The Difficulties

After this brief overview of the formalism of quantum mechanics, it is time to explore some of its implications. The first remarkable point lies in the way, within this formalism, the description of a classical system—based on the concepts of position and velocity, thus on the notion of trajectory—is replaced by a descrip-tion based on the notion of the state vector. In this framework, the abandonment of the pair (x,p) is justified by the impossibility of conceiving a state in which these two quantities would be simultaneously well-defined, as we have clarified earlier. This point constitutes one of the most revolutionary aspects of quantum mechanics, as the human mind—whether of a layperson or a physicist—remains deeply attached to the idea of localizing an object in space as well as its continuous evolution within this space.

This renunciation of what one could call classical realism was not without resistance and, in fact, is not yet fully accepted by everyone. However, for the vast majority of practitioners in the field, quantum mechanics, as a system of pure experimental predictions, has overwhelmingly proven its effectiveness. It is therefore appro-priate to stick to this, that is, not to question too much the nature of “quantum reality”, or even to consider this question as a non-issue. This pragmatic attitude can be perfectly summarized by the famous ironic formula of American physicist David Mermin: “Shut up and calculate”.24 25 One can largely subscribe to this posi-tion of ideological—or more precisely, epistemic—neutrality by recognizing how much the question mentioned above and, more generally, that of the properties of a quantum system, has become a real quagmire. There are, at the very least, twenty distinct attempts to clarify this situation, grouped under the generic term “interpretations of quantum mechanics”, as mentioned below. This neutrality can also prove fruitful, as it preserves the possibility of achieving a deeper understand-ing of these issues within the scientific practice itself. The answers to the questions raised might, indeed, emerge within an expanded conceptual framework, such as that of a theory of quantum gravity.

Nevertheless, examining the relationship between the elements of the formalism, as presented above, and what can be called the question of ontology—that is, the question of the existence in itself—of quantum systems, deserves attention. This question has indeed been raised by eminent physicists, such as Albert Einstein and, later, John Stewart Bell, who contributed to the emergence of one of the most revolutionary concepts in quantum mechanics: entanglement. Again, we will adopt as neutral a position as possible, presenting the various viewpoints that have developed around this issue.

A simple way to enter this intellectual maze without getting lost is to closely examine the nature of the terms used within the formalism. What immediately strikes is that the fundamental element of this formalism, the state vector, plays a purely probabilistic role and, in a strictly operationalist perspective, a statistical role. Indeed, as mentioned earlier, strictly speaking, the predictions of the theory do not apply to an individual system but to a collection, an ensemble of systems prepared identically. In this context, the state vector |Ψ(t)⟩ provides the statistical distribution of measured values for any given physical quantity at a specific time t. The theory, however, does not make any statements about what the state of an individual system is.

To summarize:

1) Quantum theory provides the probabilities of the values that physical quan-tities, called observables, can take when measurements are performed on a sta-tistically prepared ensemble of identical systems.26