Challenges to a Quantum-Theoretic Social Theory

The Quantum-Theoretic Challenge to Wendt’s ‘Will’

In this section I briefly discuss the notions of ‘proto-consciousness’ and ‘will’ that Wendt introduces as a way of explaining the collapse of wave functions. In developing this idea, Wendt adopts panpsychism as a metaphysics. However, this metaphysics does not necessarily connect with quantum theory of the brain; there is a jump to be made here as Wendt does indeed submit. In order to bring the two together Wendt draws on two physicists, Conway and Kochen, who demonstrate what they call a ‘free will theorem’, that is:

If the choice of directions in which to perform spin … experiments is not a function of the information accessible to the experimenters, then the responses of the particles are equally not functions of the information accessible to them. ¹

Elaborating, Conway and Kochen write that:

Why do we call this result the Free Will Theorem? It is usually tacitly assumed that experimenters have sufficient free will to choose the settings of their apparatus in a way that is not determined by past history. We make this assumption explicit precisely because our theorem deduces from it the more surprising fact that the particles’ responses are also not determined by past history. ²

Much later in the article, the two authors, however, make a startling admission as far as Wendt’s project is concerned; they clearly state that:

our assertion that “the particles make a free decision” is merely a shorthand form of the more precise statement that “the Universe makes this free decision in the neighbourhood of the particles.” It is only for convenience that we have used the traditional theoretical language of particles and their spins. ³

This is a much more acceptable physics statement – even from a quantum theory perspective – than claiming rhetorically for the sake of convenience as they did at the beginning of the article that:

if indeed there exist any experimenters with a modicum of free will, then elementary particles must have their own share of this valuable commodity. ⁴

This admission creates a serious challenge for Wendt’s adoption of the idea that particles have free will, which he uses to speak of Will as causing the collapse of the wave function. It is a challenge because Wendt is not using ‘free will’ as a shorthand to state (like Conway and Kochen do) that ‘the Universe makes this free decision in the neighbourhood of the particles’. Had Wendt done so he would not have been able to speak of the inside of a wave function and subjectivity as he does. ⁵ This thus undermines the claim of an insider’s view of the wave function since Conway and Kochen are clear that it is the universe that makes the free decision in the neighbourhood of the particle. And in more operational terms, that is, in terms of what happens actually in experiments, they explain that what happens is that ‘real macroscopic things such as the locations of certain spots on screens are not functions of the past history of the Universe’. ⁶ Although Conway and Kochen subsequently presented a stronger version of ‘free will theorem’, ⁷ it does remain plagued with a poor conceptualisation of what a human free choice is, that is, as put by Landsman,

The (Strong) Free Will Theorem (FWT) of Conway and Kochen (2009) on the one hand follows from uncontroversial parts of modern physics and elementary mathematical and logical reasoning, but on the other hand seems predicated on an undefined notion of free will (allowing physicists to “freely choose” the settings of their experiments). This makes the theorem philosophically vulnerable. ⁸

Landsman, after reviewing a large body of work on the issue and engaging in quantum theoretic calculations, concludes that:

Although the intention of Conway and Kochen was to support unspecified versions of libertarian free will through modern physics, our reformulation of their theorem … gives a more subtle picture: the FWT (revisited) challenges one particular version of compatibilist free will. ⁹ As such, it only provides indirect support for libertarian free will, namely by weakening one of its competitors. ¹⁰

Such a ‘negative’ proof of the ‘free will’ is far away from Wendt’s claim that there is a ‘Will’ operating inside the ‘wave function’ to provoke its collapse. Alternatively, Wendt could decide to argue that he is working through analogies or metaphors, which of course would be very damaging to the nature of his project as he portrays it.

The Background-Independence Challenge to Wendt’s Flat Ontology

Wendt’s speculative effort to construct an argument for a flat ontology that unifies physical and social ontologies overlooks a major challenge ensuing from a hard-to-ignore issue that philosophers and physicists are dealing with today, that is, a unification of the theory of general relativity and quantum theory – the two best physics theories that have been both theoretically and experimentally vindicated over and over. Wendt does indeed mention this issue and the problem of formulating a theory of quantum gravity but does not bring it to bear in a sustained way on his discussions of ontology and time. ¹¹ This is a serious challenge to Wendt’s work because unifying quantum theory and general relativity leads to the necessity of a so-called background-independent theorisation which jettisons the positing of any role for ontology, or, more precisely, metaphysics, flat or otherwise. In the language of philosophy, background-independence means there are no presupposed metaphysical primitives (and in the language of social theory there is no presupposed ‘ontology’). ¹² In the theory of general relativity this means that all that we can formulate are local parametrisations of space and time and any other feature of the universe that one might be interested in. Phrased using, for example, Stephen K. White’s jargon, this would stand for local prefigurations, none of which has the status of metaphysical primitives. ¹³

This issue poses two philosophical/conceptual difficulties. First is the question of how to conceptualise ‘background independence’ proper. That is, besides saying that there is no metaphysical background or primitives whatsoever, what does this notion entail conceptually speaking? Mathematically speaking this is effectuated through various mathematical procedures and ideas such as the idea/operation of diffeomorphism. Simply put this means that theories should not refer in any foundational way to any coordinate (parametrisation) system, including time defined in any way. Background independence thus means that if we were to displace all dynamical objects existing in the universe, this is not tantamount to generating a different state of the world. Rather, this should lead to an equivalent representation of the same physical state. This is referred to as diffeomorphism invariance (also known as gauge symmetry). ¹⁴ The question at hand here is: how to incorporate this insight and deploy it in a conceptual framework that seeks to theorise about the social world? And why is it so difficult anyway? Because we must translate from the theory of general relativity, which is expressed in the complex and abstract language of mathematical formalism of tensorial calculus, into a conceptual language more amenable to philosophy’s and social theory’s jargon. And this requires creativity so as not to fall into conceptual traps that would nullify the insights of general relativity. For example, we must not resort to analogising and metaphorising when translating from general relativity since doing so will be following the conceptual logic of pre-general relativity conceptualisations within which our natural languages are wired. In other words, our natural languages and discourses rarely offer us notions and ideas that are suitable to explicating the subtleties of sophisticated mathematical theories that are not wired in classical physics. Speaking, for example, of spacetime warping or quantum entanglement simply defies any expression in terms of our everyday language except by resorting to analogies and metaphors, which then gives the wrong presentation of the ‘weirdness’ of the issues at stake. And the idea of no background – that is, not even empty space – is just impossible to portray in human natural language.

This is different from the perspective of the special theory of relativity wherein the spacetime continuum is taken to be a background ‘container’ within which the universe unfolds (just like in a Newtonian world), with the added feature that event simultaneity ¹⁵ becomes relative to where one is located in space, which means that time is not uniformly flowing anymore. However, time is still one-dimensional (1-d) linear and space is three-dimensionally (3-d) isotropic (that is, the geometry of space is uniform in every spatial direction at any point) space is three-dimensional (3-d) Euclidean. Indeed, the special relativity notion of spacetime continuum – as a foliation of 1-d linear time and 3-d isotropic space – is replaced in the theory of general relativity by the notion of a dynamical curved pseudo-Riemannian manifold. ¹⁶ General relativity presents spacetime geometry and gravity as one and the same thing – the spacetime continuum is but the gravitational field (much like we speak of an electromagnetic field which we experience as electric and magnetic forces). And because space and time are inseparable, time is much like space also part of 4-dimensional geometry (and hence gravity). This dynamic spacetime geometry, or, equivalently, gravitational field, is not contained in anything. Put differently: spacetime does not exist against a background of any sort – there is no background! The Newtonian idea of spacetime as the container of the universe is jettisoned. All what we have are fields interacting with fields, such as, for example, the gravitational field interacting with electroweak field (which combines weak and electromagnetic forces). It is only at the local level that one can more or less still speak in the usual way of space and time because the spacetime manifold is a pseudo-Riemannian manifold which is locally homeomorphic (that is, there is a one to one smooth mapping) to a Euclidean 3-dimensional flat space plus one dimension for time. Although the universe exists with all its phenomena which we can observe both at the nano (and smaller) scale and at the scale of billions of lightyears away, we cannot speak of a ‘global container’ anymore, and everything is relativised ¹⁷ beyond the local spacetime ‘neighbourhood’, including time.

Unifying the theory of general relativity with quantum theory to formulate a consistent theory of quantum gravity has however proven to be a daunting challenge for decades. It is only within the last two or so decades that much progress has been made with the advent of so-called loop quantum gravity, ¹⁸ string theory, and a few other frameworks. ¹⁹ Not only are the difficulties technical, that is, requiring new, sophisticated and highly complex mathematics, they also are conceptual and philosophical. All successful quantum theories (called quantum field theories) of the fundamental interactions other than gravity presuppose spacetime as a background, whereas general relativity is about spacetime itself, thought of as a dynamical geometric field, and the theory is background-independent. Moreover, quantum theory assumes a notion of time which is pre-general relativity. Relativistic quantum field theory – quantum theory plus special theory of relativity – incorporates the notion of spacetime as developed in the theory of special relativity only, and the latter still considers time and space as absolute ‘containers’, even though they are relativised in the sense that there is no universal parametrisation thereof. Therefore, in addition to the daunting problem of background independence we also have a so-called problem of time (discussed in the next section).

To end this section, let me raise the following question: why should the requirement of background-independence be an issue for Wendt’s project? Two quick answers. First: the issue of background-independence is a major challenge to quantum theory and physicists understand this, especially those who are interested in the foundations of physics. Because general relativity is continually confirmed and reconfirmed the background-independence requirement has become a ‘must’ for quantum theory at the level of foundations of physics. And because Wendt’s project is at its roots about metaphysics and ontology he cannot ignore this issue. Second: social theory and political theory as well as IR theory have of late been seriously engaged in profound debates about what is termed as the ‘turn to ontology’ and which Colin Wight terms as ‘ontology as politics’. ²⁰ Stephen White describes the ontological turn of late modern times as ‘a growing propensity to interrogate more carefully those “entities” presupposed by our typical ways of seeing and doing in the modern world’. ²¹ He suggests that we divide ontologies into two broad categories: strong and weak ontologies. Strong ontologies are claims made on how the world ‘truly’ is. In contrast, for weak ontologies all ontological conceptualisations are contestable and yet such conceptualisations are necessary or unavoidable ‘for an adequately reflective ethical and political life’. ²² Wendt’s proposal will then be a strong ontology in White’s sense. These two points together – and the spirit of Wendt’s project seeking to unify social and physical theory behoves us to take them together – are mutually reinforcing in solidifying the requirement of background independence. ²³ And this poses an existential challenge to Wendt’s project of a realist flat ontology.

The ‘Problem of Time’ Challenge to Wendt’s ‘Time’

In the context of developing his understanding of ‘experience’ as part of his model of the quantum man, Wendt presents a discussion of what he terms as ‘non-local experience in time’. The entry point for this discussion is the debate over whether we can change the past (which he terms ontological view) or just interpretations thereof (which he terms the epistemological view). Based on a limited set of readings from quantum theory, Wendt opts for an ‘ontological interpretation of changing the past’, ²⁴ thereby arguing that ‘experience is temporally non-local’. Temporal non-locality specifically stands for the idea that we can change the constitutive (not the causal) nature of the past.

However, Wendt’s speculative enterprise on time, which is anchored in the Copenhagen version of quantum theory, runs into serious difficulties when considered in tandem with what physicists call ‘the problem of time’. Not only does this problem go against the notion of temporal non-locality that Wendt espouses, it also goes against the whole discussion about time symmetry breaking which, Wendt posits, is effectuated by the Will.

The problem of time is indeed a serious challenge to any quantum theory based on the Schrödinger formalism (and hence the notion of wave function) when seeking to unify it with general relativity. In the former the time variable is considered as linear and symmetric (between past and future) whereas general relativity makes time meaningful at the local level only, that is, within a small neighbourhood of the spacetime point (termed as event) under consideration. In other words, quantum theory à la Schrödinger is based on a smooth, continuous and one-dimensional topology of time (represented by the line of positive real numbers) whereas general relativity requires a much richer topology with the added feature that time as such (as we are used to it) exists only within the spacetime manifold which is definitely neither an absolute nor a universal container.

We know now, more than ever before, and with stronger scientific certainty and accuracy, that spacetime, that is, the very texture and fabric of the universe, is dynamic. ²⁵ The universe is not a flat Euclidean space but rather a pseudo-Riemannian manifold, that is, we have a spacetime manifold with a curved dynamic geometry where the universal field of gravity is nothing but the dynamic geometry of the spacetime manifold. This is a radical departure from the ‘comfort zone’ of Newtonian thinking of time as a universal, uniform ‘container’ within which everything that exists unfolds. We can therefore find different topological configurations of spacetime and going from one configuration to another can happen not only smoothly but also abruptly, hence not smoothly.

Let me briefly digress here to introduce some necessary notions of topology. Topo comes from the Greek τόπος or place, and logy comes from the Greek λόγος or study. Topology is commonly taken to be the study of the properties of space as the latter undergoes continuous deformations that can stretch or bend space without tearing any regions of space apart or gluing regions together. Speaking of topology means paying attention to continuities, connections, disruptions, breaking points, jumps, and singularities in the fabric of spacetime, which make the topography not smooth or continuous. Speaking of, and experiencing, such an unhingedness of spacetime fabric is as real an experience as any other experience of reality can be. A topologically invariant topography is one wherein distortions can occur but in continuous and smooth ways. You could for example shrink, elongate and bend surfaces and curves and thus transform them into other surfaces and curves in a continuous way, that is, without ever breaking them, like much of what you can do with a rubber band without breaking it. From a topological perspective, a doughnut is not different from a coffee mug in the sense that you can continuously, smoothly deform the coffee mug to obtain a doughnut (torus), and vice versa. In topology there is no notion of length or distance, nor is there a notion of angle either. ²⁶

Moreover, today’s far-reaching achievements in many branches of mathematics such as differential geometry, general topology, and algebraic topology make it easier to concisely and systematically conceptualise distorted and warped geometries, spaces, and manifolds. Thinkers, who are not necessarily mathematicians by training or profession, speak of Möbius strip and torus geometries in analysing many aspects of human life. Lacanian psychoanalysis comes to mind where we find it speaking of the Möbius strip and other geometrical objects, the topologies of which defy our common-sense experience. That, for example, Hamlet would speak of a ‘time out of joint’ is hence not that surprising since spacetime has a dynamic topology which can display disjointedness. We can also speak, as Derrida put it, of spacing of time – espacement du temps – which cannot be escaped and should not be ignored any more in analysing human and social phenomena. In Derrida’s words:

An interval must separate the present from what it is in order for the present to be itself, but this interval that constitutes it as present must, by the same token, divide the present in and of itself, thereby also dividing, along with the present, everything that is thought on the basis of the present … In constituting itself, in dividing itself dynamically, this interval is what might be called spacing, the becoming-space of time or the becoming-time of space. ²⁷

According to the theory of general relativity, there is no unique way or physical sense for defining a notion of universal time any more. Basic physics is explainable and describable without having resort to any notion of time (at least not in the traditional sense of the term, that is, Newtonian or even in the sense of the theory of special relativity). Einstein’s equations of general relativity admit many solutions, one of which (formulated by Kurt Gödel in 1949) allows for the possibility for a notion of closed time-like curves through every event of the spacetime. This implies that time travel is possible in such a universe, and where, as pointed in Einstein’s comment on Gödel’s solution, there will not be any good physical way to discern whether a given event has happened earlier or later than any other event on the curve. Physicists usually discount such solutions as physically undesirable in the sense that they defy conventionally agreed upon notions of time as unidirectional. However, this is no more than a common-sense-type of argument which is not theoretically justified within the theory of general relativity.

Generally speaking, any number of (more or less arbitrary) notions of time can be defined and used in a consistent way with the theory of general relativity; the following three stand out: clock time, coordinate time, and proper time. Bear in mind however that none of these has an ontological/metaphysical status as such. Clock time is defined by conveniently choosing certain physical variables as benchmarks (e.g. periods of a pendulum or vibrations of a cesium atom). These are then used as locally (and very approximately only) independent and objective measures of time. Coordinate time is a choice of a variable coordinate in an arbitrary way as part of a four-dimensional frame of reference, just like we can arbitrarily choose x, y, and z spatial coordinates in the three-dimensional space. Proper time is defined along what is called a world-line, which is the trajectory tracing the history of an object’s location in space at each instant in time in four-dimensional spacetime.

Although proper time resembles our usual notion of temporality it differs from one world-line to another and is therefore far from being uniform in the universe. Most importantly, proper time depends on the local gravitational field and the latter’s interactions with matter and energy. This feature makes proper time problematic if used in trying to formulate a theory of quantum gravity because a quantisation – transformation from classical to quantum theory – of the metric (just like we quantise, say, position and momentum of a particle in going from classical to quantum mechanics) would lead to a quantum superposition of different metric structures, thereby making it hard to define a notion of time (proper time) at the quantum level. Nor would using clock time be more helpful since the ‘clocks’ would be subject to quantum fluctuations, which would make them not that useful in defining a notion of time as we are used to it.

Therefore, preserving background independence when going into the quantum realm makes time ill-defined, if defined at all. In fact, the most prominent approaches to quantum gravity show that the notion of time drops out from all considerations. ²⁸ Applying both quantum theory and the theory of general relativity at very small length and/or very high energies forces us to abandon the notion of spacetime continuum and hence its (very vague and imprecise) sense of temporality (or temporalities). This then raises the question of how to conceptualise the dynamical behaviour of physical phenomena.

This question can be expressed in terms of the debates between relationalism and substantivalism unfolding in the philosophy of physics. ²⁹ Whereas substantivalism considers the spacetime continuum as a background stage, relationalism argues that we must think of reality in terms of relations between observable phenomena with no background stage. The world would then consist of interactions between fields and matter/energy, including the spacetime geometry or gravitational field. The four-dimensional dynamics are not an evolution in time but rather defined by the relative ‘locations’ and displacement of whatever exists in the ‘universe’. Relationalism thus requires that physical theories should be independent of any spacetime geometry and the values of any matter/energy fields interacting with the spacetime manifold.

Going back to Wendt, I do not see how one can forget about all these complexities and hard-to-resolve issues in theoretical physics and then assert with Wendt, for example, that:

my idea for how the past can be changed begins by interpreting memory recall as a process of delayed choice. ³⁰

What this shows is that wave functions are nonlocal not only in space but in time, such that “there is a collapse of the wave function on all the temporal duration bounded by the moment the photon has been emitted by the source and the moment it has been detected”. ³¹

Note that the retroactivity that Wendt speaks of when he discusses his notion of time is nothing new in social theory and humanities. Suffice it to say that Jacques Lacan’s major contribution to psychoanalytical theory through what he calls the logic of the signifier is precisely an explication of the concept of retroactivity, and, of course, Slavoj Žižek has put to work this idea in a large number of his writings as well as public lectures. Likewise, Derrida’s idea of originary performativity is also constructed around the notion of retroactivity as a coup de force (see for example, his ‘Force of Law’). ³²

The gist of Wendt’s argument starts by accepting Wheeler’s delayed-choice experiment, which according to Wheeler detects non-local temporal effects. ³³ As Wendt puts it, ‘measurement creates a particular past that was indeterminate or “open” until that moment’ ³⁴ . Wendt is claiming too much for this experiment (partly due to a selective/limited reading of the physics literature on the issue), which is far from being accepted by physicists. ³⁵ In addition, Wendt’s line of drawing conclusions in this discussion is analogical (in phrases such as ‘just as the past of a photon’) ³⁶ and he does not explicate the criteria that might convince the reader that making such an analogy is justified in the first place. As creative as these speculations on changing the past might be, they unfortunately fall short when put into the context of the general discussions about the problem of time that theoretical physics and philosophers of physics are enthralled by today.

Wendt and Other Advocates of Quantum-Theoretic Social Theory

Wendt’s is undoubtedly an ambitious agenda. He is not, however, alone on this path. There are others who also endeavour to formulate quantum-theoretic approaches that are not merely metaphors-based, analogies-driven or undergirded through conceptual translations. Karen Barad’s book, Meeting the Universe Halfway, is such an effort; in her words:

In this book I offer a rigorous examination and elaboration of the implications of Bohr’s philosophy-physics (physics and philosophy were one practice for him, not two). I avoid using an analogical methodology. ³⁷

Her argument is built around the thesis that ‘the primary ontological unit is not independent objects with independently determinate boundaries and properties but rather what Bohr terms “phenomena”’, where phenomena, in her formulation of what she terms as ‘agential realist’ framework, ‘do not merely mark the epistemological inseparability of observer and observed, or the results of measurements; rather, phenomena are the ontological inseparability of agentially intra-acting components’. ³⁸ Barad characterises the gist of her approach as reflected in the notion of intra-action. She explains that ‘The neologism “intra-action” signifies the mutual constitution of entangled agencies. That is… the notion of intra-action recognises that distinct agencies do not precede, but rather emerge through, their intra-action’, with the proviso that the ‘“distinct” agencies are only distinct in a relational, not an absolute, sense, that is, agencies are only distinct in relation to their mutual entanglement; they don’t exist as individual elements’. ³⁹ … ‘phenomena are ontologically primitive relations – relations without preexisting relata’. ⁴⁰ She explains that:

the primary ontological units are not “things” but phenomena – dynamic topological reconfigurings/entanglements/relationalities/(re)articulations of the world … the primary semantic units are not “words” but material-discursive practices through which (ontic and semantic) boundaries are constituted. This dynamism is agency. Agency is not an attribute but the ongoing reconfigurings of the world. The universe is agential intra-activity in its becoming. ⁴¹

This means that ‘relata-within-phenomena emerge through specific intra-actions’. ⁴² Barad explains that her methodological approach consists in not using ‘the notion of complementarity as a springboard’. It rather ‘directly interrogate[s] particular philosophical background assumptions that underlie specific concerns’. ⁴³ She specifically focuses ‘on the development of widely applicable epistemological and ontological issues that can be usefully investigated by a rigorous examination of implicit background assumptions in specific fields’. ⁴⁴ She describes her methodology as being diffractive ‘in analogy with the physical phenomenon of diffraction’ without implying ‘that the method itself is analogical’. She indeed aims ‘to disrupt the widespread reliance on an existing optical metaphor – namely, reflection – that is set up to look for homologies and analogies between separate entities. By contrast, diffraction … does not concern homologies but attends to specific material entanglements’. ⁴⁵

Wendt and Barad have much in common, especially in critiquing the dominant classical-physics based approaches to epistemology and ontology in social theory (and IR). For example, they both attribute a key constitutive role to the notions of entanglement and superposition. However, there is a key difference between the two: whereas Barad’s project remains at the level of the concepts of quantum mechanics (if diffracted through what she calls agential realism), Wendt does adopt one specific mathematical formulation of quantum theory, that is, the Copenhagen/Schrödinger formulation of quantum mechanics, through which he seeks to recast social. Wendt seeks strictu sensu to mould social life and consciousness into Copenhagen’s exact quantum theoretical formalism, hence his claim that he is suggesting a flat ontology that unifies both physical and social ontologies. Barad’s project is not just about presenting a framework for social theory; she contends that she is offering a new approach to quantum mechanics anchored in ‘the possibility that the agential realist account provides the basis for a more coherent and robust interpretation of quantum theory’. ⁴⁶

Whereas one must salute Barad for her ambition, I think that her project falls short in an important way. Indeed, why specifically follow (even if in a diffracted way as she puts it) Niels Bohr’s approach to the epistemology/philosophy and ontology of quantum theory? While Barad does bring into the discussion many more recent attempts that seek to address many lingering foundational issues of quantum theory (such as the problem of quantum gravity), she stops short from advancing our understanding of quantum theory. Why? Because theorists and philosophers of physics have advanced so far in their quests that one cannot simply claim to be providing a new understanding of quantum theory and social theory without giving them due attention. Wendt’s project similarly stops short. The question that essentially challenges both projects is as follows: why deploy the quantum theory of the first few decades of the 20th century (as a mathematical formalism as Wendt does or as an interpretation of Bohr’s philosophy as Barad does) in the 21st century when the physics and mathematics communities, who are interested in the foundational issues of quantum theory, have developed radically new ways that clearly demonstrate the short-sightedness of the early 20th century quantum theories and their philosophies? Both Wendt and Barad critique, and rightly so, much of social theory for still navigating a realm where much of its logic and conceptual frames are constituted by the spirit of classical physics and I would add classical logic. However, I fear that they are also falling into a similar trap by navigating their ambitious projects within the realm of early 20th century quantum mechanics. What then?

I suggest a strategy that first, will enable us to avoid moulding the ‘social’ into a given version of quantum theory and that, second, by the same token examines rigorously what is foundationally essential (which is not to say ontological or metaphysical) in the ‘quantum’ as such. ⁴⁷ Nowadays, a revolution is radically reshaping the worlds of mathematics and theoretical physics, a revolution which is anchored in the application of so-called category theory to both. ⁴⁸ Category theory begins with categories, that is, collections (not necessarily sets) of objects and the directed relations (called arrows or morphisms) linking these objects. ⁴⁹ We can also form categories of categories and the relations among these categories – called functors. Functors relate objects in one category to objects in another category and arrows in one category to arrows in the other category while preserving the structures of the categories being related. One can then define sets of functors and relations among functors called natural transformations. Relations between objects, morphisms, categories, functors and natural transformations are the ‘tools’ used to relationally theorise (so to speak), and everything is expressed in terms of directed relations (as morphisms, functors, or natural transformations). This is essentially very much in tandem with Alfred North Whitehead’s process-based approach to philosophy and science. ⁵⁰ Category theory provides nowadays the foundations for all branches of mathematics and logic, and much of theoretical physics, including quantum theory. ⁵¹

Some may wonder: why do we need to resort to category theory (a highly abstract mathematical approach)? Let me address this by asking first: what does actually constitute a ‘quantum theory’ as such? More precisely: how do physicists construct a quantum theory? It is undisputable that they do it through a mathematical formalism first and then experimental verification, and sometimes the other way around. However, in all cases quantum theories are mathematical in nature, through and through. The language and tools of mathematics are essential to the quantum. Obviously, Wendt does not do that. What he does instead is to adopt a number of quantum-theoretic ideas and concepts in combination with results developed by both physicists and non-physics disciplines (such as, for example, quantum biology). His work is definitely not mathematical in nature, depth or scope, but rather conceptual in a speculative way developed for the most part through analogising and metaphorising, his claim to the contrary notwithstanding. However, the ‘quantum conceptual’ is necessarily defined and developed through the quantum mathematical. Short of this, the situation would be much like somebody who claims to be doing statistical analysis by inscribing statistical concepts in a narrative without actually engaging in a statistical analysis proper using a statistical model and tools thereof, and so on.