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RQM and Molecular Composition

According to the last post, the constitution of complex natural systems should be understood using a theory of composite causal processes. Composite causal processes are formed from a pattern of discrete causal interactions among a group of smaller sub-processes. When the latter sustains a higher rate of in-group versus out-group interactions, they form a composite. While this account has intuitive appeal in the case of macroscopic systems, what about more basic building blocks of nature? Can the same approach work in the microscopic realm? In this post, I will make the case that it does, focusing on molecules.  A key to reaching this conclusion will be the use of the conceptual resources of relational quantum mechanics (RQM).

Background: The Problem of Molecular Structure

In approaching the question of molecular composition, we need to reckon with a long-standing problem regarding how the structure of molecules—the spatial organization of component atoms we are all familiar with from chemistry—relates to quantum theory.[1]  Modern chemistry uses QM models to successfully calculate the value of molecular properties: one starts by solving for the molecular wave function and associated energies using the time-independent Schrödinger equation Ĥ ψ=Eψ.[2] But there are several issues in connecting the quantum formalism to molecular structure. First and most simply, the quantum description of a multiple particle system does not “reside” in space at all. The wave function assigns (complex) numbers to points in a multi-dimensional configuration space (3N dimensions where N is the number of particles in the system). How do we get from this to a spatially organized molecule?

In addition to this puzzle, some of the methods used to estimate ψ in practice raise additional issues. Something to keep in mind in what follows is that multi-particle atomic and molecular wave equations are generally computationally intractable.  So, simplifying assumptions of some sort will always be needed. One important strategy normally used is to assume that the nuclei are stationary in space, and then proceed to estimate the electronic wave function.[3] Where do we get the assumption for the particular configuration for the nuclei in the case of a molecule?  This is typically informed by experimental evidence and/or candidates can be evaluated iteratively, seeking the lowest equilibrium energy configuration. I’ll discuss the implications of this assumption shortly.

Next, there are different techniques used to estimate the electronic wave function. For multi-electron atoms, one adds additional electrons using hydrogen-like wave functions (called orbitals) of increasing energy. Chemistry textbooks offer visualizations of these orbitals for various atoms and we can form some intuitions for how they overlap to form bonded molecules (but strictly speaking remember the wave functions are not in 3D space). One approach to molecular wave functions uses hybrid orbitals based on these overlaps in its calculations.  Another approach skips this process and just proceeds by incrementally adding the requisite electrons to orbitals calculated for whole molecule at once.[4] In this method, the notion of localized atoms linked by bonds is much more elusive, but this intuitive departure interestingly has no impact on the effectiveness of the calculation method (this method is frequently more efficient).

Once we have molecular wave functions, we have an estimate of energies and can derive other properties of interest.  We can also use the wave function to calculate the electron density distribution for the system (usually designated by ρ): this gives the number of electrons one would expect to find at various spatial locations upon measurement.  This is the counterpart of the process we use to probabilistically predict the outcome of a measurement for any quantum system by multiplying the wave function ψ by its complex conjugate ψ* (the Born rule). Interestingly, another popular technique quantum chemists (and condensed matter physicists) use to estimate electronic properties uses ρ instead of ψ as a starting point (called Density Functional Theory).[5] Notably, the electron density seems to offer a more promising way to depict molecular structure in our familiar space, letting us visualize molecular shape, and pictures of these density distributions are also featured in textbooks. Theorists have also developed sophisticated ways to correlate features of ρ with chemical concepts, including bonding relationships.[6] However, here we still need to be careful in our interpretation:  while ρ is a function that assigns numbers to points in our familiar 3D space, it should not be taken to represent an object simply located in space.  I’ll have more to say about interpreting ρ below.

Still, this might all sound pretty good: we understand that the ball and stick molecules of our school days don’t actually exist, but we have ways to approximate the classical picture using the correct (quantum) physics.  But this would be too quick—in particular, remember that in performing our physical calculations we put the most important ingredient of a molecule’s spatial structure in by hand! As mentioned above, the fixed nuclei spatial configuration was an assumption, not a derivation.  If one tries to calculate wave functions for molecules from scratch with the appropriate number of nuclei and electrons, one does not recover the particular asymmetries that distinguish most polyatomic molecules and that are crucial for understanding their chemical behavior.  This problem is often brought into focus by highlighting the many examples of molecules with the same atomic constituents (isomers) that differ crucially in their geometric structure (some even have the same bonding structure but different geometry). Molecular wave functions would generally not distinguish these from each other unless the configuration is brutely added as an assumption.

Getting from QM Models to Molecular Structure

So how does spatial molecular structure arise from a purely quantum world? It seems that two additional ingredients are needed. The first is to incorporate the role of intra-and extra-molecular interactions. The second is to go beyond the quantum formalism and incorporate an interpretation of quantum mechanics.

With regard to the first step, note that the discussion thus far focused on quantum modeling of isolated molecules in equilibrium. This is an idealization, since in the actual world, molecules are usually constantly interacting with other systems in their environment, as well as always being subject to ongoing internal dynamics.  Recognizing this, but staying within orthodox QM, there is research indicating that applications of decoherence theory can go some way to accounting for the emergence of molecular shape. Most of this work explores models featuring interactions between a molecule and an assumed environment. Recently, there has been some innovative research extending decoherence analysis to include consideration of the internal environment of the molecule (interaction between the electrons and the nuclei -- see links in the footnote).[7] More work needs to be done, but there is definitely some prospect that the study of interactions withing the QM-decoherence framework will shed light on show molecular structure comes about.

However, we can say already that decoherence will not solve the problem by itself.[8]  It can go some way toward accounting for the suppression of interference and the emergence of classical like-states (“preferred pointer states”), but multiple possible configurations will remain. These, of course, also continue be defined in the high-D configuration space context of QM. To fully account for the actual existence of a particular observed structures in 3D space requires grappling with the question of interpreting QM.  There is a 100-year-old debate centered on the problem of how definite values of a system’s properties are realized upon measurement when the formalism of QM would indicate the existence of a superposition of multiple possibilities (aka the “measurement problem”).

Alexander Franklin & Vanessa Seifert have a new paper (preprint) that does an excellent job arguing that the problem of molecular structure is an instance of the measurement problem. It includes a brief look at how three common interpretations of QM (the Everett interpretation, Bohmian mechanics, and the spontaneous collapse approach) would address the issue.  The authors do not conclude in this paper that the consideration of molecular structure has any bearing on deciding between rival QM interpretations.  In contrast, I think the best interpretation is RQM in part because of the way it accounts for molecular structure: it does so in a way that also allows for these quantum systems to fit into an independently attractive general theory of how natural systems are composed (see the last post).

How RQM Explains Spatial Structure

To discuss how to approach the problem using RQM, let’s first return to the interpretation of the electron density distribution (ρ). As mentioned above, chemistry textbooks include pictures of ρ, and, because it is a function assigning (real) numbers to points in 3D space, there is a temptation to view ρ as depicting the molecule as a spatial object.  The ability to construct an image of ρ for actual molecules using X-ray crystallography may encourage this as well. But viewing ρ as a static extended object in space is clearly inconsistent with its usual statistical meaning in a QM context. As an alternative intuition, textbooks will point out that if you imagine a repeated series of position measurements on the molecular electrons, then one can think of ρ as describing a time-extended pattern of these localizing “hits”.

But this doesn’t give us a reason to think molecules have spatial structure in the absence of our interventions. For this, we would want an interpretation that sees spatial localization as resulting from naturally occurring interactions involving a molecule’s internal and external environment (like those explored in decoherence models). We want to envision measurement-like interactions occurring whenever systems interact, without assuming human agents or macroscopic measuring devices need to be involved.

This is the picture envisioned by RQM.[9] It is a “democratic” interpretation, where the same rules apply universally. In particular, all interactions between physical systems are “measurement-like” for those systems directly involved. Assuming these interactions are fairly elastic (not disruptive) and relatively transitory, then a molecule would naturally incur a pattern of localizing hits over time. These form its shape in 3D space.

It would be nice if we could take ρ, as usually estimated, to represent this shape, but this is technically problematic. Per RQM, the quantum formalism cannot be taken as offering an objective (“view from nowhere”) representation of a system. Both wave functions and interaction events are perspectival.  So, strictly speaking, we cannot use ρ (derived from a particular ψ) to represent a pattern of hits resulting from interactions involving multiple partners. However, given a high level of stability in molecular properties across different contexts, I believe this view of ρ can still offer a useful approximation of what is happening. It gives a sense of how, given RQM, a molecule acquires a structure in 3D space as a result of a natural pattern of internal and environmental interactions.

Putting it All Together

What this conclusion also allows us to do is fit microscopic quantum systems into the broader framework discussed in the prior post, where patterns of discrete causal interactions are the raw material of composition. Like complex macroscopic systems, atoms and molecules are individuated by these patterns, and RQM offers a bridge from this causal account to our physical representations.

Our usual QM models of atoms and molecules describe entangled composite systems, with details determined by the energy profiles of the constituents. Such models of isolated systems can be complimented by decoherence analyses involving additional systems in a theorized environment. RQM tells us that that these models represent the systems from an external perspective, which co-exists side-by-side with another picture: the internal perspective. This is one that infers the occurence of repeated measurement-like interactions among the constituents, a pattern that is also influenced in part by periodic measurement-like interactions with other systems in its neighborhood. The theory of composite causal processes connects with this latter perspective. The composition of atoms and molecules, like that of macroscopic systems, is based on a sustained pattern of causal interactions among sub-systems, occurring in a larger environmental context.

Stepping back, the causal process account presented in these last three posts certainly leaves a number of traditional ontological questions open.  In part, this is because my starting point comes from the philosophy of scientific explanation. I believe the main virtue of this theory of a causal world-wide-web is that it can provide a unified underpinning for explanations across a wide range of disciplines, despite huge variation in research approaches and representational formats. Scientific understanding is based on our grasp of these explanations, and uncovering a consistent causal framework that helps enable this achievement is a good way to approach ontology.

References 

Bacciagaluppi, G. (2020). The Role of Decoherence in Quantum Mechanics. In E.N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy (Fall 2020 Edition). https://plato.stanford.edu/archives/fall2020/entries/qm-decoherence/

Esser, S. (2019). The Quantum Theory of Atoms in Molecules and the Interactive Conception of Chemical Bonding. Philosophy of Science, 86(5), 1307-1317.

Franklin, A., & Seifert, V.A. (forthcoming). The Problem of Molecular Structure Just Is the Measurement Problem. The British Journal of the Philosophy of Science.

Mátyus, E. (2019). Pre-Born-Oppenheimer Molecular Structure Theory. Molecular Physics, 117(5), 590-609.

Weisberg, M., Needham, P., & Hendry, R. (2019). Philosophy of Chemistry. In E. N. Zalta, (Ed.), The Stanford Encyclopedia of Philosophy (Spring 2019 Edition). https://plato.stanford.edu/archives/spr2019/entries/chemistry/

 

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[1] For background, see sections 4 and 6 of the Stanford Encyclopedia article “Philosophy of Chemistry”. Also, see the nice presentation of the problem of molecular structure in Franklin & Seifert (forthcoming) (preprint); this paper is discussed later in this post. For a perspective from a theoretical quantum chemist, see the recent paper from Edit Mátyus, which also features a good discussion of the background: Mátyus (2019) (preprint).

[2] Here ψ is the wave function, E is the energy, and Ĥ is the Hamiltonian operator appropriate for the system. For example, the Hamiltonian for an atom will contain a kinetic energy term and a potential energy term that is based on the electrostatic attraction between the electrons and the nucleus (along with repulsion between electrons).

[3] This assumption is justified by the vast difference in velocity between speedy electrons and the slower nuclei (an adiabatic approximation). For molecules, this is typically referred to as the “clamped nuclei” or Born-Oppenheimer approximation.

[4] These methods are known as the valence bond (VB) and molecular orbital (MO) techniques.

[5] The rationale behind DFT is that it can be demonstrated that for molecules the ground state energy and other properties can be derived directly from ρ (Hohenberg-Kohn theorems).  This kind of equivalence between ψ and its associated density is clearly not generally true for quantum systems, but in this case the existence of a minimum energy solution allows for the result to be established.

[6] Of particular note here is the Quantum Theory of Atoms in Molecules (QTAIM) research program, initiated by R.W.F. Bader. QTAIM finds links to bonding and other chemical features via a detailed topological analysis of ρ. I discuss this in a 2019 paper (preprint).

[7] For decoherence studies involving the external environment, see the references cited in section 3.2 of Mátyus (2019) (preprint). Two recent ArXiv papers from Mátyus & Cassam-Chennai explore the contribution of internal dccoherence (see here and here).

[8] The present discussion is a specific instance of a more general point that now seems widely accepted in discussions of the QM interpretations: decoherence helps explain why quantum interference effects are suppressed when systems interact with their environments, but it does not solve the quantum measurement problem (which seeks to understand why definite outcomes are observed upon measurement). See the excellent SEP article by Bacciagaluppi.

[9] For more, see my earlier post, which lists a number of good RQM references.

Composing Natural Systems

An interesting feature of Relational Quantum Mechanics (RQM) is its implication that discrete measurement-like interaction events are going on between natural systems (unobserved by us) all the time.  It turns out that this offers a way to incorporate quantum phenomena into an attractive account of how smaller natural systems causally compose larger ones.  In this post I will discuss the general approach, including a brief discussion of its implications for the ideas of reduction and emergence. In a follow-up post, I will discuss the quantum case in more detail with a focus on molecules.

Composite Causal Processes

The ontological framework I’m using (discussed in the last section of the prior post) is a modified version of Wesley Salmon’s causal process account (Salmon, 1984). The basic entities are called causal processes, and these comprise a network characterized by two dimensions of causation, called propagation and production. Propagation refers to the way an isolated causal process bears dispositions or propensities toward potential interactions with other processes--aka its disposition profile. Production refers to how these profiles are altered in causal interactions with each other (this is the mutual manifestation of the relevant dispositions).

The entities and properties described by science correspond to features of this causal web. For example, an electron corresponds to a causal process, and its properties describe its dispositions to produce change in interactions with other systems.

Given this picture, we can go on to form an account of how composite causal processes are formed.  What is exciting about the resulting view is that it can provide a framework for systems spanning the microscopic-macroscopic divide.

For background, I note that neither Salmon nor others who have explored causal process views provide a detailed account of composition. Recall that Salmon’s intent was to give a causal theory in service of underpinning scientific explanations.  In this context, he did outline a pertinent distinction between etiological explanations and constitutive explanations. Etiological explanations trace the relevant preceding processes and interactions leading up to a phenomenon. A constitutive explanation, on the other hand, is one that cites the interactions and processes that compose the phenomenon:

A constitutive explanation is thoroughly causal, but it does not explain particular facts or general regularities in terms of causal antecedents. The explanation shows, instead, that the fact-to-be-explained is constituted by underlying causal mechanisms. (Salmon, 1984, 270)

However, while Salmon sketches how one would divide a causal network into etiological and constitutive elements, he doesn’t provide a recipe for marking off the boundaries that define which processes/interactions are “internal” to what is to be explained by the constitutive explanation (see Salmon 1984, p. 275).

Going beyond Salmon, and drawing on the work of others, we can offer an account of composition for causal processes.  They key idea is to propose that a coherent structure at a higher scale arises from patterns of repeated interactions at a lower scale. We should pick out composite causal processes and their interactions by attending to such patterns at the lower scale.

In Herbert Simon’s discussion of complex systems, he notes that complexity often “takes the form of hierarchy (Simon, 1962, 468)” and notes the role interactions play in this context:

In hierarchic systems we can distinguish between interactions among subsystems, on the one hand, and the interactions within subsystems—that is, among the parts of those subsystems—on the other. (Simon, 1996, p.197, emphasis original)

The suggestion to take from this is that differential interaction rates give rise to a hierarchy of causal processes. When a group of processes interacts more with each other than with “outsiders” then it can form a composite. For example, a social group like a family or a business can be marked off from others (at a first approximation) by the differential intensity with which its members interact within vs. outside the group.

As part of his discussion of analyzing complex systems, Bill Wimsatt also explores the idea of decomposition based on interactions, i.e., breaking down a system into subsystems based on the relative strength of intra vs extra-system interactions. (Wimsatt, 2007, 184-6).  And while he describes how different theoretical concerns lead us to utilize a variety of analytical strategies, Wimsatt makes it clear that patterns of causal connections are the ultimate basis for understanding complex systems:

Ontologically, one could take the primary working matter of the world to be causal relationships, which are connected to one another in a variety of ways—and together make up patterns of causal networks…Under some conditions, these networks are organized into larger patterns that comprise levels of organization (Wimsatt, 2007, 200, emphasis original).[1]

Wimsatt explains that levels of organization are “compositional levels”, characterized by hierarchical part-whole relations (201). This notion of composition includes not just the idea of parts, but of parts engaged in certain patterns of causal interactions, consistent with the approach to composite causal processes suggested above.

To summarize: a composite causal process consists of two or more sub-processes (the constituting group) that interact with a greater frequency than each does with other processes.  Just like any causal process, a composite process carries its own disposition profile: here the pattern of interacting sub-processes accounts for how composite processes will themselves interact (what this means for the concepts of reduction and emergence will be discussed below). Consider social groups again, perhaps taking the example of smaller, pre-industrial societies. Each may have its own distinctive dispositions to mutually interact with other, similarly sized groups (e.g., to share a resource, trade, or to engage in raids or battle). These would be composed from the dispositions of their constituent members as they are shaped in the course of structured patterns of in-group interaction. We can also envision here that the higher scale environmental interactions also impact the evolution of the composite entity, but its stability is due to maintaining its characteristic higher-frequency internal processes.

Let me add a couple of further comments about composite processes.  First, as already indicated, a group of constituting sub-processes may be themselves composite, allowing for a nested hierarchy. Second, the impact of larger scale external interactions can vary.  Some may have negligible impact. Other interactions (especially if regular in nature) can contribute to shaping the ongoing nature of the composite. At the other extreme, there will be some external interactions that could disrupt or destroy it. The persistence of a composite would seem to require a certain robustness in the internal interaction pattern of its components. Achieving stability (and the associated ability to propagate a characteristic higher scale disposition profile) may require the differential between intra-process and extra-process interactions to be particularly high, or else there may need to have a particular pattern to the repeated interactions.  There will clearly be vague or boundary cases as well.

Why go to all this trouble of fairly abstract theorizing about a web of causal processes?  Because this account fleshes out the notions that underwrite the causal explanations scientists formulate in a variety of domains.

In the physical sciences, the familiar hierarchy of entities, including atoms, molecules, and condensed matter, all correspond to composite causal processes. Of course, in physical models, what marks out a composite system might be described in a number of ways (for example, in terms of the relative strength of forces or energy-minimizing equilibrium configurations).  But I argue this is consistent with the key being the relative frequency of recurring discrete interactions in-system vs. out-system. (This will be explored further in the companion post.)

In biology, the complexity of systems may sometimes defy the easy identification of the boundaries of composites. Also, a researcher’s explanatory aims will sometimes warrant taking different perspectives on phenomena. In these cases, scientists will describe theoretical entities that do not necessarily follow a simple quantitative accounting of intra-process vs. extra-process interactions. On the one hand, the case of a cell provides a pretty clear paradigm case meeting the definition of a composite process. On the other hand, many organisms and groups of organisms present difficult cases that have given rise to a rich debate in the literature regarding biological individuality. Still, a causal account of constitution is a useful starting point, as noted here by ElliottSober:

The individuality of organisms involves a distinction between self and other—between inside and outside. This distinction is defined by characteristic causal relations. Parts of the same organism influence each other in ways that differ from the way that outside entities influence the organism’s parts. (Sober, 1993, 150)

The way parts “influence each other”, of course, might involve considerations beyond a mere quantitative view of interactions, and connotes an entry point where theoretical concerns can create distance from the basic conception of the composite causal process. In a biological context, sub-processes and interactions related to survival and reproduction may, for example, receive disproportionate attention in creating boundaries around composite entities. Notably, Roberta Millstein has proposed a definition of a biological population based on just this kind of causal interaction-based concept (Millstein 2009).

It is also worth mentioning that constitutive explanations in science will rarely attempt to explain the entire entity. This would mean accounting all of its causal properties (aka its entire dispositional profile) in terms of its interacting sub-processes. It is more common for a scientific explanation to target one property corresponding to a behavior of interest (corresponding to one of many features of a disposition profile).

Reduction and Emergence

I want to make a few remarks about how this approach to composites sheds light on the topics of ontological reduction and emergence. In a nutshell, the causal composition model discussed here gives a straightforward account of these notions that sidesteps some common confusions and controversies, such as the “causal exclusion problem.”

When considering the relationship between phenomena characterized at larger scales and smaller ones, the key observation is that a larger entity’s properties do not only depend not only on the properties of smaller composing entities. They also depend on their pattern of interaction.  This is in contrast to the usual static framing that posits a metaphysical relationship (whether expressed in terms of composition or “realization”) between higher-level properties and lower-level properties at some instant of time.  This picture is conceptually confused (if taken seriously as opposed to a being a deliberate simplifying idealization): there is no reason to think such synchronic relationships characterize our world.

Recall that, in the present account, a property describes a regular feature of the disposition profile of a causal process. A composite causal process is made up of a pattern of interacting sub-processes.  The disposition profiles of the sub-processes are changing during these interactions: they are not static.  The dispositions of the composite depend on this matrix of changing sub-processes.  Note that both the forming of a higher-scale disposition (and its manifestation in a higher-scale interaction) takes more time than the equivalents at the smaller scale.  No composite entity or property exists at an instant:  this is a fiction concocted by us facilitate our understanding. Unfortunately, contemporary metaphysicians have taken this notion seriously.  It is perhaps easiest to see the problem in the case of a biological system:  nothing is literally “alive” at an instant of time.  Living things are sustained by temporally extended processes.  Less intuitively, the same is true of inanimate objects.

Emergence and reduction are clearer, unmysterious notions when based on this dynamic conception of the composition relationship.  Properties of larger things “emerge” from the interacting group of smaller things. The “reduction base” includes the interaction pattern of the components and their (changing) properties.  The exclusion problem says that since higher-level properties are realized by lower-level properties at any arbitrary instant of time, they cannot have causal force of their own (on pain of overdetermination). We can see why this is a pseudo-problem once a better understanding of composition is in place. Causal production occurs at multiple scales.

This take on reduction and emergence is obviously not unique to the causal process model discussed here.  It is implied by any approach that recognizes that properties of composites depend on interacting parts. For example, Wimsatt discusses at some length how notions of reduction and emergence should be understood given his understanding of complex systems. He offers a definition of reductive explanation that shows a similarity to the causal process view of constitutive explanation:

A reductive explanation of a behavior or a property of a system is one that shows it to be mechanistically explicable in terms of the properties of and interactions among the parts of the system. (Wimsatt, 207, 275)

This approach to reductive explanation is perfectly consistent with a form of emergence, in the sense that the properties of the whole are intuitively “more than the sum of its parts (277).” The key idea here, again, is that composition includes the interactions between the parts. For comparison, Wimsatt introduces the notion of “aggregativity”, where the properties of the whole are “mere” aggregates of the properties of its parts. For this to happen, “the system property would have to depend on the parts’ properties in a very strongly atomistic manner, under all physically possible decompositions (277-280)”. He analyzes the conditions needed for this to occur and concludes they are nearly never met outside of the case of conserved quantities in (idealized) physical theories.

Simon had introduced similar notions, describing hypothetical idealized systems where there are no interactions between parts as “decomposable,” which are then contrasted to “nearly decomposable systems, in which the interactions among the subsystems are weak but not negligible (Simon, 1996, 197, emphasis original).” To highlight this distinguishing feature, Simon considers a boundary case: that of gases. Ideal gases, which assume interactions between molecules are negligible, are, for Simon, decomposable systems. In the causal process account, we would similarly point out that an ideal gas doesn’t have a clearly defined constituting group: the molecules do not have a characteristic pattern of interacting with each other at any greater frequency than they do with the external system (the container). An actual, non-ideal gas, on the other hand, with weak but non-negligible interactions between constituent molecules, would correspond to the idea of a composite causal process.

Some contemporary work in metaphysics, focused on dispositions/powers and their role in causation, has incorporated similar views about composition and emergence. Rani Lill Anjum and Stephen Mumford describe a “dynamic view” of emergence:

 The idea is that emergent properties are sustained through the ongoing activity; that is, through the causal process of interaction of the parts. A static instantaneous constitution view wouldn't provide this (Anjum & Mumford 2017, 101)

In their view, higher scale properties are emergent because they depend on lower-level parts whose causal properties are undergoing transformation as they interact, consistent with the view discussed here.  Most recently, R. D. Ingthorsson's new book, while not discussing emergence and reduction explicitly, also presents a view of composition based on the causal interaction of parts which is in the same spirit (Ingthorsson, 2021, Ch. 6).

Conclusion

I think composite causal processes provide a good framework for understanding how natural systems are constituted.  A puzzle for the view, however, might arise via its use of patterns of discrete causal interactions to define composites. How would this work in physics, where the forces binding together composites, such as the Coulomb (electrostatic) force, are continuous?  One possible answer is to point out that physical models employ idealizations, and claim their depictions can still correspond to the “deeper” ontological picture of causal processes. But I believe we can find a better and more comprehensive answer than this.  To do so, we must look more carefully at physical accounts of nature’s building blocks, atoms and molecules, and see if we can uncover a correspondence with the causal theory. I think we can, assuming we utilize the RQM interpretation.  This is the subject of the next post.

References

Anjum, R., & Mumford, S. (2017). Emergence and Demergence. In M. Paolini Paoletti, & F. Orilia (Eds.), Philosophical and Scientific Perspectives on Downward Causation (pp. 92-109). New York: Routledge.

Ingthorsson, R.D. (2021). A Powerful Particulars View of Causation. New York: Routledge.

Millstein, R. L. (2009). Populations as Individuals. Biological Theory, 4(3), 267-273.

Salmon, W. (1984). Scientific Explanation and the Causal Structure of the World. Princeton: Princeton University Press.

Simon, H. (1962). The Architecture of Complexity. Proceedings of the American Philosophical Society, 106(6), 467-482.

Simon, H. A. (1996). The Sciences of the Artificial (3rd ed.). Cambridge, MA: MIT Press.

Sober, E. (1993). Philosophy of Biology. Boulder: Westview Press.

Wimsatt, W. C. (2007). Re-Engineering Philosophy for Limited Beings. Cambridge, Massachusetts: Harvard University Press.

Photo: Alina Grubnyak via Unsplash

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[1] This passage goes on to mention other, less neat, network patterns: “Under somewhat different conditions they yield the kinds of systematic slices across which I have called perspectives. Under some conditions they are so richly connected that neither perspectives nor levels seem to capture their organization, and for this condition, I have coined the term causal thickets (Wimsatt, 2007, 200).”

Why I Favor Relational Quantum Mechanics

I think Relational Quantum Mechanics (RQM), initially proposed by Carlo Rovelli, is the best interpretation of quantum mechanics.¹ It is important to note right away, however, that I depart from Rovelli’s thinking in one important respect. He takes an anti-realist view of the wave function (or quantum state). As I will discuss below, I endorse a view that sees the wave function as representing something real (even if imperfectly and incompletely).

There are two reasons I prefer RQM. First, I think it makes better sense of QM as a successful scientific endeavor compared to other interpretations. Second, it fits neatly with an attractive ontology for our world.

Quick Introduction

Orthodox or “textbook” QM features a closely knit family of mathematical models and recipes for their use. The models describe the state of a microscopic system characterized by certain physical quantities (typically given in the form of a wave function). It gives a formula for calculating how the system evolves in time (the Schrödinger equation). Notably, because of the nature of the mathematical formalism, one typically cannot ascribe definite values to the physical quantities of interest. However, QM also offers a procedure for calculating (probabilistically) the outcomes of particular measurements of these quantities. The problem with taking orthodox QM as a universally applicable physical theory can be described in several ways (this is usually called the measurement problem). One simple way is to note an inconsistency arising from the presence of what appears to be two completely different kinds of interaction.

In the absence of any interaction, a system evolves in time as described by the Schrödinger equation. But interactions are handled in two different ways. On the one hand, we have the measurement process (utilizing the Born rule), that is, an interaction between the quantum system under investigation and a scientist’s experimental apparatus. On the other hand, we can also describe an interaction between two systems that are not subject to measurement. In the first kind of interaction, a definite value of a system’s physical quantity is found (we say the wave function of the system collapses). In the second kind of interaction, we represent two (or more) systems, previously considered isolated, as now correlated in a composite system (we say they become entangled). This system evolves in the same fashion as any isolated system. And as such the composite system may be in a superposition of states where no definite values for a given quantity can be ascribed.

In a nutshell, the RQM solution is to stipulate that a physical interaction is a measurement-style event. However, this is only true for those systems directly involved: the systems are merely entangled from the standpoint of other “third-party” systems. The appearance of two sorts of interaction arises from a difference in perspective. This is weird, of course, since particular values of the physical quantities revealed in an interaction are manifest only relative to the interaction partner(s) involved. They don’t exist in a fully objective way. All interpretations of QM ask us to accept something unintuitive or revisionary. This is the “ask” made by RQM.

Reason One: RQM Validates Quantum Theory as Successful Science

Before discussing the interpretation further, I can quickly outline a reason to prefer RQM to many competing approaches. This point is primarily a negative one. In contrast to other approaches, RQM is an interpretation that delivers a satisfying account of QM as a successful scientific theory: one that draws appropriate connections between the results of our experimental investigations and a meaningful picture of the world around us.

I obviously won’t be doing a deep dive into all the options, but will quickly sketch why I think RQM is superior. First, for a quick cut in the number of alternatives, I eliminate views that are merely pragmatic, or see QM as only describing what agents experience, believe, or know. I insist that alongside its other aims (such as prediction and practical control), a scientific theory should contribute to our understanding of nature. To do so, the theory should offer successful explanations of worldly phenomena, that is, ones that tell us (broadly speaking) what kind of things are out there and how they hang together. This means, in turn, that at least some of the elements of the mathematical models that we use should represent features of the world (allowing that the fidelity of any given representation is significantly constrained by reasons having to do with the aims of the scientist and the tools employed). I will outline in the next section of this post how I think this works in the case of RQM.

As for the remaining alternatives, I will limit the conversation to the three most prominent broadly realist approaches to thinking about QM: Everett-style interpretations, Bohmian mechanics, and objective collapse approaches, such as Ghirardi-Rimini-Weber (GRW) theory (the implied ontology of these approaches might be fleshed out in more than one way, but I will not pursue the details here.)

For these alternatives, a different issue rises to the fore. An interpretation should not just consider how the features of formal QM models might correspond to reality. It should also respect the status of quantum theory as a hugely successful experimental science. Orthodox or “textbook” QM includes not just the mathematical formalism, but also the recipes for how it is used by investigators and how it connects to our experiences in the laboratory. And here is where I think Everettians and Bohmians in particular fall short.

Note first that all three of the alternative approaches depart from orthodox QM by adding to, subtracting from, or modifying its basic elements.² GRW changes things by replacing the Schrödinger equation with a new formula that attempts to encompass both continuous evolution and the apparent collapse onto particular outcomes observed in measurement. Bohmian mechanics adds new elements to the picture by associating the quantum state with a configuration of particles in 3D space and adding a new guidance equation for them. Everettian approaches just drop the measurement process and seek to reinterpret what is going on without it.

For the Everett framework in particular, I’m not sure the extent of its departure from orthodox QM is always appreciated. It is sometimes claimed to be the simplest version of QM. This is since it works by simply removing what is often seen as a problematic element of the theory. But in doing so it divorces QM from its basis in experimental practice. This is a drastic departure indeed.

To see this, note that to endorse Everett is to conclude that the very experiments that prompted the development of QM and have repeatedly corroborated it over nearly a century are illusory. For the Everettian, to take one example, no experimental measurement of the spin of an electron has ever or will ever have a particular outcome (all outcomes happen, even though we’ll never perceive that).

Bohmian mechanics also turns our experiments into fictions. For the Bohmian, there is actually no electron and no spin involved in the measurement of an electron’s spin. Rather, there is an orchestrated movement of spinless point particles comprising the system and the laboratory (and the rest of the universe) into the correct spatial positions.

GRW-style approaches are different, in that they are testable alternatives to QM. Unfortunately, researchers have been busy gradually ruling them out as empirically adequate alternatives (see, e.g., Vinante et.al, 2020). It is also worth noting, however, that GRW also distorts the usual interpretation of experimental results by stipulating that all collapses are in the position basis.

Unlike these approaches, RQM is truly an interpretation, rather than a modification, of orthodox QM, a successful theory that was motivated by experimental findings and is extremely well supported by decades of further testing. The measurement process, in particular, is not some problematic add-on to quantum theory – it is at the heart of it. Human beings and our experiences and interventions are part of the natural world. RQM does justice to this fact by explaining that measurements—the connections between quantum systems and ourselves—are just like any other physical interaction.

Reason Two: RQM Offers an Attractive Ontological Picture

Laudisa and Rovelli (in the SEP article) describe RQM’s ontology as a “sparse” one, comprised of the relational interaction events between systems. This event ontology has attractive features (akin to the “flash” ontology sometimes discussed in conjunction with objective collapse interpretations). There is no question of strange higher-dimensional spaces or other worlds: the events happen in spacetime. Also, one of the goals of science-inspired metaphysical work is to foster the potential unification of scientific theories. Importantly, a QM interpretation that features an event ontology offers at least the promise of establishing a rapport with relativity theory, which is typically seen as putting events in the leading role (see a recent discussion by Maccone, 2019).

But does giving this role to interaction events preclude a representational role for the wave function? Given that physical properties of systems only take definite values when these events occur, perhaps systems should not be accorded any reality apart from this context. And, in fact, Carlo Rovelli has consistently taken a hard anti-realist stance toward the wave function/quantum state. In his original presentation of RQM he gave it a role only as record of information about one system from the point of view of another, and thought it was possible to reformulate quantum theory using an information-based framework. This conflicts with my insistence above that such anti-realism was inconsistent with the aims of a good scientific theory.

Thankfully, there is no need to follow Rovelli on this point. Instead, I concur with a view outlined by Mauro Dorato recently. He suggests that rather than view non-interacting systems as simply having no real properties, they can be characterized as having dispositions:

In other words, such systems S have intrinsic dispositions to correlate with other systems/observers O, which manifest themselves as the possession of definite properties q relative to those Os. (Dorato, 2016, 239; emphasis original)

As he points out, referencing ideas due to philosopher C.B. Martin, such manifestations only occur as mutual manifestations involving dispositions characterizing two or more systems.³ Since these manifestations have a probabilistic aspect to them, the dispositions might also be referred to as propensities.

So, here the wave function has a representational role to play. It represents a systems’s propensities toward interaction with a specified partner system(s). The Schrödinger equation would show how propensities can be described across time in the absence of interaction. Now, it is true that the QM formalism does not offer a full or absolute accounting for a system’s properties, given its relational limitations. But here we should recall that models across the sciences are typically incomplete and imperfect. In addition to employing approximations and idealizations, they approach phenomena from a certain perspective dictated by the nature of the research program. But we can say the wave function represents something real (if incompletely and in an idealized way). Reality has two aspects, non-interacting systems with propensities, and the interaction events that occur in spacetime.

The idea that properties are dispositional in nature is one that has been pursued increasingly by philosophers in recent years. It fits well with physics, since both state dependent and independent properties (like mass and charge) are only known via their manifestations in interactions.⁴ While advocates disagree about the details, the idea that the basic ontology of the world features objects that bear dispositions/propensities has also been used more widely to address a number of difficult philosophical topics (like modality). Most importantly, perhaps, dispositions and their manifestations provide a good basis for theorizing about causation.⁵

Fitting Both Quantum Systems and Scientists Into the Causal Web

To conclude, I’ll briefly describe how I would flesh out this ontological picture, putting an emphasis on causation.

I mentioned above the role representational models play in explanation. To be more specific, scientific explanations are typically causal explanations: they seek to place a phenomenon in a structured causal context. When successful explanations feature models, then, these models represent features of the world’s causal structure. The suggestions above on how to view the ontology associated with RQM fit into a particularly attractive theory of this structure.

This is a modified version of Wesley Salmon’s causal process account (Salmon, 1984). Here the basic entity or object is labeled a causal process, and there are two dimensions of causation: propagation and production. Propagation refers to the evolution of a causal process in the absence of interaction, while production refers to the change that causal processes undergo when an interaction occurs. As described by Ladyman & Ross:

The metaphysic suggested by process views is effectively one in which the entire universe is a graph of real processes, where the edges are uninterrupted processes, and the vertices the interactions between them (Ladyman & Ross, 2007, 263).

According to Salmon, a propagating causal process carries or “transmits” causal influence from one spacetime point to another. The character of this causal influence is then altered by interactions. I theorize that this causal influence takes the form of a cluster of dispositions or propensities toward mutual interactions (aka a propensity profile). The interactions produce a change in this profile.⁶

To summarize:

1. The web of nature has two aspects: the persisting causal process and the causal interaction event (a discrete change-making interaction between processes).

2. The quantum formalism offers a partial representation of the propensity profile of a causal process. It is partial because these are only the propensities toward manifestations that take place in interactions with (one or more) designated reference systems. The Schrödinger equation represents the propagation of these propensities from one interaction to the next.

3. All manifestations are mutual, and take the form of a change in the profile of each process involved in the interaction. A quantum measurement is an interaction like any other. Humans may treat the wave function as representing the phenomena we are tracking, but we are also causal processes, as are our measuring devices. It is just that the changes manifest in us in an interaction (our altered propensity profiles) are conceptualized as epistemic.

4. Per RQM, when two physical systems interact, they are represented as an entangled composite system from the perspective of a third system. This relational representation of the composite system might in practice be thought of as a limitation on what the third system “knows.” Under certain conditions, however, this entanglement can have a distinctive indirect impact on the third system—interference effects—revealing it is not only epistemic (as always, decoherence explains why we rarely experience these effects).

There is much more to flesh out, of course. I would add to this summary an account of how composite systems form higher-level propensities of their own, based on the pattern of repeated interactions of their constituents. Also, there is an interesting question of how serious of a (relational or perspectival) scientific realist to be about the properties identified in quantum theory. My preference is to be a realist about the (singular) causal network, but view the formalism as offering only an idealized depiction of regularities in the propensity profiles of the underlying causal processes.

Notes

¹ For background, see the Stanford Encyclopedia article (Laudisa & Rovelli, 2019). Rovelli’s original paper is (Rovelli, 1996 - arXiv:quant-ph/9609002). Good philosophical discussions include Brown (2009; link via academia.edu), Van Fraassen (2010; link via Van Fraassen website), Dorato (2016; preprint here, but note final version has significant changes), and Ruyant (2018; preprint here).

² For a recent attempt to carefully describe the principles of orthodox QM, see Poinat (2020); link (researchgate).

³ What Martin calls “reciprocal disposition partners.” See Martin (2008), especially Ch. 5. 

⁴ In addition to contemporary work by Dorato and others, there have been a handful of theorists over the decades since QM was formulated who have employed dispositions/propensities to interpret QM. See Suárez (2007) for a survey of some of these.

⁵ Important work here includes Chakravartty (2007) and Mumford & Anjum (2011).

⁶ The main changes from Salmon’s own work are as follows. The first is to be a realist about dispositions/propensities, whereas Salmon’s version of empiricism drove him to reject any suggestion of causal powers. He characterized causal processes in terms of their transmission of an observable “mark” or, in a subsequent version of the theory, the transmission of a conserved physical quantity. The second change is that causal processes cannot be said to propagate in spacetime, as Salmon envisioned, since this would be inconsistent with the non-local character of quantum systems.

References

Brown, M. J. (2009). Relational Quantum Mechanics and the Determinacy Problem. The British Journal for the Philosophy of Science, 60(4), 679-695.

Chakravartty, A. (2007). A Metaphysics for Scientific Realism. Cambridge: Cambridge University Press.

Dorato, M. (2016). Rovelli's Relational Quantum Mechanics, Anti-Monism, and Quantum Becoming. In A. Marmodoro, & D. Yates (Eds.), The Metaphysics of Relations (pp. 235-262). Oxford: Oxford University Press.

Ladyman, J., & Ross, D. (2007). Everything Must Go. Oxford: Oxford University Press.

Laudisa, F., & Rovelli, C. (2019). Relational Quantum Mechanics. Retrieved from The Stanford Encyclopedia of Philosophy, Winter 2019 Edition: https://plato.stanford.edu/entries/qm-relational/

Maccone, L. (2019). A Fundamental Problem in Quantizing General Relativity. Foundations of Physics, 49, 1394-1403.

Martin, C. (2008). The Mind in Nature. Oxford: Oxford University Press.

Mumford, S., & Anjum, R. L. (2011). Getting Causes from Powers. Oxford: Oxford University Press.

Poinat, S. (2020). Quantum Mechanics and Its Interpretations: A Defense of the Quantum Principles. Foundations of Physics, 1-18.

Rovelli, C. (1996). Relational Quantum Mechanics. International Journal of Theoretical Physics, 35, 1637-1678.

Ruyant, Q. (2018). Can We Make Sense of Relational Quantum Mechanics. Foundations of Physics, 48, 440-455.

Salmon, W. (1984). Scientific Explanation and the Causal Structure of the World. Princeton: Princeton University Press.

Suárez, M. (2007). Quantum Propensities. Studies in History and Philosophy of Modern Physics, 38, 418-438.

Van Fraassen, B. (2010). Rovelli's World. Foundations of Physics, 40, 390-417.

Vinante, A., et.al. (2020) Narrowing the Parameter Space of Collapse Models with Ultracold Layered Force Sensors. Physical Review Letters, 125, 100401-100401.