On the role of hidden variables in the fundamental structure of physics

Виктор Павлович Маслов

Eduardo Gonzalez-Granda Fernandez

This work investigates the compatibility of hidden-variable modifications with the analytic structure of relativistic quantum field theory (QFT). Working within the framework of tempered distributions, we analyze three fundamental properties: the spectral condition, analyticity in the forward tube, and causal localization. We prove a rigidity result showing that any modification satisfying all three conditions must vanish identically. This establishes a structural obstruction linking analyticity and causal constraints in QFT. Building on this result, we provide a systematic classification of nontrivial hidden-variable extensions according to which analytic assumptions fail. We identify three distinct regimes: (i) delocalized modifications compatible with standard QFT, (ii) causally localized modifications that violate the spectral condition and introduce negative-frequency components, and (iii) localized modifications that necessarily break analyticity. These results show that nontrivial hidden-variable theories cannot be embedded within the standard analytic framework of relativistic QFT without violating at least one of its fundamental structural principles. The work provides a unified analytic perspective on the constraints governing hidden-variable extensions and clarifies the role of analyticity as a rigidity mechanism.

Simon Kochen, Ernst P. Specker

Alexander D Panov

The main objective of the present article is the methodological analysis of the structures of physical theories that could apply to the theory of quantum gravitation or the unifi ed theory of all interactions (other terms are the “Final Theory” or “the Theory of Everything”, TOE). In the fi rst step of this discussion, it is shown that, unlike widely believed, quantum theory, in principle, allows representation by local classical hidden variables. The possibility of such representation is proved by the possibility of an exhaustive simulation of quantum systems by means of a local and classical device — the computer equipment plays a role of the local classical hidden variables. Details regarding the realization of such a representation are discussed using the example of an actual computer program simulating a correlation experiment using Eeinstein-Podolsky-Rozen pairs. This example explicitly violates the theorems of impossibility for hidden classical variables in quantum theory. The fact that these theorems ignore the possibility for a situation, which, in this article, is characterized as the splitting of the layers of reality, is the reason that a possible violation of the theorem of impossibility for hidden variables exists. There are two such layers in the computer example — a reality layer where computer equipment exists, and a layer for simulated quantum reality. The analysis of this example results in a general idea about the layers of reality, which are the main subject of the subsequent discussion. The computer example plays a role of the existence theorem. It follows that, in principle, a fundamental local and classical structure may exist behind physical quantum reality. However, such a “local realism” leads to the idea that an immense “space container” exists for classical objects of such a layer of reality. The problem is overcome if the fundamental ontology is classical, but nonlocal. Then, a space container for it is not required. It is shown that such a classical, but nonlocal, structure is very similar to a formal mathematical system. It leads to a thought that the ideal mathematical system can be a fundamental ontology of the TOE, or it is reminiscent of something beyond mathematics — a nonreducible pseudomathematical structure. In this regard, the analysis of the nature of mathematics is given. It is shown that mathematics are not only a result of the imagination of people, but that mathematical forms and all mathematics holistically exist objectively. Moreover, the statement about the objective existence of mathematical forms has an empirical status based on Popper’s criterion of falsifi ability. It transfers a question of objectivity for mathematics from the fi eld of philosophy to the fi eld of empirical science. Then, a connection on the bases of mathematics and physics is established — namely, with the existence of the classical sector of quantum theory and with a causal structure of space-time. In this sense, the existing mathematics are not only objective, but they also possess physics. That is, mathematics, in a sense, is a thing but it is not a thought, and this quality can be considered as an objective layer of reality that can be a substrate of the physical world. In the fi nal part of this paper, several modern directions in the quantum gravity theory or TOE (string theory, loop quantum gravity, and causal sets) are considered regarding, as far as these theories are concerned, the formation of an abstract mathematical substratum. It is shown that the tendency to develop a of structure like an abstract mathematical substratum defi nitely exists. This means that a TOE can be not just a physical theory, but rather an abstract mathematical structure

Simon Kochen, Ernst P. Specker

Dirk John Pons, Arion Pons, Aiden Jasper Pons

The conventional conceptual framework for fundamental physics is built on a tacit construct: the premise of particles being zero-dimensional (0-D) points. There has never been a viable alternative to this, and the Bell-type inequalities preclude large classes of alternative designs with hidden variables. Although they do not absolutely preclude the possibility of particles having non-local hidden-variable (NLHV) designs, there is the additional difficulty of finding a solution within the very small freedom permitted by the constraints. Nonetheless we show that it is possible to find such a design. We propose the internal structures and discrete field structures of this ‘cordus’ particule, and the causal relationships for the behaviour of the system. This design is shown to have high conceptual fitness to explain a variety of fundamental phenomena in a logically consistent way. It provides insights into the fundamentals of matter, force, energy and time. It offers novel explanations to long-standing enigmas and suggests that a reconceptualisation of fundamental physics is feasible. We thus show that the 0-D point premise can be challenged, and is likely to have profound consequences for physics when it falls.