The situation is quite different in the context of measuring a quantum sys-tem. Indeed, in this case, the measuring apparatus, which is always of a classical nature—both in terms of its material constitution and the nature of the quantities measured—interacts with a system that is quantum. The latter, as indicated in (1), is generally described by a superposition of states corresponding to different values of the measured physical quantity. However, the classical measuring apparatus, by its very definition, can only result in the selection of a single value for this quantity. Therefore, it can be stated that, in general, the measurement of a quantum physical quantity does not simply reveal a pre-existing property of the system, as is the case in classical physics31. It is thus natural to think that something fundamen-tal occurs when two radically different physical categories, namely the classical measuring apparatus and the quantum system, are confronted.

However, the preceding discussion relies on an implicit double assumption. The first, which translates into the common semantic shift I mentioned earlier (32)33, consists of assuming that the state vector describes a single system, not a collection of systems. It is this assumption that allows the interpretation of a superposition of states, as in expression (1), as an intrinsic property of a particular system, rather than as a statistical property of a collection of such systems34.

The second implicit assumption lies in considering the state vector as an objec-tive property of a physical system. However, in what is traditionally known as the Copenhagen Interpretation, formulated by Bohr, Heisenberg, Born, and others, this is absolutely not the case. Instead, the state vector is considered a subjective quantity that does not pertain to the physical system as such, nor to its properties, but only to the state of our knowledge about that system. Bohr is very clear—and very radical—on this point: “There is no quantum world. There is only an abstract description of quantum physics. It is a mistake to think that the task of physics is to discover what nature is made of. Physics is concerned with what we can say about nature”. In such a position, typically referred to as “positivist”, the transi-tion from deterministic evolution (4) to non-deterministic evolution (6) is neither fundamental nor dramatic, as it merely reflects the shift from one subjective state, where multiple possibilities coexist—symbolized by the sum over states {| an⟩}—to another subjective state—symbolized by the state |ak⟩.

This opposition between two radically different viewpoints—one defending the existence of an objective reality for quantum systems, considering the measure-ment apparatus merely as an instrument for investigating their properties, and the other emphasizing a physics reduced to the organization of knowledge that we can derive from these experiments—lies at the heart of debates about the interpretation of quantum mechanics.

Quantum Mechanics: An Incomplete Theory?

For proponents of a realistic view of physics, such as Einstein and Bell, physics cannot be reduced to a mere description, especially a probabilistic one, of what we can know about the world. According to them, there must exist an objective reality, independent of observation and the observer, at the origin of quantum phenomena. The possibility of a more objective quantum mechanics rests on the fact that, as we have highlighted, this theory merely provides probabilistic predictions, testable only on a statistical ensemble of systems, while remaining silent about the properties of an individual system. Einstein, along with others, thus hypothesized that quantum mechanics, in its current form, is an incomplete the-ory. This means that there must be a more fundamental level, where a system is characterized by objective properties, represented by so-called “hidden” variables. In this hypothesis, the use of the probabilistic formalism is merely a provisional solution, awaiting a deeper level of understanding.