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1 Introduction

Among the different areas of philosophy of science, and more generally of philosophical and scientific enquiry, on which Evandro Agazzi has extensively worked, often with innovative and original results, is no doubt philosophy of physics, a discipline introduced in Italy by his groundbreaking treatise (Agazzi 1969). That work soon established itself in the philosophical debate for the depth and robustness of the analysis carried out and for the perspective from which Agazzi interpreted the role and function of philosophy of science, which he believes cannot be limited to a formal analysis of scientific languages, as claimed by at that time dominant neopositivistic philosophy.

This conviction derived to him also from his studies on the history of physics in the late nineteenth and early twentieth century, culminating in the publication of the critical edition of Maxwell’s Treatise of electricity and magnetism (Maxwell 1973). These studies had shown that the mentioned neopositivistic claim had been largely dismissed by the most advanced developments of modern physics. In fact, a merely formal approach to physical theories left completely unsolved the most problematic issues posed by the theories of new physics, for instance the problem of unobservable entities, like ether, absolute space and time in relativitivistic theories, and the problems of simultaneously unobservable entities, as position and momentum, of the uncontrollable disturbance of the measurement processes, and of the dual nature, both wave-like and particle-like, of micro-objects in quantum mechanics.

For the previous reasons Agazzi believes that the philosophy of physics, and more generally of science, should focus its attention on the study of the foundations of scientific theories, addressing also the issues of philosophy of nature, such as the reality and the structure of physical objects, the subject/object relationship in the measurement theory, and the role of the principle of causality. These issues were considered metaphysical, in the sense of meaningless in the light of the neo-empiricist philosophy. The latter was in fact modeled on the operationalistic methodology developed by the theories of physics of the early twentieth century, without a genuine critical confrontation with them and with their open problems.

As a matter of fact, the identification of the meaning of a concept with the procedures for its measurement, which led Einstein to the elimination of the non-measurable concepts of absolute space and time, was subsequently systematized by Bridgman through the operational definition of concepts in a new conception of science, which became a sort of benchmark for neo-positivist philosophy, which aimed to defend the same anti-metaphysical instance in philosophy.

To achieve this goal, it was necessary to find a linguistic analogue of the operationistic definition, i.e. a criterion through which meaningless propositions could be eliminated, like operationism had banished non-measurable concepts from physics, and later also from other sciences (think for instance of behaviourism in psychology, which required the abandonment of non-overt phenomena as consciousness, feeling and emotion). Neopositivists found a linguistic correlate of operationism with their criterion of verification, or verifiability, according to which the meaning of a statement is given by the method for its verification. Therefore, when this is not possible and, moreover, we are not dealing with an analytic and tautological sentence, we have a meaningless pseudo-proposition, and this was the case of philosophical principles.

2 Beyond Bohr’s Complementarity: A Realist View on the Wave-Particle Duality

The most significant example of this itinerary in Agazzi’s reflection is undoubtedly constituted by the question of the wave-particle duality, considered by the neopositivistic perspective of the orthodox interpretation as a metaphysical pseudoproblem devoid of meaning. At a variance with such a view, Agazzi on the grounds of his wide knowledge of the history of physics, considers the wave particle duality as the new and fruitful experimental evidence from which quantum mechanics originated, as a theory that unified at the elementary level the classical concepts of matter and radiation and their different descriptions given in classical physics respectively by Newtonian mechanics and Maxwell’s electromagnetic theory. Moreover Agazzi stresses the ambiguous and unsatisfactory response to that question given by Bohr’s principle of complementarity, which according to him could be viewed from two completely different points of view.

From the first viewpoint complementarity can be narrowly interpreted as synonymous with uncertainty in the sense that the wave properties and the particle properties of a micro-object are to be considered incompatible, as position and momentum, or as energy and time, according to the Heisenberg principle. This interpretation is due to the most definitely antirealistic variant of complementarity, shared by the theorists of the German school in Göttingen like Heisenberg and Jordan , and it establishes a form of unsurpassed incompatibility between the wave description and the particle description of atomic phenomena, an incompatibility that Pauli extended even to the logical and mathematical level.

From the second viewpoint complementarity is more properly considered as a synonym of the wave-particle duality, i.e. in terms of a real dilemma between one or the other of these different representations of physical reality, because on the one hand the use of both concepts seems to be required by an adequate explanation of the dual behavior of micro-objects, and on the other hand such descriptions appear experimentally incompatible within any one physical situation.

According to Agazzi this second interpretation, corresponding to the original formulation of Bohr’s principle of complementarity, is however at the origin of the most serious epistemological and ontological contradictions, that would result from the assumption of a different nature of the same object in different situations.

This is one of the problems that led Agazzi to develop his concept of scientific realism, which constitutes the core of his philosophical reflection. The point is to establish the cognitive value of scientific theories, when it appears in question, or at least when it is doubtful whether an objective value can be attributed to our theories. In this regard Agazzi highlighted the existence of three different meanings that can be attributed to the term ‘objectivity’, i.e. “objectivity as intersubjectivity, as invariance, and as correspondence” (Agazzi 1969: 364). Through an effective and very detailed analysis (Agazzi 1969: 339–357, 1979) he showed that these three senses can be identified.

The conditions that make possible that intersubjectivity, invariance and correspondence (to objects) may coincide from a conceptual and epistemological point of view are essentially, at least for what concerns Agazzi’s contribution to the philosophy of physics, three:

  1. 1.

    the operationistic foundation of scientific concepts and the fact that, although based on operations, these concepts cannot be reduced to a purely operationistic dimension;

  2. 2.

    the finding that the meaning of scientific terms is essentially contextual;

  3. 3.

    the fact that scientific objects, though made of properties established in an objective manner through operations, are not simple aggregates of those properties, but well defined structures of relationships between these properties.

As we shall see, these three points are strongly interconnected, especially for what concerns the scientific concepts expressed by the so-called theoretical terms, i.e. concepts of non directly observable entities, like that of the wave function of quantum mechanics. Let’s look briefly at each of these three points of Agazzi’ perspective.

1. Scientific theories are built on the basis of theoretical terms, but their purpose is to provide explanations for the facts of immediate experience, describable by empirical (or observational) terms. This raises the problem of how theoretical terms could keep a link with the empirical reality (Agazzi 1969: 138–139). A theoretical concept like ‘electron’ is a “theoretical construct around which we group many properties operationally definable” (ibid: 146). And it is precisely this operational aspect that allows theoretical terms to maintain a contact with experience, and so to have a physical meaning (Agazzi 1997: 49–65). However, these theoretical terms cannot be reduced directly to operational terms denoting sets of operations:

(…) We would not even dream of saying that theoretical concepts can be reduced to operational concepts: who pretended this, would like those who thought of reducing the house to the bricks that make it up (Agazzi 1969: 147–148).

The various combinations of empirical (operational) terms produce constructs, the theoretical terms, which are no longer themselves directly operational. This point is relevant as it provides the philosophical basis for the attribution of a physical reality to the wave function, although it is not directly “observable” (or measurable), i.e., even if it cannot be defined directly in operational terms. Still, any theoretical entity must be associated with some detectable properties.

2. It follows that the meaning of theoretical terms is always a contextual meaning. As specified by Agazzi, this

is not to say (…) that the physical meaning [of theoretical terms] comes from observational terms thanks to a context (…), but that it precisely comes from the context in which observational terms are present, but not alone, because the context actually consists even of all the mathematical and logical connections that link the various concepts, observational and not observational (Agazzi 1969: 148).

The context within which the theoretical terms assume a definite meaning is nothing but the theory in which they appear, and which they contribute to form. Only a theory as a whole can be empirically interpreted and then be put in relation with possible observations. This point is of the utmost importance for a realistic interpretation of the quantum mechanical wave function. According to Agazzi, most of the problems in the interpretation of quantum mechanics derive from the attempt to apply concepts of classical derivation to the objects of quantum theory. Because of this contextualistic nature of theoretical terms, the solution cannot be sought through some unusual combination of classic, corpuscular and wave-like concepts: “Not only we can, but we must say that it is not the same particle, it is not the same wave of which we speak in classical mechanics, because the contexts are different” (ibid: 271).

From this arises the need to explore really new concepts to overcome the difficulties associated with a realistic interpretation of quantum mechanics, concepts that are new “not only, as already happens, for the simple fact that they derive from the combination in a new way of classical concepts, but also for the fact that they replace all or part of these classical ‘components’ with something really new” (ibid: 285).

3. In relation to the third point mentioned above, we have already recalled that the scientific objects denoted (very often) by theoretical terms, are relational structures of operationally definable properties, but they cannot be completely reduced to such properties. This idea, which as we have seen is fundamental in Agazzi’s thought, is closely linked to the contextual nature of theoretical terms:

The object is always a structure, a structure of relationships, most of which can be the result of operations, but whose co-existence is not justified by any operation, although they should be objectively verifiable (ibid: 374).

Now, trying to reconstruct this structure is really the main task of scientific theories, for “the structure is not what lies underneath the experimental determinations and the characteristics objectifiable, but it is what is made of them: it is precisely the object.” (ibid).

On the other hand, it is precisely this structure that makes the world what it is; and it is because of this structure that our theories, as attempts to reconstruct the structure, may be wrong, to the extent that the structure they describe is not that of world, or of the universe of objects that constitute the domain of the theory. This conception of the structural nature of theoretical entities will be crucial to understand what kind of reality can be attributed to the wave function.

We have already mentioned the considerable difficulties connected with the interpretation of this theoretical term and we also saw that Agazzi very pointedly identified the roots of the problem in an inadequate emancipation of the orthodox interpretation of quantum mechanics from classical concepts, deriving from a too narrow operationistic conception that completely identified the meaning of physical concepts with measuring operations performed on them.

Agazzi’s rejection of a rigidly operationistic and phenomenalistic view of physical theories is indeed one of the main aspects of his philosophy of physics, based on a refusal of the distinction, dear to positivism and considered by Agazzi as completely artificial, between observational and theoretical concepts. Thus he proposes his original solution, according to which “a physical concept does not denote a single operation (or a single set of operations), but an equivalence class of operations (or sets of operations), which originates from an operation, but cannot be identified with it” (Agazzi 1969, p. 128). This solution, improved and formalized in Agazzi some years later (1976), will then be largely developed in a systematic logical approach to the foundations of physical theories (Dalla Chiara and Toraldo di Francia 1979).

A very persuasive example that it is not the use of the instrument to determine in a strict sense the meaning of the physical concept investigated by means of it, is provided from electromagnetic phenomena that can be, and often are, measured through mechanical instruments. Nevertheless this fact does not prevent, as stressed by Agazzi, the recognition of peculiarities of these phenomena and the introduction of new concepts such as charge, current and induction, all of which are clearly non-mechanical, although they are detectable on the basis of their mechanical effects recorded by mechanical instruments.

The explanation lies in his thesis of the contextualist nature of the meaning of physical concepts, according to which, as we saw earlier, a single physical concept is subject to different characterizations that depend on the different levels or contexts in which it appears. In this way, a concept such as “material particle” is seen in the context of classical physics as an object that has both a well defined position and well defined momentum; instead in the context of quantum physics, because of the uncertainty relations, it loses the simultaneous possession of such properties, but it takes on new properties, like spin.

According to his contextualistic perspective, perhaps even the conceptual difficulties of the complementary interpretation of the wave-particle duality could then be solved by assuming that the classical concepts, considered at a formal level, appear as the elements of a semantic combination in which the original contradiction disappears, because it is not formally linked to the concepts themselves, but only to their classic denotation.

3 A New Non-classical Concept for a Testable Realist Interpretation of the Wave Function

Agazzi believed, however, that this view cannot provide a definitive solution to the ontological problem of the nature of micro-objects. He pointed out, with extraordinary intuition, the need to introduce in microphysics concepts that are new not only because they represent the result of a new combination of classical concepts, but also because they are able to replace their classic components with something new. As he emphasized again some years later:

Only by inventing some new concepts, that is, new in this fundamental sense, we could possibly overcome the present uneasy state of affairs, which is not related to the regret of losing the old concepts, but to the lack of new concepts capable of adequately replacing them (Agazzi 1988).

It seems really surprising that in the same year in which Agazzi emphasized the need of a new philosophical concept to solve the problem of wave particle duality, Franco Selleri proposed a realistic interpretation of the wave function of quantum mechanics based on the introduction of such a new concept. This was the concept of empty wave, later replaced by that of quantum wave, which can be considered as a sort of synthesis with respect to the three different concepts of duality between waves and particles that had been proposed by the main founders of quantum theory.

That notion was reminiscent in the first place of Einstein’s point of view: the founder of relativity, despite having reintroduced in physics a corpuscular theory of radiation by his famous hypothesis of light quanta, believed that interference and diffraction phenomena were not explicable on the basis of a purely corpuscular theory, but required also a wave to accompany and guide the quanta in their motion. But the fact that all the energy was concentrated in the quantum, and that the wave associated with it was consequently devoid of this fundamental property, led Einstein to introduce for such a wave the term ‘Gespensterfelder’ (ghost field).

When de Broglie, with his wave theory of matter, then extended the duality from radiation to matter, in an attempt to overcome the contradiction due to the “existence” of an entities without the properties that characterize any other physical object, like his pilot waves, he found no other way to ensure their reality, than attributing to them an extremely small portion of energy, almost entirely localized in the corpuscles (de Broglie 1927). But since no one has been able so far to reveal this very small amount of energy, the typical objection to de Broglie’s waves is that they are metaphysical rather than physical.

A third conception bearing significant similarities to the preceding one, but also unable to achieve an adequate empowerment towards classical notions, was introduced by Bohr, Kramers and Slater in their attempt to reformulate a purely undulatory theory of radiation in opposition to the corpuscular hypothesis of light quanta (Bohr et al. 1924). This was the concept of virtual wave, to which these authors attributed the fundamental characteristic of carrying neither energy nor momentum and of producing only “stimulated transitions” in the atoms the wave interacted with. Atomic transitions would thus allegedly occur in open violation of the laws of conservation of such physical quantities, since any given atom could pass from one energy level to another, without any energy exchange with the electromagnetic field. The concept of virtual wave, however, was soon abandoned as a result of the experiments by Bothe and Geiger (1924) and by Compton and Simon (1925), who provided a decisive confirmation of Einstein’s hypothesis of the corpuscular nature of radiation.

None of the above authors therefore, while elaborating concepts quite similar to that of quantum wave, succeeded in formulating a really new concept: neither Einstein, who having contributed more than any other to the definition of the concept of energy, and turned it into the central notion of physics modern, found contradictory to assert the existence of objects without this fundamental property; nor de Broglie, who after establishing the wave theory of matter, could not conceive waves without energy and momentum, and proposed to ascribe them an uncontrollable amount of the previous properties; nor Bohr, Kramers and Slater , whose virtual waves had been introduced as an alternative to the corpuscular hypothesis of light quanta, and who after the failure of their purely undulatory theory of radiation prudently replaced it with Born’s probabilistic and strictly corpuscular interpretation of the wave function of 1926, before Bohr’s dualistic solution of the complementarity principle.

Selleri’s paper of 1969 already contained the basic elements of the decisive conceptual turning point in the interpretations of the wave particle duality, of which Agazzi had clearly highlighted the need in the same year.

Starting from Einstein’s and de Broglie’s realistic conception that waves and particles exist objectively, and from the fact that experiments show beyond any reasonable doubt that all the energy, momentum, angular momentum and charge are closely associated with the particle, Selleri asked what could be an entity existing without being associated with any directly observable property. He considered unsatisfactory de Broglie’s response that all physical properties would be primarily associated with the particle, but that a small fraction of them, so small as to have escaped all possible observations, is associated with the wave. He then proposed that “even if devoid of any physical quantity associated with it”, and therefore not directly observable, “the wave function can still give rise to observable physical phenomena” (Selleri 1971: 398). He pointed out that we do not measure energies, momenta, or similar physical quantities only, but also probabilities, as in the case, for example, of the average life of an unstable physical system. According to Selleri, the wave function could therefore “acquire reality independently of the associated particles, if it could give rise to changes in the of transition probabilities of the system it interacts with” (ibid.).

On the basis of this new idea of a non-classical wave, he proposed the first version of his experiment for detecting the physical properties of quantum waves. To this end he considered a piece of matter composed of unstable entities, such as nuclei, atoms or excited molecules, traversed by a flux of neutrinos. The experiment then consisted in measuring the average life of such entities under these conditions, and comparing them with the average life of the same entities in the absence of any particle flux. If any difference was observed, the only logical explanation, according to Selleri , was that such difference was due to the action of the wave function, since neutrinos are particle that interact very weakly and only few of them, in the best case, can interact with the piece of matter (ibid.).

Some years later Selleri improved his original idea by the experiment shown in Fig. 1 (Selleri 1982): instead of a flux of neutrinos we have photons emitted by a Laser, and we have no longer a piece of matter composed of unstable entities, but a laser gain tube LGT. Moreover we have two detectors DT and DR and a semireflecting mirror SM. The latter behaves in the same way as the double slit: the particle is propagated in one direction only, depending on whether it has been transmitted or reflected by SM, whereas the wave, according to Selleri’s hypothesis, is both transmitted and reflected.

Fig. 1
figure 1

Selleri’s original experiment on quantum waves

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Selleri proposed to focus on the cases in which DR, located along the reflected beam, detects a photon: this means that in the transmitted beam only the quantum wave is present. According to Selleri’s hypothesis, however, the wave can reveal its presence by generating the stimulated emission of photons; these in turn can be detected by DT) after passing through the laser gain tube LGT, whose molecules are at an excited level corresponding to the wavelength of the incident wave. In this way the coincidences between the detection of DT and DR would reveal the propagation of a quantum wave, transmitted by SM. The space-time propagation of these entities could be studied by verifying whether the DT–DR coincidences disappear when an obstacle is placed in the transmitted beam in front of LGT. According to Selleri, a positive result of this experiment would have shown that “something having neither energy nor momentum but that can produce transition of probabilities propagates in space and time.” (ibid.)

Louis de Broglie, welcomed and endorsed Selleri’s idea as an important attempt

to obtain a more satisfactory interpretation of wave mechanics than that presently adopted, confirming the idea that guided me when in 1923-24 I proposed the basic conceptions of wave mechanics (de Broglie 1969).

However framed this new idea within his old classical conception of the pilot wave: “The experiment you propose to prove the existence of this wave Ψ will be of great interest to prove the existence of this very weak (très faible) wave, which carries the particles” (ibid.).

Selleri’s realist interpretation was received with great favor a decade later by another great opponent of the Copenhagen interpretation, the philosopher Karl Popper , who joined to it unconditionally, abandoning its original statistical and closely particle-like interpretation:

Franco Selleri has suggested, continuing the work of de Broglie, that waves without particles may exist. The consequences (of this proposal) would seem to be revolutionary … They would establish in place of the “complementary” character of particles and waves (wavicles) the interaction of two kinds of real objects: waves and particles (Popper 1985 ) .

But neither de Broglie nor Popper, while expressing the greatest interest and appreciation for the hypothesis of quantum waves, grasped the essential novelty of this concept, which instead was perfectly understood by Agazzi, since it was an instance of the radically new concepts of which no one before him had so lucidly pointed out the need in order to resolve the contradiction arising from the wave particle duality.

In his contribution to a volume of Italian studies on the foundations and philosophy of physics (Agazzi 1988), Agazzi noted that this conceptually new hypothesis of quantum waves was important for its refusal of the symmetrical nature of duality, and different from the classical approach of de Broglie:

The essential novelty of this concept is represented by the acceptance of de Broglie’s realist interpretation of the wave-particle duality, but not of the symmetrical nature of this dualism. In Selleri’s approach both particles and waves are simultaneously real, but the latter can be characterized only by its relations with the particles, i.e. by the observables properties of producing interference and stimulated emission. Such a possibility implies an ontological priority of particles over waves, which therefore belong to a weaker level of physical reality, containing objects which are sensible carriers of exclusively relational predicates (Agazzi 1988: 73).

Several experiments have been proposed for this new realistic interpretation of the wave function, whose interest, as pointed out by Agazzi, is twofold: on the one hand they allow to test this realist interpretation against the Copenhagen one, experimentally discriminating between two different philosophical interpretation of a given physical theory, an opportunity without a precedent in the history of science. On the other hand, these experiment could also provide the opportunity to control the well known axiom of the reduction of the wave function. Concerning this last point Agazzi noticed that by using the properties of quantum waves it seemed possible to ascertain the paths followed by a photon within an interferomentric device, revealing at the same time the interference pattern in the distribution of their recordings, a possibility utterly excluded by the reduction postulate.

Thus it seemed possible to establish an important connection between the wave-particle duality and the other fundamental problem of quantum measurement. Unfortunately, however, none of the experiments carried out so far has revealed the assumed properties of quantum waves, nor refuted the postulate of reduction.

4 Realism of Properties, Realism of Entities and Their Role in Microphysics

Already during my university studies between 1973 and 1977 I came in contact with the work of Evandro Agazzi, in particular with his work in the philosophy of physics (Agazzi 1969). I remained deeply impressed by his refusal of the identification of philosophy of science with epistemology, and by his consequent belief that the former cannot be limited to matters concerning the form and language of scientific theories, according to the neo-empiricist perspective, but it should also address issues related to their contents, namely problems of philosophy of nature. He held that philosophy of physics must be identified with a survey on the fundamentals, in the sense both of an enquiry in the epistemological foundations of physical theories and an analysis of their philosophical implications, and this soon became the perspective guiding my research on the foundations of quantum mechanics.

In addition to this fundamental methodological lesson on the need to conduct the research in philosophy of science as a study of the foundations of scientific theories, Agazzi influenced my philosophical perspective in an even more direct way, by his conception of scientific realism, and its specific application to the fundamental concept of theoretical quantum mechanics, that of the wave function, which we have discussed so far.

Unlike the neo positivists Agazzi vindicated a substantial autonomy of the philosophical inquiry with respect to scientific research, and as we saw from his discussion of the principle of complementarity he had an approach to scientific theories very different from neopositivism. However, to this philosophy he recognized the merit of not having upheld the cognitive value and the intersubjectivity conception of science:

Neopostivist epistemology, despite having been deeply influenced by Mach’s thought, has come to accept more or less explicitly a realist view of science. We do not care to discuss here how consistently this could happen: it is sufficient to note that such an outcome was imposed by the cultural program of the entire movement, which was characterized by a view of science as the only authentic source of knowledge (Agazzi 1985: 173).

Besides,

the obsession with which neo-empiricism tried to impose absolute fidelity to experience, and the reducibility to it of the very theoretical components of science, can also be seen as an effort to ensure a solid connection with reality (ibid.).

Moreover we know that the main theses of traditional philosophy, including those of realism, had been refuted by the logical empiricists as meaningless, as generally corresponding to propositions of existential content that are not empirical and for which there is no method for determining their truth value.

Instead research on the EPR paradox showed the possibility of supporting a completely different point of view, by showing a clear form of logical incompatibility (which through Bell’s theorem could be turned into an experimental discrepancy) between the quantum description given by some particular state vectors, the so called entangled states, and a very reasonable principle of reality, which identified scientific objectivity with predictability with certainty, considered as a sufficient condition for physical reality (Einstein et al. 1935). It was thus shown uncontroversially that such a realistic principle could meet those requirements of verifiability that the neo positivists believed to be completely inapplicable to philosophical propositions. Thus it became clear that the acceptance of confirmability as a criterion of meaning (but not of scientificity, since scientificity is subject to the stronger requirement of Popper ’s falsifiability) allows to reformulate some of the main metaphysical theses in terms of philosophical principles endowed with factual meaning. In a nutshell, according to my point of view, scientific propositions must be falsifiable, whereas philosophical ones can only be disconfirmable.

It has also be shown that there are other formulations of realism endowed with meaning. The first was discussed one year after EPR by Carnap , who analyzed a realistic hypothesis proposed by Lewis in terms of the proposition: “If all minds disappeared from the universe, the stars would still go in their courses” (Carnap 1936–1937). Moreover he highlighted that this statement satisfied the most stringent requirements of factual significance, since it is controllable, albeit incompletely.

Other non-metaphysical variants of the reality principle include various probabilistic generalizations of the EPR criterion: for instance, while the original EPR criterion required predictability with certainty (a strong idealization with respect to actual physical situations), I suggested to replace it with predictability with a high degree of inductive probability (Tarozzi 1979); later on, together with Selleri , I modified it by considering the a priori probabilities themselves as real properties (Selleri and Tarozzi 1983).

The common feature of these different realistic principles (EPR, probabilistic EPR, Carnap) is the attribution of reality not to the object but to its predictable properties. This agrees with the logical empiricist refutation—anticipated by Kant’s critique of existence as a predicate—of the identification of reality with a (further) property of a physical object, an error that persisted for a long time in the debate on the EPR paradox.

Nonetheless, the shift of reality from the object to its predictable properties allows to preserve the notion of independence from the observer (and from his mind or consciousness), which is at the basis of metaphysical realism. The latter, in fact, as defined by Hume , is the doctrine that reality is what would exist, though we and every sensible creature were absent or annihilated. There is a perfect continuity between metaphysical and empirical realism, and the main difference is that the latter, considering the predictability through our best theories as a guarantee for reality, appears to be based on science, and in our case on physics, whereas, according to the former it is science that is to be based on realism.

It was Agazzi’s analysis of the relationship between scientific objectivity and reality, in particular his claim that the latter includes the former (i.e., that being objective takes more than just being real) to be seminal for my investigations, since it enabled me to understand the EPR principle of physical reality in the new light, as I have explained earlier.

He however rightly points out a kind of opposition between this realism of properties or attributes and his realism of objects or entities, and since many years ago and up to the present (Agazzi 2014) he advised me to supplement the reality of the properties, which seems to him rather dim, with that of the object. His exhortation was one of the reasons that led me to investigate, after the EPR problem, also the possibility of an alternative realistic interpretation of the wave function, and to design experiments to test it.

In any case, I feel that empirical realism of the properties and scientific realism of the objects are both fundamental and indispensable issues to any scientific theory; and my dissatisfaction with quantum mechanics stems from the fact that this theory seemed rejects the attribution of physical reality both to its predictable properties and to its basic concepts.

But a recent ideal experiment, which might be easily converted into a real experiment, seems to show that this double anti realistic claim of the standard interpretation is no longer sustainable, and that either Agazzi’s realism of theoretical entities, and or empirical realism of (predictable) properties correspond to an essential condition in the interpretation of quantum mechanics.

The experiment aims to assess the possibility that quantum waves produce correlations at distance of the EPR type, identifying in this way a new perspective that would establish a deep and hitherto unsuspected relationship between the two previously discussed ways of interpreting realistically quantum mechanics.

In fact, consider a pair of photons produced by a non-linear crystal, which propagate in the device illustrated in Fig. 2. Any photon can be detected by the two “near” detectors (D1 and D2), which are placed after a shorter path, or by the two “far” detectors (D3 and D4), placed after a longer path. If we do not take into account all the cases in which both photons are detected by D1 or D2, the physical situation will be described by the state vector

Fig. 2
figure 2

Another experiment discriminating between the realistic interpretation of the wave function and the reality of the predictable properties

Full size image
$$ \left|\uppsi \right\rangle = \frac{1}{\sqrt 2 }\left[ {\left| 1 \right\rangle \left| 4 \right\rangle + \left| 2 \right\rangle \left| 3 \right\rangle } \right] $$

that presents some formal analogies with an entangled state, but is actually an ordinary superposition state.

According to the previous description, if detector D1 clicks, we can predict with certainty that D4 will click, and, if D2 clicks, we can predict that D3 will click. In this case the observed correlations can be considered as a consequence of a wave-like behavior.

It is interesting, now, to see what happens if we displace detectors D3 and D4 to a position before BS4 (broken lines), once a photon has already been detected by D1 or D2. We have then a delayed-choice experiment (Wheeler 1978), but with an important difference: in our case, an event has already occurred (D1 or D2 has already clicked) before the choice. In this case, we can obtain information about which photon has been detected by D1 or D2 and which photon has been detected by D3 or D4. Now, although we can know which photon has been detected by which detector and therefore the paths they follow, we cannot predict whether detector D3 or detector D4 will reveal the photon after either detector D1 or detector D2 has clicked.

We also observe that, on account of the first interference (by BS2) and of the superposition of the two components of the i-photon and of the superposition of the two components of the s-photons, the latter situation (when detectors D3 and D4 are placed before BS4) is not the classical situation that would arise if both BS2 and BS4 were removed. In this case, if D1 clicks, we know with certainty that the i-photon has been detected and that the s-photon (if not detected by D2) will reach D3. On the other hand, if D2 clicks, we know with certainty that the s-photon has been detected and that the i-photon (if not detected by D1) will reach D4. Our proposed experiment differs from others designed to test the complementarity principle, because in those experiments, in general, many runs are needed in order to obtain an interference (wave-like) pattern at the detectors. In our experiment, on the contrary, the effect of the wave-like pattern is shown in single runs, hence for individual systems.

Now, if we are able to predict something different and new (i.e., whether D3 or D4 will click) when we have wave-like behaviour relative to the predictions allowed by the particle-like behaviour, we see no reason for not attributing an ontological reality to the wave. Still, it is clear that they cannot have the same kind or degree of reality as particles, which are well localized and possess directly measurable properties. On the contrary, measuring directly waves or quantum states is intrinsically impossible: the existence of these objects can only be inferred.

5 Conclusions

This weakness represents also the strength of our point of view, which allows us to highlight the possibility that an entity could exist without possessing intrinsic properties. For, as we have seen, the wave-like properties of the two photons depend strongly on the experimental context. This means that the decisive reason for which it is not possible to directly detect the quantum waves is that they would belong to a level of reality inherently relational, as it was clearly underlined both by Selleri and Agazzi.

For the orthodox interpretation, which completely denies the physical reality of the wave function, this relational character would be peculiar to atomic particles. To a certain extent this is true, given that in an experiment of complementary type, such as that considered above, what we reveal depends on our experimental arrangement. However, the very act of detection is by definition the detection of a particle or the recording of an event (and this result can also be stored and communicated), and this explains the asymmetry between ontological recordable events and relational wave-like entities, the assumption that Agazzi, as we saw in Sect. 3, considered as the truly new element in the conception of the quantum wave.

Another strong reason to ascribe physical reality to quantum waves is that between wave-like and particle-wave behavior, there is a continuum of possible cases, as it has been shown by the existence of the so called smooth complementarity, i.e. the possibility of a smooth variation between wave-like and particle-like behaviour and consequently of infinite intermediate possibilities between the two extreme alternatives (Mittelstaedt et al. 1987). Obviously, this runs against Bohr’s idea that complementarity is a sharp relation in which we have either the wave or the particle.

Our proposed experiment seems to show that perhaps one could distinguish experimentally between EPR’s realism of properties and the realism of theoretical entities: the presence of correlations between remote detections of photons would highlight the physical reality of the quantum wave, violating the realism of EPR and confirming the predictions of quantum mechanics, as happened with the experimental controls of Bell’s theorem, while the absence of correlations would disprove quantum mechanics in favor of EPR’s empirical realism.

The former result, which is certainly the more probable (although we cannot rule out the second one without before running our experiment) would be a direct experimental confirmation of Agazzi’s realism of entities, and of the need to find a counterpart in physical reality for fundamental theoretical concepts.

A new feature of our experiment is also that it does no longer discriminate between a realistic and an antirealistic (Copenhagen like) interpretation, but between two different realistic interpretations of quantum mechanics. In my opinion this represents a decisive confirmation of the necessity of a realist interpretation of scientific theories, which Agazzi has always considered an epistemological assumption indispensable to any serious philosophical inquiry.