identical, i.e., possessing the same intrinsic properties, such as mass, charge, spin, etc., cannot be assigned distinct individual states. For such particles, the notion of individuality even loses all relevance. This concept of identity, specific to quantum mechanics, is particularly difficult, even impossible, to intellectually conceive. This is reflected, moreover, by the absence of truly suitable vocabulary: the term “indiscernibility” evokes an external judgment, as if the observer were simply unable to differentiate one particle from another, like two tennis balls. As for the term “identity,” although it does not explicitly appeal to the senses, it implicitly refers to the idea of vision. In reality, it refers to an intrinsic and structural identity inherent to these particles, far beyond a simple observation-related limitation. Furthermore, this notion of identity, as we will see, has no natural translation in the formalism of quantum mechanics.

So, consider two particles, 1 and 2, initially far from each other, described by states �ΨA⟩1 and |ΨB⟩2, where A and B index distinct states. If these particles approach, causing a mix, a possible overlap of their state vectors, the overall state describing these two particles must then reflect their intrinsic identity. As we mentioned, this implies the impossibility of assigning them a well-defined individual state—or number.

As we have pointed out, there is no natural or immediate way to formalize this situation. However, we can proceed with the following manipulation to describe it: we still assign the state �ΨA� to particle 1 and �ΨB� to particle 2. Then, to com-pensate for this illegitimate assignment of individual states to the particles, we also consider the symmetric situation in which the roles of particles 1 and 2 are exchanged. Finally, we construct the resulting global state of this operation by forming a superposition of the two configurations:

|Ψ⟩ = |ΨA⟩1 ⊗ |ΨB⟩2 ± |ΨA⟩2 ⊗ |ΨB⟩1.

The global state is then a combination of the individual states of the particles, which can be either symmetric (sign +, applying to a certain category of particles called bosons) or antisymmetric (sign −, in the case of particles from the category known as fermions). This (anti-)symmetry of the final state ensures its independ-ence from the attribution of individual states to the particles.

This approach is perfectly operational, as it allows us to mathematically obtain the correct state of the system, as confirmed by numerous experiments involv-ing identical particles. However, the crucial point remains that, in general, it is impossible to construct the global state of the particles without first making an arbitrary assignment of individual states to the particles78, followed by an (anti-)symmetrization of this configuration.

This example clearly illustrates a fundamental limitation of human ability to com-prehend the identity property of particles. However, the mathematical technique, through the quantum formalism, allows us to overcome this limit and handle this situation adequately, the price to pay being this “subterfuge” that consists of considering the identity of the particles as... the negation of their otherness.

By extension, it is tempting to imagine that the very notion of superposition of states, although once again extremely operational, is, in reality, just a compro-mise solution to our inability to describe the singularity of quantum systems more precisely. Indeed, we superimpose states of well-defined energy, position, or momentum in order to account for the spectral spreading of these quantities, much like we superimpose states of dissimilar particles to account for their iden-tity. But this process of superposition can be seen as a way of “smoothing out” the inherent complexity of quantum phenomena, in order to make them under-standable in terms of the language and concepts available to us. In other words,