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.

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

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

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.

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.

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.

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.

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