Most literature on analogue experiments has focused on their confirmatory power, assessing the question: Can analogue experiments, otherwise known as “analogue simulations,” provide confirmation for claims about their target systems? Analogue Quantum Simulation: A New Instrument for Scientific Understanding breaks new ground, providing the first detailed analysis of the relationship between analogue experiments and understanding.Footnote 1
Focusing on analogue quantum simulations in particular, it draws a distinction between two species of investigation. Analogue quantum computations aim to learn about formal features of an abstract model of a target system, whereas analogue quantum emulations aim to learn about features of a physical target system.
The authors adopt a “modified simple view of understanding,” inspired by Reutlinger et al. (Reference Reutlinger, Hangleiter and Hartmann2018), and suggest that there are two varieties of understanding that an analogue quantum simulation can provide about its target. How-understanding arises if three conditions are satisfied:
1. The explanation condition: The simulation provides an explanation of a target phenomenon.
2. The veridicality condition: That explanation is true.
3. The grasping condition: The simulation helps the experimenter to grasp the explanation.
According to the book, however, this is not the only useful form of understanding that analogue quantum simulations can provide. Both computations and emulations can provide weaker how-possibly understanding even if the veridicality condition is not known to be satisfied.
The authors demonstrate these claims by appeal to four experimental case studies: analogue quantum computation of many-body localization (MBL), analogue quantum computation of the Higgs mechanism in two dimensions, analogue quantum emulation of environment-assisted quantum transport (ENAQT), and analogue quantum emulation of Hawking radiation in dispersive optical media.
Along the way, they map the relations between the source and target systems in terms of a hierarchy of system models and simulation models. The source system model is the most quantitatively accurate available theoretical description of the source system; it is typically highly complex and involves a low degree of idealization. The target system model, similarly, is the best available theoretical description of the target system. The source simulation model and target simulation model, by contrast, are highly idealized and simplified models of both systems. They exist in formal relation to each other and to their respective system models—typically through “limiting relations in specific parameter regimes” (Hangleiter et al. Reference Hangleiter, Corolan and Thébault2022, 18).
Three distinctions are therefore key to the view advanced by this book: between analogue quantum computation and analogue quantum emulation, between how-possibly understanding and how-understanding, and between the simulation model (of a source or target system) and the system model (of the same source or target).
One of the book’s main contributions is its clear articulation of these distinctions, which have not before been acknowledged in the analogue simulation literature.
The distinction between analogue quantum computation and emulation highlights the variety of useful roles that analogue simulations can play; they are not only useful when they teach us about a concrete physical target system, they can also fruitfully teach us about abstract theoretical models. The distinction between how-possibly and how-understanding, reinforced by appeal to practical examples, cements the value of analogue simulations that are only able to teach us about how a target system might behave.
The authors write that “[s]peaking of the source or target model is misleading as there typically will in practice be several descriptions of the system at hand that play different roles in the simulation process” (ibid., 16). By separating the source and target simulation models from their respective system models, and elucidating the relations between each, Hangleiter et al. show both why it is misleading to speak of a single source or target model, and how we can more clearly approach the frameworks at play. Finally, by focusing on understanding rather than confirmation throughout, they continually demonstrate that confirmation is not the only outcome that we can or should desire to achieve in analogue simulation.
These developments are a clear step forward from the existing literature.Footnote 2 Given the wide range of analogue platforms available—as demonstrated by Hangleiter et al. in their case studies, and by Jacquet et al. (Reference Jacquet, Weinfurtner and König2020) in the context of analogue gravity—an open-minded assessment of analogue simulation and its many possible roles is both timely and significant.
The authors argue, in particular, that analogue quantum computations are uniquely well posed to provide explanations for target phenomena, for two reasons. First, analogue computations can allow the experimenter to dynamically observe the onset of a phenomenon: “[O]ne not only obtains knowledge of the equilibrium properties of a system (the solution of the analogue computation) but also how those properties came about dynamically.” Second, such computations can provide the possibility to explore wide parameter regimes, and thereby explore a wide variety of counterfactual scenarios (Hangleiter et al. Reference Hangleiter, Corolan and Thébault2022, 89).
These points fit well with one of the core claims of Field (Reference Field2021b): that the exploratory power of analogue experiments has been undervalued. The book could in fact be seen to strengthen that claim, by connecting it to Woodward’s well-established counterfactual account of explanation.
Elsewhere, Hangleiter et al. emphasize that the veridicality condition is the most difficult to satisfy in both analogue quantum computation and emulation. This is where they come closest to engaging with the controversy over analogue simulations’ confirmatory power. They establish sufficient conditions for analogue computations and emulations to satisfy the veridicality condition in section 8.5.
One of these conditions, for analogue emulations, is that “the target simulation model is validated as an empirically adequate model of the target system across the relevant parameter regime” (Hangleiter et al. Reference Hangleiter, Corolan and Thébault2022, 124). It is worth noting that we must then be interested in learning about something from our emulation over and above what is already captured by what we label the “simulation models” of the two systems, otherwise we risk running into the circularity concern raised by Crowther et al. (Reference Crowther, Linnemann and Wüthrich2019).
That implicit requirement is certainly possible to satisfy. For example, we might be interested in finding out how or why a phenomenon appears in the target system, when the target simulation model predicts that it should arise but does not explain how it should arise dynamically. Or, if we are interested simply in confirming the presence of a target phenomenon, we must be able to adopt simulation models of the two systems that do not include the feature whose presence we are trying to confirm.
Relatedly, for analogue gravity emulations that avoid circularity by invoking a universality claim (see Dardashti et al. [Reference Dardashti, Hartmann, Thébault and Winsberg2019]), the authors suggest that “doubt may be mitigated by performing multiple independent emulations on platforms of different material constitution to gain trust in the empirical adequacy of the universality claim…. This suggests a general strategy for supporting the veridicality of emulations by building multiple distinct types of source system” (Hangleiter et al. Reference Hangleiter, Corolan and Thébault2022, 107). It is worth noting that the value of P (M T |X) − P (M T | ∼ X)—which captures the relevance of the universality claim to the target system—is a limiting factor for this strategy.Footnote 3
An interesting open question is whether understanding should be seen as the chief contribution of all analogue emulations. Hangleiter et al. (Reference Hangleiter, Corolan and Thébault2022, 91) write, for example, that “the key scientific virtue of analogue quantum emulation is not tied to the superior explanatory power over pure model-based explanations, but rather to us being able to directly observe how the explanandum follows from the explanans.”
However, it is possible to imagine situations in which analogue emulations do not allow us to make that kind of observation, and nevertheless should be considered highly successful. Imagine, for example, that we have a good theoretical explanation for why, and how, phenomenon X should dynamically follow from phenomenon Y. We are able to observe that our target system displays phenomenon Y, but we are in principle unable to observe and verify whether it displays phenomenon X. Imagine, furthermore, that we set up an analogue emulation that does successfully display both X and Y, but not the mechanism by which they are related.
The chief contribution of such an emulation is surely that it shows phenomenon X, which would otherwise be left unobserved—not that it deepens our understanding of how X comes about as a result of Y. In other words, the chief contribution of this kind of emulation would sit closer to the confirmatory goals discussed in the earlier literature on analogue simulation.
This in fact only serves to strengthen the authors’ closing remark: that “[i]t is precisely because analogue quantum simulations function in some contexts like material analogies or toy models, in other contexts like computer simulations, and in still others like experiments, that looking for a unified and unequivocal analysis of what we can and cannot learn from them is simply inappropriate” (140). Some analogue simulations are useful because they show whether or not certain phenomena arise; others are useful because they show how or why phenomena arise, and the means by which those phenomena are related to each other. Both kinds of analogue simulation are useful whether they show how their target systems do behave, or merely how they might, possibly, behave. Although Analogue Quantum Simulation: A New Instrument for Scientific Understanding focuses on examples of analogue quantum simulators, these morals hold for analogue simulation—and, arguably, simulation—much more generally.
