6.4.1. Waves/Particles?

The concept of a (non-elementary) particle, which is conceptually close to the notion of a subsystem/part, is also a physical convention and can only arise from the |**Ξ** or its models: Bose-condensates, deformation excitations in crystal lattices, quasi-particles in a superfluid phase, quantum theories of various fields (relativistic or non), and more. Here, by particle we mean the classical kinematic conception. "What do we detect? The presence of a particle? Or the occurrence of a microscopic event?" wondered R. Haag (2013). H. Zeh and G. Ludwig do answer: "There are no particles in reality" [161], "we must abandon the notion of a microscopic "object", one to which we have been accustomed" ([87], p. 69).

Clearly, the QFTs is a subclass of QM rather than its extension; not that we have ye<sup>t</sup> given a definition of QM. In particular, it is common knowledge in QFT that there is no logical way to distinguish a particle from a certain state—normally, a vacuum excitation. One word should therefore be used for both. To this extent, the familiar "dualism of . . . the *particle picture* and the *wave picture*" [78] (Section 7.2), [91], [108] (p. 28) simply disappears. K. Popper is rather emphatic concerning this "problem" and puts it, in their "thirteen theses" [108], quite rightly in the following terms: "*the great quantum muddle*", "alleged "duality" or "complementarity", . . . *this* kind of "understanding" is of little value", "has not the slightest bearing on either physics, . . . ", "fashionable among quantum theorists, . . . a vicious doctrine", and the like. As a matter of fact, both the particles and waves are the classical terms [61] and, in quantum language, they turn into the derivatives of the concepts of state and mixture (23).

•Like waves, *the particle is already an appearance*—an observable one (phenomenology, derivative)—rather than a logical primitive or a fundamental substance, which is why it may not exist [161] prior to theory's principles ([126], p. 762 (!)). Paraphrasing Heisenberg, Haag remarks, in the context of their "event theory", that "Particles are the roof of the theory, not its foundation" ([88], p. 300).

Both these notions should be superseded by a mathematics of clicks.

The f-statistics also falls under observable quantities, and constant D, if declared finite, is an example of an already created characteristic: the dimension of a state space to come. A tensorial structure of this space—compound systems—also pertains to the physical properties, but we do not touch upon this point here. As an aside, this compositional structure will provide the means of distinguishing the aforementioned models under D = ∞.

In other words, the logic of the above constructs prohibits not only endowing the phraseology "internal state of an individual object S" and "the system is in a (definite) state [4,58,93,94] with a meaning but also indirectly using its numerical forms. That would work in the circumvention of empiricism, assuming the a priori availability of mathematical structures that do not rest on the state space. L. Ballentine remarks in this regard: "the habit of considering an individual particle to have its own wave function is hard to break"

([34], p. 238); cf. "To speak of a single possible initial apparatus state is pure fantasy" ([80], pp. 241–242; N. Graham).
