Abstract
Quantum mechanics seems to portray nature as nonseparable, in the sense that it allows spatiotemporally separated entities to have states that cannot be fully specified without reference to each other. This is often said to implicate some form of “holism.” We aim to clarify what this means, and why this seems plausible. Our core idea is that the best explanation for nonseparability is a “common ground” explanation (modeled after common cause explanations), which casts nonseparable entities in a holistic light, as scattered reflections of a more unified underlying reality.
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Notes
Causal Inference is intended as a rational principle of default reasoning (likewise for all subsequent principles marked ‘Inference’), akin to the principle: “If a is a bird then a can fly.” Such principles need not be perfect, and may only hold “all else equal.” Rational principles of default reasoning are an important topic in their own right (Koons 2013), but they are not our topic. For present purposes all that matters is that Causal Inference, and our subsequent principles marked ‘Inference’ are good principles of scientific inference. Whether that is a matter of rationality, or merely pragmatic, or something else entirely, is a side issue.
For a detailed discussion of these mechanisms, see the Surgeon General’s report issued by the U.S. Department of Health and Human Services (2010).
As Hofer-Szabó et al. (1999, p. 378; c.f. Arntzenius 2010) write: “Reichenbach’s Common Cause Principle is the claim that if there is a correlation between two events A and B and a direct causal connection between the correlated events is excluded then there exists a common cause of the correlation...”
We follow Fine (1994, p. 271) in holding that nonempty sets are dependent on their members.
On this combinatorial way of thinking, basic objects are treated as independently varying elements. Their quantities are treated as dimensions along which they vary internally, and their relations are treated as degrees of freedom in the configurations they can assume. This yields a space of ways a world can be built, from a given collection of individuals displaying a fixed range of quantities and standing in a fixed range of relations. To yield a full notion of metaphysical possibility the approach then needs to be generalized to allow for variation in the individuals, quantities, and relations found in a world. What is metaphysically impossible, in this sense, is what is not constructively possible. Independent variation of objects with a common ground turns out to be metaphysically impossible for the same reason that independent variation of the facts about Jenann’s friend and about Jonathan’s friend is metaphysically impossible.
Wilson (2010, p. 601) suggests that two notions of distinctness have been conflated in the literature: nonidentity, and the capacity for either entity to exist without the other. We are suggesting a third sense of the notion, in grounding-theoretic terms. Our notion of distinctness may not be so far from what Hume himself (1978, p. 634) had in mind:
Whatever is distinct, is distinguishable; and whatever is distinguishable, is separable by the thought or imagination. All perceptions are distinct. They are, therefore, distinguishable and separable, and may be conceiv’d as separately existent, and may exist separately, without any contradiction or absurdity.
We allow that brute necessary connections are intelligible in a setting in which we have already formed clear and distinct ideas of objects a and b. For then we can conceive of absolute constraints on their covariation by imaginatively imposing a brute metaphysical restriction on their covariation on top of these preconceived objects. We leave open, however, whether it is possible to form clear and distinct ideas of objects that we cannot discriminate by their observable effects or otherwise preconceive, as is standard with the posits of physics. For a general discussion of the role of modality in an empiricist setting, see Ismael (manuscript-a).
There is a difficult background issue lurking, concerning when a given notion (such as our notion of “common source explanation”) should be regarded as generally unified, or perhaps unified just by analogy, or perhaps unified purely nominally. We think that common source explanation is generally unified, but strictly speaking we only require the claim that Source Inference is a default rational explanatory approach. For more on the systematic analogy between causation and grounding, see Schaffer (2016).
The mathematical objects that represent the reduced states of the multiple components do not in general uniquely determine the state of a whole system in an entangled state, but are instead compatible with multiple states of the whole.
Singlet is what one predicts if an excited hydrogen molecule with x-spin 0 decays into a pair of hydrogen atoms. By conservation of angular momentum the total x-spin of the pair of atoms must be 0. (Also, by conservation of momentum, the two atoms must head in opposite directions.) Such entangled (or non-factorizable) states are mathematically permitted in quantum mechanics, since not every vector in the Hilbert space can be written as the tensor product of arbitrary basis vectors. Indeed there is reason to think that entangled states are generic in quantum mechanics, and that any plurality of particles whatsoever will be in an entangled state.
There is an escape clause: strictly speaking the Kochen-Specker Theorem only applies to noncontextual hidden variable theories, where a noncontextual theory is one on which the value of a given observable is independent of which other observables happen to be measured along with it, or the disposition of the device used to measure it. One might still adopt a contextual hidden variable theory. But noncontextuality is a deep principle in quantum mechanics, connected to the standard principles of individuation for quantum observables. So while denying noncontextuality is a formal possibility, the option has found few defenders, and there is little in the way of a clear positive proposal for a contextual hidden variable theory. See Shimony (1984) and Cabello (1997) for some further discussion.
For a useful overview of Bell’s Theorem and surrounding issues, see Shimony (2009).
In this vein, Cramer (1986) develops a “transactional” interpretation on which the measurement outcome sends a backwards propagating absorber wave (“the confirmation wave”), which interacts with a forward propagating emission wave (“the offer wave”) at the start of the experiment, to form a standing wave between the start of the experiment and the site of measurement. For further discussion of the transactional interpretation see Wharton (2010), Kastner (2013), and Wharton and Price (2013).
See Maudlin (2002) for a detailed discussion of the interaction between quantum nonlocality and relativity.
In this vein d’Espagnat (1979, p. 181) concludes: “Most particles or aggregates of particles that are ordinarily regarded as separate objects have interacted at some time in the past with other objects. The violation of separability seems to imply that in some sense all these objects con-stitute an indivisible whole.” Likewise Maudlin (1998, p. 56) says: “The physical state of a complex whole cannot always be reduced to those of its parts, or to those of its parts together with their spatiotemporal relations... The result of the most intensive scientific investigations in history is a theory that contains an ineliminable holism.” And to add just one more of the many examples which could be given, Gisin and Aspect (2014, p. 43; in a section entitled “Quantum Holism”) write: “Roughly speaking, the strange theory of quantum physics tells us that it is possible and even commonplace for two widely separated objects in space to form in reality a single entity! And that’s entanglement. If we then prod one of the two parts, both will quiver.”
In what follows we move back and forth between object talk (Alice and Bob) and event talk (Alice-up and Bob-down). Our underlying view is that the events are not distinct precisely because the objects they involve are not distinct. Just as the event of Jenann’s friend riding a horse is not distinct from the event of Jonathan’s friend riding a horse if there is a single common friend, so the event of Alice-up is not distinct form the event of Bob-down if Alice and Bob themselves spring from a common ground.
We expect replacement theories to preserve the core mathematical structure and empirical successes of the theories they replace, and entanglement looks to have both features. See Ruetsche (2013) for a deeper, albeit more equivocal, assessment of quantum field theories.
As noted in Sect. 3.1.2, there is still the option of a nonlocal retrocausal common cause story, but we are operating under the working assumption that this is not a preferred option. That said we do acknowledge that the retrocausal approach has at the very least an aspect of plausibility, precisely for providing a sort of common source explanation for the correlated randomness of entangled systems. So we see Source Inference as helping to account for some of the plausibility that the retrocausal account can boast.
Our thanks to Ned Hall for helping us clarify these issues.
One alternative is to add fundamental entanglement relations to the ontology (Teller 1986; see Morganti 2009, pp. 276–280; Calosi 2014, pp. 922–926) for specific application of this idea to the inference under discussion in the main text). On this alternative approach the coordinated randomness found in Alice’s and Bob’s behaviors is to be explained by positing a new fundamental relation alongside their spatial relations. See Sect. 4.3 for further discussion.
The idea of the whole being prior to its parts is reminiscent of the classical monistic idea in metaphysics. In this vein Proclus (1987, p. 79) writes: “[T]he monad is everywhere prior to the plurality... In the case of bodies, the whole that precedes the parts is the whole that embraces all separate beings in the cosmos.” See Schaffer (2010a), Appendix, (2010b) for more historical discussion.
More precisely, the partial trace operation allows one to recover the density operator for any partial subsystem A from the whole system AB by tracing out B. Wallace and Timpson (2010, p. 710) are right that we need a decomposition of the universe into parts like A and like B to make sense of this, but it does not follow that we need to assign any density operator to A or to B in the fundamental ontology. Once we have a universe replete with parts, the only fundamental density operator needed is the universal one. (We thank David Wallace for discussion of these points.)
For a system of n particles, the associated configuration space has 3n dimensions. Imagine that one has a system of two particles in a three-dimensional space, where one is only interested in positions at times. Then one needs to specify, for each time, six pieces of information: the x-, y-, and z-coordinates of particle1, and the x-, y-, and z-coordinates of particle2. One can equally specify six pieces of information in terms of a point in six-dimensional space, where the location of the point in the first three dimensions represents the x-, y-, and z-coordinates of particle1, and the location of the point in the second three dimensions represents the x-, y-, and z-coordinates of particle2. So explained, configuration space might seem like a (perhaps perverse) way of mathematically representing the action in manifest space. But in quantum mechanics, configuration space has a life of its own. The wave function is a complex amplitude field living in configuration space. Schrödinger’s equation describes the temporal evolution of the wave function. To the extent that Schrödinger’s equation gives the dynamics, there is then a “face value” reading of the dynamics as describing the temporal evolution of a field in configuration space. There is thus a “leave your preconceptions at the door” way of thinking about quantum mechanics—which the wave function realist adopts—on which the fundamental action is in configuration space.
We thank Ned Hall for raising this line of questioning.
One option would be to treat causal connections pragmatically, as strategic pathways to bringing about ends for creatures that can only intervene on the world at the macroscopic level. The approximate, emergent separability of the world at the macroscopic level would then be enough to support Causal Inference as a good principle for such creatures. See Ismael (2013) for further exploration of this view.
Maudlin (2014, pp. 11–12) says: “Einstein offers two possible ways to reject the conclusion of his argument: accept telepathy or reject the claim that systems spatially separated from one another even have ‘independent real situations’. Unfortunately, Einstein never discusses this second option in detail.” Maudlin also says that it is obscure what this second option would be, or how it would impact Einstein’s argument. We are attempting to clarify exactly this. (Maudlin then supposes that the theory might posit no local beables whatsoever; we are suggesting that the theory may posit no local fundamental beables but may still posit local derivative beables, and thereby make sense of laboratory experiments.)
Indeed Einstein’s Inference clashes with many historical philosophical ideas, ranging from Aristotle’s idea that the heart and the lungs are both grounded in the common organism, to the classical monistic idea that all separate parts of the cosmos are grounded in the encompassing whole. We are not saying that these ideas are correct, but only that they are coherent and not obviously false.
For a defense of something more sophisticated but in the vicinity of Manifest Principle, based on the idea that a physics which would explain the manifest world needs at least a foothold of “primitive ontology” in manifest space, see Allori (2013). Though for a development of the alternative picture, based on the idea that the fundamental space plays an individuative role vis-à-vis the fundamental entities, see Ismael (manuscript-b).
Thanks to Heather Demarest, David Glick, Ned Hall, Richard Healey, Michael Townsen Hicks, Carla Merino-Rajme, George Musser, David Wallace, the participants at the White Stallion Ranch Metaphysics Workshop, and two anonymous Synthese referees.
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Ismael, J., Schaffer, J. Quantum holism: nonseparability as common ground. Synthese 197, 4131–4160 (2020). https://doi.org/10.1007/s11229-016-1201-2
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DOI: https://doi.org/10.1007/s11229-016-1201-2