purported cases of psychokinesis, e.g., when people claim to bend spoons with their minds. If one explains the bending of a spoon in terms of an individual’s mental effort, then one is offering a nonlocal explanation, since there is no spatiotemporally continuous series of causes and effects connecting the mental effort and the spoon bending. 1 Common sense rejects such nonlocal explanations and presumes a hidden local cause of the spoon bending. And there is a good reason for this. A nonlocal explanation of X in terms of Y only tells us that X happens given Y. But an explanation should enable us to understand why X happens given Y. This is what local causal explanations offer. We understand why the window broke given the stone-throw because we understand the spatiotemporal continuity between the cause and the effect. Thus, if any type of explanation deserves to be called “common sense explanation”, it is local causal explanation. The point is a general one and is not specific to macroscopic objects. Whether we scale up to planets and galaxies or scale down to elementary particles, a causal explanation that leaves behind “gaps” in spacetime will in turn leave behind gaps in our understanding. Presumably this is why Einstein (1935) famously referred to action at a distance as “spooky”. In philosophy, there is an approach known as the common sense tradition. This approach takes various common sense beliefs as data for philosophical reflection and rejects those philosophical views that conflict with them (Lemos, ch.10, this edition). Here, we employ a similar approach in the context of physics. In particular, we argue that locality is a necessary condition for causal explanations to be commonsensical. We then take it as a requirement on an adequate physical theory that it be able to offer local causal explanations of all experimental outcomes. In the next section, we discuss how the demand for local causal explanation shaped classical physics. In section 3, we introduce quantum physics in the context of a simple experiment, which, while strange, can be explained locally. We then specify three refined common sense principles of locality. These principles are satisfied by classical physics and by the simple quantum experiment. However, in sections 4 and 5, we present several quantum experiments that do seem to violate the principles and therefore defy common sense. Finally, in section 6, we show that common sense can be restored to quantum theory if we adopt the many worlds interpretation (MWI). We show how the MWI is capable of giving local causal explanations of all these experiments. We conclude by discussing the significance of our results to debates over the interpretation of quantum mechanics. In particular, many reject the MWI by an appeal to common sense. As one philosopher puts it, “The most obvious disadvantage is that its burgeoning world of duplicate histories seem repugnant to common sense.” (Papineau 1995, 239). We will argue that our results suggest the contrary, that the advantages to common sense that the MWI provides outweigh its disadvantages. 2 2. Common sense explanation in classical physics The philosopher of science W.V.O. Quine (1957, 229) once said, “Science is not a substitute for common sense but an extension of it”. Accordingly, physicists seek local causal explanations of the motions of physical objects. This is clear in classical physics. For example, in Newtonian mechanics a body’s motion in a given region and time is explained by a force applied at that region and time. The exception is Newton’s law of gravitation. According to this law, a planet’s motion at a time is explained by a force applied by a distant planet at that time. However, Newton himself described this action at a distance as an “absurdity” and proclaimed the source of gravitational forces to be “hitherto unknown”. In fact, Newton went so far as to say: “Tis inconceivable that inanimate brute matter should (without the mediation of something else which is not material) operate upon and affect other matter without mutual contact. […] [T]hat one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it.” (Newton 2004, 102–3) Newton’s appeal to “a competent faculty of thinking” is an appeal to common sense. Newton is then proclaiming that his theory of gravity cannot offer any commonsensical explanation of gravitational motion, since it cannot offer a local causal explanation. (For recent debate over Newton’s views on action at a distance see Ducheyne (2014).) Later, Newton’s Law was understood in local terms by adding the concept of a gravitational field created by massive bodies. Classical (i.e. non-quantum) physics, then, describes point particles (“point-masses”) and fields spread out in spacetime. The point-masses create the fields which propagate with finite velocity. The motions of the point-masses are then affected locally by the fields of other point-masses. This physical ontology, together with Newton’s laws, Maxwell’s electromagnetic theory, and relativity theory, provides local explanations of many things we see around us. The common sense picture of classical physics ultimately consists in the motions of particles on continuous trajectories and the continuous propagation of waves with multiple trajectories, which includes the local phenomena of (constructive and destructive) interference. The motion of particles and the propagation of waves provide (common sense) causal connections. This includes continuous traces that moving particles and propagating waves leave behind in their local environments. The continuous propagation of waves and their local causal effects are illustrated by the Mach-Zehnder interferometer (MZI) (Zehnder 1891, and Mach 1892), see Fig.1. The electromagnetic wave (i.e. the photon) splits at the beamsplitter, passes through two arms of the interferometer and reunites at the second beamsplitter. The reuniting of the waves creates interference, which leads to observable effects. When the interferometer is properly 3 tuned, only detector D2 detects light. This is due to constructive interference towards D2 and destructive interference towards D1. If the distance of one path is lengthened by half of the wavelength of the electromagnetic wave, then only detector D1 receives light. Formally, classical physics places no constraints on interactions except that they be local. It is assumed that these local interactions never vanish completely and that the electromagnetic wave leaves some trace, e.g. heating of the air in the arms of the interferometer. Any such trace can in principle be detected, so the interferometer tuned as in Fig. 1a leaves an observable trace of the same form, see Fig. 1b. Figure 1: Mach-Zehnder interferometer (MZI). A beam of light is sent towards a beamsplitter, resulting in two beams of light. Each beam is then deflected towards a second beamsplitter, and then detected by one or both of the detectors. a) The interferometer is tuned so that the light comes only to detector D2. b) The trace left by the light in the interferometer tuned as in a). 3. Common sense explanation in quantum physics In 1986 Grangier et al. showed that the MZI exhibits interference when we send single photons through the interferometer. MZI interference is also routinely observed with neutrons (Rauch 1974). But even before that, the double slit experiment with attenuated light, where single photons would one-by-one build up an interference pattern on the detection screen, led to the radical picture of quantum theory: In some sense particles are waves! Let us first discuss a quantum particle and a single beamsplitter, Fig. 2. We observe that sometimes the particle passes undisturbed and sometimes it bounces from the beamsplitter 4 as if the beamsplitter was a mirror.

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