What strikes the mind, secondly, is that measurement plays a fundamental role in the theory. Indeed, the central object of the formalism, the state |Ψ(t)⟩, is actually just a tool designed to calculate the probabilities of obtaining a given value of a physical quantity A during a measurement. It is, in no way, related to the probabilities of revealing a preexisting value of this quantity within the physical system before the measurement, as clearly stated by the Born postulate (5). No one has better articulated the profound renunciation imposed by this situation than Bell: “In the beginning, natural philosophers tried to understand the world around them. In pursuing this goal, they had the brilliant idea of designing artificially simple situations where the number of factors involved is minimized. Divide and conquer. Thus, experimental science was born. But experience is just a tool. The goal remains: to understand the world. Restricting quantum mechanics to mere insignificant laboratory operations betrays this great endeavour. A serious formulation cannot exclude the vast world outside the laboratory”.

In terms of renunciation, things do not stop there. Schrödinger’s equation (4) appears, in quantum formalism, as the analogue of the fundamental principle of dynamics (or Newton’s second law) which describes the motion of clas-sical objects. Just as the latter allows for predicting the evolution of a classical system under the influence of forces, Schrödinger’s equation governs the tem-poral evolution of a quantum system’s state within a given energy landscape. However, while in the classical framework there is a fundamental, universal, and unique law of temporal evolution, the quantum formalism, in contrast, appears schizophrenic when it comes to the temporal dynamics of the system27. Indeed, the temporal evolution postulate stipulates that, in the absence of measurement, the system evolves according to Schrödinger’s equation (4), that is, in a perfectly deterministic manner: the state |Ψ(t = 0)⟩ being known, the state |Ψ(t)⟩ is known at any time t. On the other hand, during a measurement, the evolution of the state vector becomes random, and it is projected into one of the states |ak⟩ with a probability 𝒫(ak).

But that’s not all. The evolution described by (4) respects the unitarity property, meaning that the norm (or “length”) of the state |Ψ(t)⟩ remains constant over time. This characteristic reflects the conservation of total probability. In contrast, during a measurement, the evolution of the state, which corresponds to a projection, generally does not conserve the vector’s norm (see figure (1)). This constitutes a break with the unitary evolution, implying that the measurement induces a trans-formation that does not respect the conservation of total probability28.

To summarize:

2) In quantum mechanics, the temporal evolution of a system is deterministic and unitary in the absence of measurement, whereas it becomes non-deterministic and non-unitary in the presence of a measurement.

With regard to difficulty29 2) mentioned above, a comparative analysis of meas-urement in classical and quantum cases proves enlightening. Indeed, in classical physics, measurement does not play a fundamental role. This is explained by the fact that both systems—the measuring apparatus and the system being meas-ured—are of the same nature, which can be simplistically described as macro-scopic, although the classical/quantum distinction does not always coincide with the macroscopic/microscopic one. This situation implies that, even if the measurement requires interaction between the two systems, it can always be considered non-in-vasive with respect to the system under study, affecting the result obtained in only a negligible manner30. In other words, measurement merely reveals a pre-existing property of the system without significantly altering it.