De Rerum (Incerta) Natura: A Tentative Approach to the Concept of “Quantum-like”

Abstract

In recent years, the term “quantum-like” has been increasingly used in different disciplines, including neurosciences, psychological and socio-economical disciplines, claiming that some investigated phenomena show “something” in common with quantum processes and, therefore, they can be modeled using a sort of quantum formalism. Thus, the increasing use of the term “quantum-like” calls for defining and sharing its meaning in order to adopt it properly and avoid possible misuse. There is a fil rouge linking both pre-Socratic and Eastern philosophies and quantum physics, suggesting an epistemological symmetry between them. In our opinion, the concept of “quantum-like” may be successfully applied to macroscopic phenomena and empirical sciences other than physics when the following two conditions are satisfied: (a) the behavior of the investigated phenomena show logical analogies with quantum phenomena; (b) it is possible to find a criterion of truth based on an experiential/scientific approach applied to a probabilistic model of description of the phenomena. This is only a first small step in the approach to the concept of “quantum-like”, which will hopefully be helpful in promoting further discussion and achieving a better definition.

1. Introduction

“Truth is born as a paradox and dies as the obvious”

A. Schopenhauer

Since the birth of the Galilean sciences, physics has been considered the most rigorous scientific discipline, relying on mathematics as the essential tool for demonstrations and discovering immutable laws of nature from a deterministic perspective. This view is embedded in the century-old Western rationalist thought, from Aristotle through to Aquinas’ rational theology, the 17th century rationalist revolution, Enlightenment, Empiricism, and Positivism. As a result, one perceives physics as a source of rock-hard certainties, a fact also favored by the naïve optimism and the faith in science permeating the end of the 19th century. In this climate, the great physicist Lord Kelvin emblematically stated before the British Association for the Advancement of Science, in Bradford, in September 1900, that:

“There is nothing new to be discovered in physics now. All that remains is more and more precise measurement”

(quoted by Alexander [1])

It was only a brief Victorian calm before the quantum storm unleashed by Max Planck; the revolution he introduced on 8th October of the same year is known today as quantum physics.

Quantum physics was not only a new theory. Indeed, it initiated a slow cultural evolution that now, over after 120 years from its introduction, has extended far beyond the boundaries of physics to spread to other disciplines (e.g., biology and neurosciences) and every aspect of life, promising to yield a shift of paradigm and a change of Weltbild (image of the world). Actually, it has led to the foundation and the inflexible certainties of the classic Western thought being dismantled and the realization that knowledge cannot be as rock-hard and immutable as formerly believed, at least if the teaching of Max Plank is not left behind.

The quantum theory stems from the concept of quantum, a term often misunderstood; it is usually perceived as “the smallest”, while it in fact means “an amount of”, i.e., it indicates a quantity; if this is the case, it calls for defining the thing it refers to. According to the original definition by Plank, the quantized object was energy [2]. Then, according to Einstein’s interpretation of the photoelectric effect [3], it became light (and the quantum of light took the definition of “photon” in 1926), and, following the novelty of the double nature of light, it was also extended to matter (the electron), due to the work of De Broglie [4]. In other words, the stuff of the quantum has evolved over time, encompassing different “things”.

The huge impact of quantum physics is not limited to the knowledge of the infinitely small world; it deeply involves philosophy and culture as a whole and, as such, a profound change of the human way of perceiving and comprehending reality [5]. If this is the case, it is endowed with inescapable metaphysical, epistemological, and psychological implications. As a result, the approach to the concept of “quantum-like” calls for outlining the following: (a) what the term quantum refers to; (b) the main logical and philosophical issues raised by quantum physics, especially the metaphysical constraints of the classical way of reasoning hindering the comprehension of a part of reality and making the realm of quantum world ostensibly absurd; (c) the compatibility of the quantum paradigm with pre-Socratic and Eastern philosophies; (d) the main mathematical–physical aspects involved in the “quantum-like” approach and their application in disciplines other than physics.

2. From Rei to Rerum

The Latin term res (from Sanskrit rāḥ, “thing, ownership, wealth”) has been widely used in philosophy to define the nature of reality, from the De Rerum Natura (The Way Thing Are) by Titus Lucretius Carus (based on Democritus’ atomism) to the Cartesian concepts of res cogitans and res extensa. Indeed, ontology is the study of “things” and their nature, of what exists, of universals, of properties of entities, as well as their relationship. Any res is generally considered to exist as a separate entity, while, from a linguistic standpoint, the term is used to name an undefined object or entity. Therefore, in this context, one can use the term res to deal with physical objects, using it in the singular or the plural form as appropriate. If one introduces the concept of “reference”—namely, describes its features in the attempt to define it—what is dealt with are attributes of the “thing”, justifying the use of the Latin res in the genitive, where the singular and the plural form have different meanings. Here, the term rei can indicate the object of the quantity initially defined by the word “quantum”—i.e., what properly belongs to quantum physics—while the term rerum (such as in Lucretius’ poem) entails a broader meaning encompassing the logic of quantization in other contexts. Therefore, it does not pertain to a single object but involves other entities, including matter, and may also extend to other things belonging to the macroscopic reality when the rerum behavior shows some likeness with quantum phenomena in a broader sense.

According to Lucretius, when dealing with the rerum definition ‘without considering the intervention of the gods’, the aim is the rational explanation of natural phenomena. Since physics (from Greek φύσις) is the first and fundamental reality—the principle and cause of all things—and the pre-Socratic philosophers were considered physicoi (physicists), the term “physics” has been generally regarded as synonymous with nature. It follows that the meaning of De Rerum Natura is an attempt to explain physical phenomena, in a broad sense, rationally. Since everything is part of nature, virtually every field of knowledge can be included in the description of rerum, going beyond the proper definition of rei in quantum physics to arrive at the more general definition of rerum as any physical object. Thus, it seems appropriate to add the term “like” to the definition of “quantum”—viz., quantum-like—when dealing with phenomena in other fields of knowledge showing some likeness with those described by quantum physics.

3. A Question of Logic

In recent years, the term “quantum-like” has been increasingly used in different disciplines, including neurosciences, and psychological and socio-economical disciplines, claiming that some investigated phenomena show “something” in common with quantum processes and, therefore, they can be modeled using a sort of quantum formalism. Accordingly, several neologisms—such as quantum economics, quantum finance, quantum cognition, quantum hypnosis, quantum psychology, and quantum medicine/neurology [6,7,8,9,10,11]—have been introduced in the literature, leading to the quantum interpretations being involved over an increasingly wide range of rerum. This highlights the great appeal of quantum physics, despite its ostensible unintelligibility, when approached through the prism of classic post-Aristotelian thought; a fact, in turn, revealing an increasing dissatisfaction with its method of interpretation of reality. Thus, the problem is endowed with substantial epistemological and metaphysical implications; accordingly, there is also a need to shift from the original physical definition of the term quantum to make it compatible with its use in various aspects of the macroscopic world.

Given all this, it is necessary to address the point relating to the “logic”, understood as the study of the laws and functions that characterize the structure of thought. While the logic of classical physics has been deterministic, in quantum physics it has become probabilistic and admits some contradictions—due to its various interpretations, especially the Copenhagen interpretation in 1927—a fact entailing a shift of paradigm with respect to the ruling post-Aristotelian logic. The latter may work in many instances of everyday life, but may not correctly confront events appearing inevitably probabilistic (e.g., weather forecast [12]). Therefore, the rationale behind quantum phenomena might be extended to understand other wonders of the macroscopic world, where the classical, determinist model may fail to define them properly.

In the climate of post-Enlightenment rationalism, it is not surprising that science adopted a determinist approach; it can be considered the long-term result of the claim to know the substance and the essence of phenomena in a Weltbild ruled by the principle of causality. This led to the Newtonian universe being conceived as a “big clock”, and human beings and animals being reduced to “small clocks”, with their machinery immersed in the bigger clock they belong to.

The full expression of scientific determinism has been introduced by Laplace:

“We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain, and the future just like the past would be present before its eyes”

[13]

Laplace’s statement is axiomatic and/or hypothetical at best, since no human being might ever reach such knowledge; it is tantamount to a faith stating that God knows everything, but, even admitting His being, He would anyway be in the dimension of eternity, beyond the space–time in which humans live. Accordingly, Popper rejected determinism, defining it as an ideology rather than a theory [14]. A full determinism is hypothetical rather than real, entailing a conventional approximation—i.e., the threshold above which the effects are considered as the result of the initial conditions, neglecting the variability below the established threshold. As a result, predictability is necessarily approximate; according to Popper et al., “Causality yes. Mathematical causality, or exact causality, no” [14]. Thus, the introduction of a criterion of truth based on an experiential logic applied to a probabilistic model seems more reasonable with respect to an alleged determinism, and a properly defined concept of “quantum-like” might be more flexible in the interpretation of physical phenomena, understood as De Rerum Natura.

In our opinion, the concept of “quantum-like” may be successfully applied to macroscopic phenomena and empirical sciences other than physics, when the following two conditions are satisfied: (a) the behavior of the investigated phenomena show logical analogies with quantum phenomena; (b) it is possible to find a criterion of truth based on an experiential/scientific approach applied to a probabilistic model of description of the phenomena.

4. Why a Concept of “Quantum-like”: Epistemological Implications

The increasing appeal of the quantum paradigm, justifying the introduction of the term “quantum-like”, seems to be dependent on the limits of Western classical thought to interpret all phenomena of the macroscopic world properly. Hence, an insight into its limits, as well as its advantages, is an essential step to frame the problem properly. Its detailed discussion is far beyond the aims of this article, but outlining a few fundamental aspects is necessary to envisage the reasons for the introduction of the “quantum-like” concept (for a detailed analysis, see [15,16,17]).

Aristotle is the philosopher that has contributed more to the development of rational thinking in the West. In fact, in his Metaphysics and in Prior and Posterior Analytics, he funded a rigorous logical strategy that aimed to discern the real from the false through a clear distinction of logical and illogical reasoning and, as a result, of facts from fancies. The Western way of reasoning has followed Aristotle’s strategy, based on his tripartite logical system—i.e., the principle of identity, the principle of non-contradiction, and the principle of excluded middle (or Third)—and his metaphysical assumptions, also adopted by modern sciences; this entails that both metaphysics and scientific knowledge are logical and closely connected.

Western philosophy has pursued the ἐπιστήμη (epistème, from the Greek ἐπι- and ἱστάναι, that means “what stands above”), i.e., a certain, indisputable knowledge overcoming any doubt and negation, seeking the immutable, the essence, and substance of phenomena. This has led to a static way of reasoning, taking the unchanging for truthful, and, what seems to be contingent, swinging between being and not-being becoming illusory or irrelevant.

Subsequently, the posterity turned the Aristotelian logic into an undiscussed, dogmatic doctrine [15,16,18]. The overestimation of the power of syllogism, induction, definitions, tripartite logic, and the split of reality according to a stiff dichotomous criterion (true vs. false; 1 vs. 0) has led to nature being a priori constrained within one’s mental categories. This, in turn, has led to the relative being taken for absolute and the particular for universal. Given the underestimation of the limits of available knowledge at any given time, one has been inclined to judge truthfulness or falsity according to one’s ignorance, as well as one’s knowledge. As emphasized by Popper, this also entails the possibility of retransmission of falsity by logic in empirical sciences [19], including the risk of deviation from reality yielded by the closure of investigated phenomena within the limits of selected facts, theories, and mental categories—what Edgar Morin defined as the delusion of abstract conceptual coherence [20].

Unlike Socrates and Democritus, Aristotle—referred to by Dante as “Who teaches to all who know”—knows to know, while post-Aristotelian thought has been strongly inclined to believe to know, also taking beliefs for knowledge. In other words, Aristotle introduced a positive knowledge, while Democritus and Socrates were fully aware of not knowing, “for truth lies in the abyss” (Democritus, fragment DK 68 B 117). Their stance is in line with the Greek concept of ἀλήθεια (alḗtheia, truth)—etymologically stemming from the privative alpha in front of -lḗtheia, in turn deriving from the term λανθάνω (lanthano, concealed, hidden, unknown). Therefore, alḗtheia means that knowledge and truth are only truthful fragments grasped from the unknown. Accordingly, they used the elenchus (refutation) and reductio ad absurdum, rather than the Aristotelian use of induction and syllogisms, to be taken as proofs of positive knowledge.

The century-old Western rationalism paved the way to the outstanding rationalist revolution of the 17th century and the birth of Galilean sciences. Still, they were based on a political compromise with the Church—claiming the exclusive competence on the soul (consciousness)—rather than a free epistemological reflection. The Cartesian dualism, ontologically splitting the res cogitans and res extensa, aimed to favor the compromise by saving the soul for the Church, although made it unfathomable with the scientific method based on Galileo and Descartes’ mathematical–geometrical apriorism. Therefore, it made the res extensa and res cogitans incommensurable, a sort of metaphysical guillotine, leading to the observer being excluded from the observed facts [15,16].

In broad terms, the classic Western thought has been inclined to commit a sin of naivety, i.e., the illusion to know the reality as it is in itself and possess the truth by a seemingly foolproof method. Nevertheless, despite its undeniable value, it is neither the only possible method, nor the perfect one, to be exclusively adopted. Especially in empirical sciences, its products remain dóxa (as for all axiomatic knowledge, as emphasized by Aristotle himself (Metaphysics 1005b, 1–5)), providing valuable partial models of the reality, at best. Metaphorically, some brittle bricks have been inadvertently used to build up the inflexible Western rational scaffold, leading to it being cracked by the quantum quake of the early 20th century.

If this is the case, the pre-Socratic and Eastern philosophies may help find a fil rouge—or, perhaps better, a sort of epistemological symmetry—between ancient thought and quantum physics, and help restore the cracks. Actually, it is no accident that quantum physicists were the first scientists to take consciousness seriously in the early 20th century, and approached both pre-Socratic and Eastern philosophies, opening their minds to a non-dualist view encompassing the whole world. This issue was well addressed in the 1970s by Frank Capra in his Tao of Physics [21], where he stated in the preface that:

“Eastern mysticism provides a consistent and beautiful philosophical framework which can accommodate our most advanced theories of the physical world”.

The topic was also appraised in 2011 by Kaiser, in his book dealing with the activity of the Fundamental Fysiks Group and its interpretation of the quantum entanglement in terms of Eastern mysticism and psychic mind reading [22].

Despite the relevance of ancient Greek and Eastern philosophies having been suggested for almost one century, many (perhaps most) philosophers and scientists are not yet familiar with their paradigms and concepts, and remain firmly anchored in the comfort zone of classic Western thought. Therefore, an outline of some essential concepts of these philosophies, with their close links and epistemic relevance, remains an essential step in terms of discussion, especially when dealing with the concept of “quantum-like”, which that extends to disciplines other than physics, and to the macroscopic (e.g., classic) world.

Pre-Socratic philosophers were called φυσικοί (physicoi, physicists) as they investigated the natural world, referred to as ὅλης φύσεως (hólēs physeos, the whole)—including both the material and (ostensibly) immaterial realms, viz. body and mind, matter and energy, atom and void—with a non-dualistic paradigm contemplating the complementarity of opposites, a paradigm akin to Taoism [23]. Then, following the parricide of Parmenides by Plato and Aristotle, the rational approach to reality was affected by nihilism (i.e., the idea that what exists is doomed to become nihil) [24] and an increasing dualism, the edge of which is Descartes’ thought embedded in an inflexible rationalist stance. Hence, the opposites were ontologized and substantialized, making them incompatible, paying the high price of an irreconcilable split of what in nature is united; this has, in turn, led to monist materialism prevailing in positive sciences, although it is an ill-founded, self-contradictory metaphysical stance, a long-term result of Cartesianism [15,17].

Quantum physicists have introduced an entirely new paradigm in the Western cultural landscape, able to explain the realm of the infinitely small and rejoin what classical thought had unduly split; at the same time, it is old as the hills, reappraising the wisdom of the first physicoi and Eastern philosophers. Democritus plays a central role in physics for his theory of atoms and void. Like other pre-Socratics, Democritus’ theory has been puzzling and considered paradoxical or self-contradictory—swinging between atomism, empiricism, and skepticism—when analyzed through the prism of post-Aristotelian thought [25]. In his theory of atoms and void, he moves a step forward, along with Parmenides’ concept of being, by defining the elementary basis of the physical world in its appearance, where the void is not tantamount to nihil but exists as an essential component of the appearance of being. Void is the complementary counterpart of matter, without which the latter could not exist and be perceived as such. At the same time, atoms serve as the basic units of the manifold, dynamic, ever-changing appearance of the world emanating from the Being. In other words, Democritus allows the merging of the concepts of Parmenides’ Being and Heraclitus’ dynamic world of becoming, into a whole, where:

“Opposition unites. From what draws apart results the most beautiful harmony. All things take place by strife”

(Heraclitus, Fragment DK 22B8)

This also accounts for the coherence of Democritus’ proto-empiricist approach to nature. In fact, his analysis starts from what is given, where he holds an epistemically sound and outstandingly modern view—compatible with Poppers’ fallibilism, the model-dependent realism introduced by Hawkins and Mlodinow [26] as well as the Popper and Eccles’ Theory of the Three Worlds and its new neurophenomenological version (NTTW) [17,27].

This model-dependent realism establishes that no concept of reality, independent from descriptions and theories, may exist. Therefore, the sciences may only provide more or less reliable partial models of reality able to make correct predictions. According to the NTTW, world 1 is the physical world, and world 3 is the world of consciousness and mind products, while world 2 is the brain–mind–sense organ unit, the processor allowing one to record information from the outer world and convert it into subjective experiences and all mind products (including philosophy and science). Likewise, in model-dependent realism, the world 3 engenders partial (more or less valid) models of world 1 and, through human creativity, can materialize its products; as a result, the reality, as one knows it, is an inseparable co-creation of world 1 and 3 through the coding rules of world 2. These theories are perfectly consistent with Democritus’ argument:

“…In reality, we know nothing about anything; but for each of us there is a reshaping-belief … to know in reality what each thing is in character is baffling” (Fragment DK 68 B 7, 8)… We know nothing in reality; for truth lies in the abyss”

(DK 68 B 117)

Rather than a skeptic stance, it is a well-founded awareness of the intrinsic limits of rational knowledge of nature, in perfect agreement with Socrates’ awareness of not knowing and Kant’s “natural illusion” of humankind, taking concept and mental images for the reality in itself [28]. It is worth underscoring the substantial agreement between Democritus’ theory and the above-mentioned theories, aiming to overcome the limits of both Cartesianism and monist materialism, and merge both the physical and mental dimensions into an integrated, inseparable whole, a fact pertaining to quantum physics and philosophy at the same time.

Democritus’ enlightened view has, unsurprisingly, made him the great father of modern physics and cosmology [29] and, we argue, of quantum physics. In fact, his intuition regarding the atomic structure of matter was confirmed by physics in the 19th century (i.e., 2300 years later), an epoch when matter’s discrete or continuous structure was still debated. The subsequent discovery of the atom as a complex, rather than indivisible, entity has seemingly overcome Democritus’ theory. On the other hand, one should refrain from simply applying to Democritus’ concept of atom the meaning it currently has.

Democritus’ ἄτομος (atomos) indicated the smallest, unperceivable, indivisible unit of the physical world, which he established by outstanding intuition. Thus, his a-tom does not necessarily correspond to what we today refer to as an atom, and may well fit the elementary subatomic particles at the deepest level of reality; if this is the case, the whole of his atom and void may also fit the concept of virtual particles and quantum vacuum. Since (a), energy is subject to transformation but never becomes anything, and (b), matter (as an expression of energy [30]) may disintegrate and disappear but cannot result in an absolute nihil, one can argue that Western nihilism is wrong; it is a result of naïve realism rather than a product of reason, as already established by both Parmenides (Perì Phýseos, 2) and Hippocrates:

“Neither a thing may become nothing nor anything not previously being be may start to be, but everything changes for mixing and separation… It is not possible that what is not may start to be”

(Hippocrates, De Diaeta I, 4, 9)

Therefore, the ancient thought was right when establishing that everything in the phenomenal reality appears and disappears by aggregation and separation from a virtual, unknown, and unobservable part of reality, what in quantum physics is referred to as Grid [31]. As a result, it seems reasonable to liken the Grid to the concept of Tao (Dao in pinyin transliteration) and Parmenides’ Being, as well as the Hindu deity शिव (Śiva), lord of the timeless cosmic dance that is the origin of the appearance–disappearance–regeneration of the world, a fact making so evocative the statue of Śiva at CERN in Geneva.

Fortunately, reason is much more than a given form of rationalism, and science is much more than the inflexible use of a given paradigm; likewise, reality is not tantamount to realism, while nature is much more than any narrow model of it, and disregards the clumsy attempts of humans to constrain it within a given set of axioms and theories established a priori. This is the fundamental reason for the scientific and concurrently epistemological revolution introduced by quantum physics.

5. Why a Concept of “Quantum-like”: The Relevance of Eastern Philosophies

A few key concepts of Chinese and Indian philosophies are relevant in this context (for a detailed analysis of their relevance and for a transcultural, metaphilosophical approach in psychology and philosophy of mind, see [23,32]).

Lăozĭ defines Dao in the Dàodéjīng as the unnamable, the mother of all creatures; it manifests itself through the Yin–Yang principle, i.e., the dynamic, ever-changing reciprocal relationship of two opposite, complementary polarities, neither of which endowed with an autonomous existence. This paradigm allowed Taoism to establish, conceptually, the mutual transformation of matter (Yin) and energy (Yang) into each other over 2000 years ago, as well as the inseparable relationship of mind–body–outer world.

Likewise, the Veda tradition includes both the dualist school Dvaita Vedānta and the non-dualist school Advaita Vedānta. The former identifies Jivatman (the individual soul) and Brahman as two separate non-interchangeable entities, while the latter holds the inseparability of individual ātman from Brahaman. Nevertheless, both the individual soul and Brahman remain components of a unique reality, allowing one to solve the ostensible contradiction between these monist and dualist stances in the Bheda-Abheda doctrine (where bheda means division, separation, and multiplicity, and abheda means unity and non-separation), establishing a simultaneous difference–non-difference, its eternal continuity, imperishability, and all-encompassing nature of the ultimate reality behind diversity.

In short, the above-mentioned principles are akin to Parmenides’ light and dark and Heraclitus’ convergence and harmony of opposites, in a non-dualistic view encompassing complementarity, a principle rediscovered by Bohr in quantum physics.

Four epistemically relevant key concepts of Buddhism are worth mentioning, which are: (a) māyā (the mask of illusion of ordinary consciousness); (b) anitya (impermanence, anicca in Pali); (c) śūnyatā (reality as vacuity); (d) pratītyasamutpāda (the interdependency of all entities, no one being endowed with autonomous and intrinsic existence). Māyā warns against naïve realism and perfectly agrees with the above-mentioned Democritus’ and Kant’s views, while anitya establishes the ceaseless transformation of the world, in line with both Daoism and Heraclitus’ view. Śūnyatā defines the reality in itself (e.g., world 1) as made of what remains once the modalities of perception, qualia, mental objects, mental images, and categories are filtered out. Nâgârjuna and the Madhyamaka-Prasangika school established the correspondence between śūnyatā and pratītyasamutpāda, emphasizing that the latter defines a related mode of being, where observable phenomena are halfway between being and not being—rather than autonomous, steady res endowed with an immutable essence and related by plain causality.

All the above-mentioned Sanskrit terms are surprisingly modern, perfectly matching the ontology of the relationship and the non-separability held by quantum physics [33]. Indeed, the paradoxes of quantum physics and its ostensible absurdity, which depends on post-Aristotelian Western ontology, can be solved by endorsing these concepts and holding a symmetric relation of co-generation, i.e., the bidirectional relationship of world 1–3 and their co-creation of the world (as it is known). Here, there is no need for claiming intrinsically existent res endowed with a definable immutable or enduring substance and essence.

6. Why a Concept of “Quantum-like”: Mathematical and Physical Implications

Quantum physics has allowed for major development of the knowledge of atomic and subatomic world, providing an outstanding insight into the intimate nature of matter and revolutionizing both its classical conception and the paradigm for its study. Thus, according to Popper and Eccles, physics—the most “materialist” and determinist of disciplines—has been able to transcend itself, leading to the dissolution of the matter–energy classical dualism [27]; furthermore, it has undergone radical criticism of the classical Western thought, leading to a shift from the ontology of properties to the ontology of relationships. The former, adopted by classical physics, conceives things as separate entities endowed with well-definable features with their essence knowable through Aristotelian induction, embedded in a local world where they may undergo reciprocal relationships. The latter, adopted by quantum physics, establishes that things manifest themselves only through reciprocal interaction, a fact implying their correlation—i.e., their description can only be obtained through the information obtained from the interaction.

The ontology of relationships, as well as the irreducibly probabilistic nature of investigated phenomena, makes quantum physics a non-essentialist discipline able to provide reliable models of investigated phenomena according to the uncertainty and complementarity principles and the inseparable relationship between the observer and the observed, rather than trying to define what things are in themselves. This stance entails the need for leaving the inclination to a static substantialization and ontologization of the res, and trying to grasp their relationship through an empirical and mathematical approach able to predict their dynamic behavior.

If the above discussion is correct, the paradigm of the quantum physics may be regarded as a bright (though ostensibly paradoxical) formal way to analyze the rerum behavior, where the reunification of observer–observed allows for its application beyond the limits of the physical world; indeed, it may justify its extension to the interpretation of the world of consciousness, cognition, social sciences, and, in general, of human and biological life, to be considered as constitutive parts of the same, single, interrelated world.

Toffano and Dubois [34] recently introduced a Quantum-like Eigenlogic Program, an operational–geometric approach moving beyond the limits of Boolean logic and admitting the superimposition of logical inputs, the non-commutativity of operators, quantum probability, and entanglement. It promises a “quantum-like” approach to logic and, being logical, the formal study of functions and laws of reasoning; it is independent of the content of involved propositions, allowing for its extension beyond the limits of quantum physics.

7. The “Quantum-like” Interpretation in Neurosciences and Social Sciences

A detailed analysis of all “quantum-like” studies in disciplines other than physics is far beyond the limits of this article. Here, it is only worth outlining a few in the field of neurosciences in order to provide the reader with a glimpse of their structure and potential relevance.

An increasing number of articles have been published in the past two decades on “quantum-like” interpretation of cognition, decision-making, and game theory, especially in uncertain or conflicting situations [35,36,37,38,39,40]. According to Bruza [36], the classical probability calculations are based on Boolean logic, and include a rationale and a heuristic approach. The former is a deductive (e.g., top–down) method based on subjective probability and expected usefulness theories, including Bayesian algebra (taking into account personal beliefs/opinions and their incorporation into the decision-making process). The latter can be considered as a bottom–up method in that it encompasses simple ad hoc rules that humans can learn during the process. At any rate, the Boolean logic is commutative, while human decision-making may be non-commutative in many instances; here, it is of crucial interest the fact that both the additive rules and Bayesian formula are violated in quantum probability calculation, where the existence of incompatible observables is closely related to the uncertainty and complementary principles, and can be managed as non-commuting operators [35]. This suggests that quantum probability calculation might be more suitable for properly confronting human cognition and decision-making processes.

For instance, Wagner et al. [41] tested a quantum probability approach, known as quantum question equality, for non-commutative decisions using data from Gallup survey experiments and two experimental studies, where the same questions were placed in different orders to determine if judgments might depend on their sequence. The results suggested the effectiveness of their quantum approach in social and behavioral science. Similar results have been reported in the two-stage gambling game and Prisoner’s dilemma game, in which participants violated the principle of sure thing of decision theory, and their behavior might be better predicted by quantum probability calculation [42].

In this regard, it is worth considering that the effects of non-commutative sequences of questions and statements on decision-making are far from new. In fact, decisions have been deeply affected by the art of rhetoric, and the art of persuading, since the times of Protagoras and Gorgias, where a proper connection of different propositions to each other may engender a sort of crescendo of perceived plausibility and truthfulness, leading to the listeners being convinced by the orator’s opinions. Plato and Aristotle themselves were strongly concerned with the power of rhetoric to strongly affect the ἀπόδειξις (apódeixis, demonstration, proof). It is eternally the same conditions of social life, including politics, buying and selling, advertising, mass media, as well as disputes in courts and scientific debates (a fact leading to the conflict of interest disclosure being introduced in order to warn participants). Therefore, what the theory of probability—be it classical or “quantum-like”—may pursue is essentially a better quantitative estimation of the results of qualitatively well-known facts since antiquity.

More recently, Khrennikov et al. have introduced a quantum model of socio-political processes based on lasing theory, referred to by the authors as social lasing [39], the operational formalism of which is a carrier of information describing them in terms of the emission and absorption of social energy with its social color. The energy source is the information overload yielded by mass media and the internet, and the Bose–Einstein statistic is used to manage indistinguishable social excitation, i.e., the bandwagon effect.

To summarize, the “quantum-like” approach is increasingly appealing, and has provided valuable models in disciplines other than physics with promising results. Its use in psychology and neurosciences is probably the most relevant, since the observer’s mind plays a central role in all disciplines, while human factors are of paramount importance in the dynamic processes of disciplines, such as economy and finance. The available studies are relevant, although the final definition of the “quantum-like” properties in the explored fields of knowledge calls for further study checking the effectiveness of the introduced models. As far as psychology is concerned, there are major implications of quantum probability calculation, as well-depicted by Sloman [43]:

“Mathematical models of cognition so often seem like mere formal exercises. Quantum theory is a rare exception. Without sacrificing formal rigor, it captures deep insights about the workings of the mind with elegant simplicity… QP [quantum probability] theory is consistent with some of the most central phenomena in psychology… At this point, QP theory is just a theoretical framework and not a fully-fledged theory of judgment. This is true of all theoretical programs in the field of judgment that attempt to do more than fit data from a small number of experiments”.

Finally, it is worth taking into account that communication is a very complex and ambiguous phenomenon, where the conceptual aspect and the sequence of statements are only a part of it; therefore, superposition and indistinguishability may depend on both the uncertainty of conditions and the ambiguity of language, while non-verbal components of communication may deeply affect the meaning of the same sentence [44]. These are factors of paramount importance in human communication; for instance, they are endowed with relevant implications in the doctor–patient relationship, where they may help improve, or be a cause of worsening, patient’s conditions through placebo and nocebo responses [45,46,47]; therefore, it is worth considering whether a “quantum-like” approach might also help to better detect and manage them as indistinguishable variables.

An example of the ambiguity of language is the term “entanglement”, which has become increasingly fashionable outside the field of quantum physics and may risk being interchangeably used as a “quantum-like” property (according to quantum entanglement) or appearing synonymous with a close relationship on a case-by-case basis. In physics, the quantum entanglement defines the condition in which the quantum states of two or more res must be described in reference to each other, even when the individual res may be spatially separated; it also raises an epistemological issue, i.e., it questions the principle of local realism. In common language, the term “entanglement” defines a situation or relationship one is involved in, and that is difficult to escape from (see the Cambridge Dictionary, https://dictionary.cambridge.org/dictionary/english/entanglement, accessed on 10 January 2022). If this is the case, the term “entanglement” is endowed with different meanings and encompasses both ordinary and quantum phenomena; as a result, there would be no reason to use its quantum meaning for its scientific appeal alone when a simple relationship compatible with the classical view of the world is dealt with. On the other hand, it may be more correct when an apparent non-local connection is investigated, such as in some intriguing studies on the entanglement between pairs of separated subjects, where a signal (e.g., a flash stimulation) delivered to a subject may be to some degree detected by the distant partner and activate his/her brain visual areas [48]. In such a case, one may arguably consider it as a “quantum-like” phenomenon, since there is no apparent information transmission. Other intriguing cases of non-causal relationships might also fit Pauli’s and Jung’s concept of synchronicity as a sort of particular case of entanglement in the world of consciousness [49]. Nevertheless, the use of the term “entanglement” according to its common meaning (indicating a close relationship) is not wrong in itself and may be correctly used. The point is not to bring up the quantum physics when it is not necessary, and to properly use the “quantum-like” approach when appropriate.

8. Conclusions

The birth and spread of the prefix “quantum-” to disciplines other than physics, and the introduction of the term “quantum-like”, reflect the increasing dissatisfaction with the perceived limits and pitfalls of classic Western thought. Of course, the latter remains valuable; what is wrong is its dogmatic use and the claim of its exclusive capacity to comprehend the world. The development of quantum physics has been paralleled by the introduction of paraconsistent logics, such as fuzzy logic and dialetheism, a clear sign of the need for smoothing the inflexibility of Aristotelian logic. Dialetheism, introduced by Priest in 1998 [50], assumes that some propositions and their negations may both be true; however, not rejecting the classical logic, it admits that some propositions (not all, in order not to fall into trivialism) may be true contradictions, i.e., both their statement and their negation may hold. In fuzzy logic, the classical binary classification true vs. false (1 vs. 0) is replaced by the full range of values between 0 and 1, where 1 is totally true, 0 is totally false, and all the other values are intermediate degrees of truth [51]. Thus, it admits the possibility of a mix of degrees of truth and falsity, allowing for the building decisional trees in systems entailing some uncertainty of parameters, a fact usually occurring in medicine where fuzzy logic has been successfully used [52,53].

The increasing use of the term “quantum-like” calls for the defining and sharing of its meaning in order to properly adopt it and avoid possible misuse. To this end, its conceptual definition is essential as the topic involves scientists and philosophers belonging to different disciplines, and that may have no or only minimal acquaintance with the mathematical formalism of quantum physics. As a result, the “quantum-like” approach may be used in different ways, entailing the following three different levels of application:

(a)

A strong version, where the term “quantum-like” is used more rigorously—i.e., it concerns experimental studies where data are analyzed by the quantum mathematical apparatus, such as the above-mentioned quantum probability calculation or the lasing theory.

(b)

A weak version, when the problem is approached from an epistemological perspective without using the quantum mathematical apparatus—such as in theoretical studies and new hypotheses analyzing the observed phenomena and their similarity with quantum behavior through a sound rational approach meeting the conceptual framework of quantum physics; for example, this may be the case of new hypotheses in disciplines, such as economy and psychology.

(c)

A wrong version, when authors unfamiliar with both the concepts of quantum physics and its mathematical formalism borrow its terminology simply for its appeal. A similar instance of this has already occurred in the past years, with the prefix “neuro-“ applied to disciplines other than neurosciences in what has been called Neuro-Mania by Legrenzi and Umiltà [54]. According to the authors, the alleged neuro-approach in studies, courses, and projects—e.g., neuro-ethics, neuro-economy, neuro-politics, neuro-marketing, neuro-design, etc.,—often reflected the wish to provide other disciplines with a whiff of scientific garb (neurological) in the hope to gain recognition, financial support, and advice. Of course, an inappropriate use of the term “quantum-like” may only detract from the glory of both physics and the involved discipline.

In fact, one should wonder whether the traditional view of individuals as separate, autonomous, independent entities is correct, or, rather, they should be considered as inseparable, interrelated parts of a single world, as already well defined by both the ancient Eastern and Western thought and the modern theory of complexity. Should this view be endorsed, there would be no need to borrow terms, such as “entanglement”, from quantum physics. Instead, the ancient thought should be seriously reappraised, submitted to scrutiny through a rigorous transcultural and transdisciplinary approach, and implemented, a fact possibly leading to a shift of paradigm and a new Weltbild. If that were the case, the term “quantum-like” might be restricted to its strong version only, or even become no longer necessary once its principles were implemented into the worldview, becoming a part of ordinary reasoning.

To summarize, the increasing use of the term “quantum-like” and other related terms borrowed from quantum physics to describe macroscopic phenomena is a relevant fact endowed with major epistemological implications; still, it needs to be better defined to avoid improper use and possible unscientific or irrational drifts. In fact, the appeal of the term “quantum-like” seems to reflect, on the surface, a deep unease with the limits of the classic Western thought and a need for moving further. If 20th century physics has undergone a radical revolution, other disciplines—e.g., medicine and life sciences—have remained anchored to Newtonian physics, for it seems to explain reasonably well the order of magnitude of the investigated phenomena. Nevertheless, the newborn quantum biology and the quantum theories of consciousness are promising fields of investigation [55,56], while several topics in disciplines other than physics seem to be better understandable using the “quantum-like” approach.

Thus, the “quantum-like” topic is worth being taken into due account and properly defined. We believe that it may be legitimately applied to macroscopic phenomena and disciplines other than physics when the conditions mentioned above are met, namely: (a) the behavior of the investigated phenomena show logical analogies with quantum phenomena; (b) it is possible to find a criterion of truth based on an experiential/scientific approach applied to a probabilistic model of description of the phenomena.

Of course, this is only our provisional opinion, which will hopefully be helpful in promoting further discussion and achieving a better definition of the term.