GENERAL PHYSICS https://doi.org/10.15407/ujpe65.1.17 I. LICATA 1, 2, 3 1 ISEM, Institute for Scientific Methodology (Palermo; e-mail: [email protected]) 2 School of Advanced International Studies on Theoretical and Non Linear Methodologies of Physics (Bari, Italy) 3 International Institute for Applicable Mathematics & Information Sciences (IIAMIS), B.M. Birla Science Centre (Adarsh Nagar, Hyderabad 500,India) QUANTUM MECHANICS INTERPRETATION ON PLANCK SCALE In the last years, many different primeval quantization theories on the Planck scale have been developed. Their goal is to provide a vacuum model able to ground the research beyond the Standard Model. Despite their goal is quite ambitious and aims toward particle physics, a necessary and notable consequence is we can read Quantum Mechanics from an emergent viewpoint. Different hypotheses on elementary cells are possible. We will focus here on the conceptual features of G. ’t Hooft and F. Winterberg theories with a special attention for the emerging of non-local correlations. These theories define a new style in the interpretation of Quantum Mechanics. K e y w o r d s: quantum mechanics interpretation, Planck scale, ‘t Hooft equivalence class, Winterberg plasma, non-locality. 1. Motivations: Deconstructing Bell mains the gap between this type of foundational de- The idea that a more subtle level of the discrete bates and the complex structure of elementary par- deterministic type may exist under quantum me- ticle physics, especially in relation to the concept of chanics (QM) is as old as the Bohr–Einstein debate “vacuum state” in QFTs (Quantum Field Theories). (1935). As a conceptual scheme, it goes back to the In particular, the theories of hidden variables have successes of statistical physics. More than half a cen- received a severe blow due to Bell’s theorem. The tury of interpretative debates has a limited confidence possibility of restoring a scheme of this type, with in the Copenhagen interpretation for APP (All Prac- measurable deviations from QM, is now confined to tical Purposes), but it is not even possible to say a very thin margin [1, 2]. To ask ourselves if this that a subquantum model has been clearly estab- is really the last word on QM is equal to propose lished. The contrast between a Bohr-type irreducible an approach to quantum theory in which the vio- non-locality and an objective realism of the Einstein lation of Bell’s inequalities is compatible with some type is continually reproposed and has also given form of locality, located in a different range from the some considerable contribution to the understanding one in which EPR–Bell experiments are usually per- of the structure of quantum theory, in particular, the formed. In other words, we need to investigate the presence of stochastic aspects. The real problem re- possibility of an emerging QM constrained from be- low on a level, where it is possible to find, at least ○c I. LICATA, 2020 partially, a structure with discrete and localized in- ISSN 2071-0194. Ukr. J. Phys. 2020. Vol. 65, No. 1 17 I. Licata formation independent of the observer. However, we b) The type of theory depends on the assumptions must expect that the observables we work with are made on ccell dynamics. The theories that we review usually not beables, but emerging variables. A theory here, by ’t Hooft and Wintenberg, are quite different is thus outlined in which the local level is not hid- also as cultural milieu, but both suggest that the in- den among the observables, but is instead placed on troduction of non-linear oscillators together with the a structurally different plane. This would clarify the very powerful hypothesis of primordial discretization failure of traditional hidden variables and proposes a allows to “rebuild” QM. An essential point is that the radically new vision between discrete/continuous and subquantum freedom degrees are equal and indistin- classical/quantum. Theories of this type exist and guishable. In this way, they ensure, at the macro- will be referred to here as theories of primitive quanti- scopic level, the isotropy and homogeneity of the zation or pre-quantization. They work on the Planck space-time; scale. There are some rather strong reasons for in- c) The hypothesis of locality and pre-determinism vestigating such a theory. The main ones are surely directly leads to that of reversibility. At the beables the Bekenstein principle and the holographic princi- level, information is never lost. However, this does ple, both firmly connected to the constraints on the not mean that information on a single cell is recov- spectrum of quantum fluctuations of the space-time erable; indeed, it is precisely the loss and selection and ultimately to the homogeneity of the tessella- of information at the emerging level that leads to tion of the same space-time [3; 4]. The main moti- the observable non-commutative notes of QM, the vations of theories of this type are related to quan- changeables and the relative equivalence classes of ’t tum gravity, they are not born as “interpretations Hooft. A quantum state is therefore a derivative con- of QM”, but this is considered a necessary step to cept and can show strong non-local correlations re- eliminate the ambiguities generated by the quantum- lated to the loss of information, which finally acquire mechanical formalism near the Planck scale and at an authentic statistical meaning. If the natural con- the cosmological level. In fact, the stochasticity has a straint on the speed limit of light is introduced onto mesoscopic flavor, and one would not expect to find the lattice, the maximal acceleration of Caianello is it at a scale of radical discretization. Ambiguities do obtained [6]. not decrease with the second quantization, but in- The bet on the emergence of these theories lies crease; in general and on all scales, the elegance of therefore in proposing an effective mechanism able to the description of physical processes through ampli- bridge the gap between the Planck scale (1019 GeV) tudes [5] is strongly limited by the probabilistic mort- and the usual one of experiments involving a quan- gage. The latter should derive from deeper reasons, tum-mechanical treatment (103 GeV). This depends and the Born rule should emerge as a sort of “regu- critically on the choice of beables and the relation- lator” of the collective dynamics and their degrees of ship between beables, Planck cells, and changeab- freedom. les. So, the primordial quantization theories do not In general, a theory of primordial quantization is tend to give a “realistic” character to the wave func- based on some general assumptions: tion or even to predict deviations from the standard a) Nature works in a similar way to a computer QM. Their character is rather explanatory of the na- on the Planck scale. This implies that information ture of the QM. Please note that the Planck cell is the at that level is finite, local, independent of the ob- extreme limit of the causal connection with the lab- server, and pre-deterministic. Therefore, no interfer- oratory [7], and the point of arrival is the “ordinary” ence figures or overlaps are possible, there are very QM. Therefore, the physically significant aspect con- precise rules that assure the transitions from one cell sists in the exploration of physical processes in that to another through a discrete sequence of states. In middle ground that allows the passage from the deter- practice we are doing a kind of classical physics ministic and local systems of the beables to quantum on the Planck cells. We will call the magnitudes of behaviors with their typical uncertainty and non-local this level, following ’t Hooft, beables, in honor of “weirdness”. J.S Bell. Beables are carriers of defined properties To understand how the goal of these theories is and, therefore, form a set of operators that always necessarily more ambitious, let us think of a classic switch. problem of QM, the so-called “collapse” problem, and 18 ISSN 2071-0194. Ukr. J. Phys. 2020. Vol. 65, No. 1 Quantum Mechanics Interpretation on Planck Scale let us look at it in relation to particle physics. The an- can therefore be assumed to be primary and funda- ticommutative nature of the observables tells us that mental at a level – it is the case of theories that in- the result will belong to the changeables class, but we troduce the non-locality ab initio –, but which does know that a particle like the electron has well-defined not exclude a local and deterministic level, where the characteristics, always, as a charge, mass, spin, like- characteristics of QM are emerging and find their full beables. The aim of the pre-quantization theories is meaning. It is the case of the relationship between therefore to merge QM and QFT by defining a sort of beables and changeables. informative pre-QFT on the Planck scale, thus realiz- In general, a model, in which the state variables ing the “it from bit” principle [8]. In the following, we and their transition laws are always defined and ac- will limit ourselves to the emergence of QM, starting quirable (indifference with respect to the measure), from the structural links between QM and emerging is called logically or informationally closed and is de- systems. terministic and local. It is the case, for example, of classical physics, where the measurement operations 2. Quantum Mechanics on all the state variables commute and are simul- as Contextual Theory of Systems taneously compatible, i.e., all measuring devices re- lated to different variables can always be used with- In recent years, the study of the physics of the emer- out interfering with one another and without any loss gency has known new developments toward a general of mutual information.