Considering that the example of the 10 € works so well in describing both the possibility for an entity to be non-spatial and for a collection of entities to be indiscernibles, but nevertheless still remain individuals, one may wonder if this could be more than a clever metaphor and point to a deeper truth about our physical reality: that its building blocks would not be object-like, but concept-like. In other words, one may wonder if (1) quantum entities would behave similarly to human concepts because they share with them the same conceptual nature and, conversely, if (2) human concepts, as entities of a conceptual nature, would in return behave similarly to quantum entities, in the sense that quantumness and conceptuality would just be two different ways of speaking about the same reality.
Point (2) is in a sense less controversial than point (1), so let us start with it. The last two decades have seen the development of a new domain of investigation, called quantum cognition, which was pioneered by researchers like Diederik Aerts, Andrei Khrennikov, Harald Atmanspacher and collaborators; see for instance Busemeyer and Bruza (2012), Haven and Khrennikov (2013), Wendt (2015) and Aerts et al. (2013, 2016). Let us briefly explain the reasons why this field of study emerged. In the beginning of last century, during their investigation of the micro-world physicists were confronted with experimental data that were not explainable using the existing physical theories, in particular their logical and probabilistic foundations. It is precisely in their attempts of explaining the unexplainable that quantum mechanics emerged: a theory founded on a completely different (non-classical, i.e., non-Kolmogorovian) probability calculus. Something quite similar happened to cognitive scientists when they were confronted with unexpected data collected in the ambit of numerous tests conducted on groups of human participants, in order to study the probabilities characterizing their behaviors, or decision makings. Indeed, it emerged that in many circumstances human behavior would defy logic. In a nutshell, humans appear to be quite irrational.
As an example, we can describe the situation known as the conjunction fallacy, as evidenced in so-called Linda problem (Tversky and Kahneman 1983; Morier and Borgida 1984). Consider the following description of a person named Linda:
31 years old, single, outspoken and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in antinuclear demonstrations.
Ponder then the following two statements: (1) Linda is today a bank teller; (2) Linda is today active in a feminist movement and is a bank teller. Which of these two statements appears more plausible to you? If your answer is (2), you have just fallen victim to the conjunction fallacy, as was the case for the average opinion of the tested subjects. Now, since the idea that the concomitance of two events is more probable than the occurrence of only one of them is in evident violation of the axiomatic rules of classical (Kolmogorovian) probability theory (which in turn is based on Boolean logic), experimental situations like those evidenced in Linda’s problem, and many others evidencing different logical fallacies, cannot be properly addressed by the latter.
This forced researchers to find a different paradigm in order to model, in a consistent and principled way, some of the accumulated data, and surprisingly the perfect choice appeared to be quantum mechanics. Well, maybe not so surprisingly after all, considering that the latter was equipped with all the needed conceptual and mathematical tools for dealing with all sorts of deviations from classical behaviors. Indeed, as we said, quantum mechanics also emerged in order to describe experimental situations which could not be explained using theories based on Boolean logic and the associated Kolmogorovian probability calculus.
It would be beyond the scope of this article to tell in a convincing way the story of quantum cognition, which by the way, to avoid possible confusions, has nothing to do with the notion of quantum brain, that is, with the speculation that quantum phenomena occurring in the brain at the micro-level would play a role in the way the brain functions, particularly in relation to the manifestation of consciousness and self-consciousness. In quantum cognition, one simply observes that quantum structures can appear at some organizational level of the mental activity, in the same way that it is possible to construct macroscopic quantum machines (for instance using elastic structures with specific geometries that can break in unpredictable ways) that are able to behave in a way that is very similar to micro-entities (Aerts et al 2000, Sassoli de Bianchi 2013a, Aerts and Sassoli de Bianchi 2014).
In that respect, one should demystify the usual belief that a quantum behavior would be only the prerogative of micro-entities, being instead a form of organization that can be found at different structural levels within our reality (Aerts and Sozzo 2015; Aerts and Sassoli de Bianchi 2018). Of course, it is at the micro-level that this organization appears to manifest itself in the most remarkable way, thanks to the non-spatial nature of the micro-entities.
But also human concepts are genuine non-spatial entities, hence in the human conceptual realm their quantum-like behavior appears to be as fully explicated as that of the micro-entities, even though, of course, not all the remarkable symmetries that govern the physical microworld are also present in the much younger human conceptual domain.
Now, considering the huge success of quantum theory in modeling different cognitive situations, like those involving decision-making, conceptual reasoning, human memory and other cognitive phenomena, i.e., that human conceptual entities, when they interact with cognitive systems, appear to be very similar to the quantum entities interacting with measuring apparatuses, it became natural at some point, for one of the initiators of quantum cognition, Diederik Aerts, to ask and take very seriously the following question (Aerts 2010a, b):
If quantum mechanics as a formalism models human concepts so well, perhaps this indicates that quantum particles themselves are conceptual entities?
Aerts then formulated the following speculative hypothesis, which is today at the basis of the so-called conceptuality interpretation of quantum mechanics (Aerts 2010a, b):
The nature of a quantum entity is ‘conceptual,’ i.e., it interacts with a measuring apparatus (or with an entity made of ordinary matter) in an analogous way as a concept interacts with a human mind (or with an arbitrary memory structure sensitive to concepts).
In other words, according to Aerts’ hypothesis, the elementary microscopic entities, which we know cannot be consistently described in terms of particles and waves (or even fields), would nevertheless behave as something very familiar to all of us, as we continually experience them in a very intimate and direct way: concepts (Aerts 2009, 2010a, 2010b, 2013).
To help understand why such a hypothesis makes sense, we have to explain that concepts, like physical systems, can be modeled as entities that can be in different states, where a state has to be generally understood as an expression of what an entity is, in terms of its actual and potential properties in a given moment (Aerts et al 2016), which can be described using different mathematical notions, depending on the specific formalism adopted. For instance, in quantum mechanics states are usually described by vectors belonging to a complex vector space, called Hilbert space.
The way a concept can change its state depends on the type of context with which it interacts. As a very simple example, consider the concept Car (we will use capital letters to distinguish abstract concepts from written words, which are the traces left by the latter on a given document). When considered in the context of itself, the conceptual entity Car can be said to be in its most neutral meaning state, sometimes referred to as the ground state of the concept. But it is also possible to combine the concept Car with other concepts. This is precisely what we humans typically do when we use our language: we combine concepts in order to create new meanings.
So, if Car is combined with Fast, say in the sentence A Fast Car, its state will not anymore be considered to be the ground state, but a different “excited” state. More precisely, when we go from Car to A Fast Car, the Car conceptual entity changes its state in a deterministic way. This is similar to what happens to the spin of a neutron when it passes through a magnetic field, also producing a deterministic change of its state that one can easily determine by solving the corresponding Schrödinger equation.
But to highlight the difference between two states, beyond considerations of a purely theoretical nature, one has to perform measurements, that is, one has to subject the conceptual entity to a given interrogative context, which in general will be indeterministic. For example, take two specific examples of cars, like a Volkswagen Beetle and a Lamborghini Countach. Then ask a group of people which one of the two best represents the more abstract concept Car. As it is not difficult to imagine, some people will choose the Volkswagen Beetle and others the Lamborghini Countach, and one can expect that both exemplars will be chosen with comparable frequencies, say 60% and 40%, respectively (see Fig. 13).
Then take another group of people (or the same) and ask them the same question but this time in relation to A Fast Car. No doubts, almost all, if not all, will now select the Lamborghini Countach (see Fig. 13). In other words, the outcome probabilities will change dramatically when using A Fast Car instead of Car, i.e., when we consider different states of the conceptual entity. The same is true when performing a measurement in quantum mechanics: different states will produce different probability distributions in relation to a given set of possible outcomes.
Having said that, let us briefly describe some of the situations where the conceptuality interpretation allows one to better understand the strange behavior of the quantum micro-entities in a way that no other interpretations allows to do [for more details, we refer to Aerts (2009, 2010a, 2010b, 2013) and to the more recent review article Aerts et al (2018a, b, c)].
Non-Spatiality
Quantum entities are usually in non-spatial states because, being conceptual entities, they can be in states having different degrees of abstractness (or different degrees of concreteness), and only the most concrete (i.e., less abstract) states would correspond to those belonging to our spatial theater. For example, in the special case of human concepts, we can observe that the concept Thing, in its ground state, is undoubtedly more abstract than when in the state The Thing Is A Car, which in turn is more abstract than when in the state The Thing Is A Car Called Lamborghini Countach, which is more abstract than the state The Thing Is A Car Called Lamborghini Countach That Is Owned By My Neighbor. Clearly, this latter state of Thing brings the concept into close correspondence with the world of objects that belong to our three-dimensional space.
Heisenberg Uncertainty Principle
If quantum entities are conceptual, then they cannot be simultaneously maximally abstract and maximally concrete, which is none other than the uncertainty principle of Heisenberg rephrased in conceptual terms, now becoming perfectly self-evident. A neutron with a well-defined momentum would be a neutron in a maximally abstract state, whereas a neutron with a well-defined position would be a neutron in a maximally concrete state, and all states in between these two limit situations would be non-spatial states having an intermediary degree of abstractness (or of concreteness). In other words, there is a necessary tradeoff between abstractness and concreteness: the more we increase the former and the more the latter will decrease, and vice versa.
Entanglement
The mysterious non-spatial connections that are responsible for the creation of correlations in joint measurements, able to violate Bell’s inequalities, would be nothing but connections through meaning. In other words, if the nature of the micro-entities is conceptual, then they are expected to spontaneously and systematically connect by sharing meaning, and since meaning connections are complex (multidimensional) abstract elements of our reality, this explains why they cannot be represented as simple spatial connections detectable in our three-dimensional theater. Note that Bell’s inequalities can be easily violated when joint measurements are conducted in the psychological laboratories, on conceptual combinations that are adequately connected through meaning, thus giving further credit to the conceptuality interpretation of quantum entanglement; see for instance Aerts and Sozzo (2011) and Aerts et al (2018a, b).
Indistinguishability
Many conceptual entities, by combining with that particular category of concepts called numerals, will produce genuinely indistinguishable entities that still remain individuals. Hence, quantum indistinguishability becomes self-evident when quantumness is understood as an expression of conceptuality. Note that non classical (non-Maxwell–Boltzmann) statistics can be easily evidenced when considering certain combinations of words appearing in collections of documents.
Take for example the Ten Animals concept, which describes a collection of ten identical conceptual Animal entities. One can consider two possible states of Animal: The Animal Is A Cat (in short, Cat) and The Animal Is A Dog (in short, Dog). Then, one can perform counts, say on the Web, using a search engine like Google, to estimates the probabilities of finding these ten indistinguishable concepts in their different possible Cat and Dog states, like Eight Cats And Two Dogs, Seven Cats And Three Dogs, etc. Without going here into details, let us just mention that one finds in this way statistical behaviors that are quite similar to the Bose–Einstein one (with some added fluctuations), thus giving further credit to the conceptuality interpretation of quantum indistinguishability (Aerts, Sozzo and Veloz 2015; Aerts et al 2018a, b, c).
Quantum Versus Classical
According to the conceptuality interpretation, what we call objects are a limit situation of conceptual entities that can permanently remain in maximally concrete states. The best example of an object in the human conceptual realm or, to put it more precisely, of a concept that behaves similarly to an object, is what we call a story, i.e., a conceptual entity that is the result of a very large combination of different concepts all connected together through the “meaning fabric” of a specific narrative.
Without entering into the details, let us just mention the following interesting observation. Within the conceptual realm, concepts can be meaningfully combined using both the “and” and “or” logical connectives. If A and B are two concepts, then A And B and A Or B are also bona fide concepts. On the other hand, if A and B are two objects, then although ‘A and B’ can still be considered to be an object (the composite object formed by the combination of object A and object B), ‘A or B’ cannot be associated anymore with any object, but only with a concept, and this is one of the fundamental differences between concepts and objects.
The situation is similar for stories. In our human cultural landscape, we can find many stories that are of the form ‘A and B’, even when A and B are very long and complex stories. As an example, think of book series, which are big composite stories of the form ‘A and B and C…” On the other hand, if A and B are two full-fledged stories, ‘A or B’ will usually not be associated with a genuine (meaningful) story within our human culture. Hence, stories behave similarly to objects and the notion of story allows one to understand how certain typologies of conceptual entities, formed by the combination of numerous elementary concepts, end up behaving in ways that are similar to the way objects behave.
For a further discussion of this subtle question, about the distinction between concepts and objects, see for instance Aerts et al (2018a, b, c) and the references cited therein.
Open Problems in Physics
The conceptuality interpretation offers interesting insights into many open problems of modern physics, like the measurement problem, quark confinement, the existence of different generations of elementary particles, dark matter, the lack of evidence for supersymmetry, etc. For the exploration of these interesting issues, we refer the interested reader to (Aerts 2009, 2010a, 2010b, 2013; Aerts et al 2018a, b, c).