Scales of the microworld are defined on the grounds of the hierarchy that can be set up within a well ordered finite or infinite countable set of well ordered sets. Indirect measurements in pure mathematical as well as physical meaning are considered as the mean to obtain information on the occurring within each scale. The general concept of the physical laws within a certain scale is defined in the framework of the set theory. The hypothesis is proposed that quarks are not within the same scale as other elementary particles are, but within the following ("smaller", exactly of lower hierarchy) scale. Maybe, in particular, this is the cause of difficulties of the free quark detection? Some other consequences of the abovementioned hypothesis are discussed. Limitations of the possibility to obtain information on the going on within sets of low hierarchy (in particular, "small" scales of the microworld, in physics) and to transfer it toward the set of the highest hierarchy (in particular, to the macroscopic observer in physics) are found as a consequences of the multi-step character of measurements. Keywords: microworld scales, set theory, information value and hierarchy, well-ordered set hierarchy, sub-quantum physics, indirect measurements, quarks PACS: 02.10.Ab, 03.65.Ta
Scales of the microworld are defined on the grounds of the hierarchy that can be set up within a well ordered finite or infinite countable set of well ordered sets. Indirect measurements in pure mathematical as well as physical meaning are considered as the mean to obtain information on the occurring within each scale. The general concept of the physical laws within a certain scale is defined in the framework of the set theory. The hypothesis is proposed that quarks are not within the same scale as other elementary particles are, but within the following ("smaller", exactly of lower hierarchy) scale. Maybe, in particular, this is the cause of difficulties of the free quark detection? Some other consequences of the abovementioned hypothesis are discussed. Limitations of the possibility to obtain information on the going on within sets of low hierarchy (in particular, "small" scales of the microworld, in physics) and to transfer it toward the set of the highest hierarchy (in particular, to the macroscopic observer in physics) are found as a consequences of the multi-step character of measurements. Keywords: microworld scales, set theory, information value and hierarchy, well-ordered set hierarchy, sub-quantum physics, indirect measurements, quarks PACS: 02.10.Ab, 03.65.Ta
Quantum theory comprises a number of physical concepts and methods of calculation applicable to bodies on an atomic scale and consequently to the explanation of the properties of macroscopic bodies in terms of the behaviour of their constituent particles. In advanced work the theory is highly mathematical, but at an elementary level the difficulties lie mostly in the appreciation of the relevant physical ideas. Wave-particle duality, indeterminacy, the nature of a quantized state of a system and the exclusion principle cause most conceptual problems.
Due to the idea of atomism, there were discovered atoms, nucleons, and electrons. The atomic theory incorporated seeds of the idea of infinite divisibility of matter aimed at perceiving the structure of the entire material world. The next step in that perceiving should have been the recognition of ether discovered in Fizeau’s experiment. However, physicists did not recognize the discovery. The neglect of ether in physical theories resulted in physicists’ failure to use the methods of “classic”, Newtonian physics to gain a detailed understanding of atomic structure, and to build a “classic” microworld theory. As consequence, there emerged the quantum hypothesis that became a basis for the quantum physics of microworld. As the quantum hypothesis appeared to be in irreconcilable contradiction with the idea of infinite divisibility of matter, because of the neglect of ether, the quantum physics failed to understand the real structure of electrons and nucleons, even though all the necessary and ample experimental facts there had been obtained on microobject accelerators. Instead of objective ideas of the structure of electrons and nucleons or further development of knowledge regarding the structure of matter, there appeared fake concepts of quarks, myons, pions, bosons, etc., that do not exist in the real material world Experimental evidence as to the lack of indivisible quanta in nature [1] seemed to have fixed the intolerable situation but quantum physicists did not “notice” that.
Recent investigations concerning foundations of quantum theory require new approaches to the problem of observation of physical events. V. Belavkin showed that standard quantum mechanics describes only the closed microworld in which there is no place for some macroscopically visible events. Though any quantum phenomenon is observable from the macroworld. That situation means non‐equivalence of Heisenberg’s representation to Schrodinger’s one in quantum mechanics. It would seem quantum theory is more general than classical mechanics. It is expressed, in particular, by well‐known Bohr’s principle of correspondence. I think the above‐mentioned Belavkin’s result puts under doubt the opinion concerning universal character of quantum theory. What ontological meaning has the concept of existence of physical event? Is distinction between observable event and non‐observable one anthropological, or not? In that context I discuss the new aspects of the observation problem in the physical theory. In my report I discuss philosophical arguments for the thesis that distinction between observable event and non‐observable one is ontological. In this connection I consider a number of objective ontological criteria of observability / non‐observability such as distinguishableness / indistinguishableness of physical states, symmetricalness and asymmetricalness of observation relations. The ontological sense of observation is analyzed in the context of relations between objects which are into spaces with different dimensions.
Why do physicists discover different equations to describe the same universe? This paper proposes a new answer by introducing the Observer Hierarchy of Physics, a general framework in which physical theories are understood as exact observer equations, each preserving the information accessible within a particular observational regime rather than replacing one another. Instead of treating Newtonian mechanics, Maxwell's equations, the Schrödinger equation, the Dirac equation, thermodynamics, and other successful theories as competing descriptions, the framework argues that each is the minimal mathematical description required to preserve the measurements available to a specific observer algebra. The central idea is that the observer algebra is not chosen arbitrarily. It is generated by the observer's physical coupling to the underlying substrate together with finite spatial resolution, temporal resolution, energy access, detector sensitivity, and measurement precision. Once that coupling-generated observer algebra is specified, the minimal sufficient field representation, observer state, and observer equation follow naturally. In this view, the universe continuously evolves its full microscopic state, while observer equations describe only the information that survives physical coupling and projection into observable records. The paper introduces five new theoretical results: • Observer Hierarchy Theorem — demonstrating that a single physical system may admit multiple exact observer equations corresponding to different observational regimes. • Observer Sufficiency Theorem — establishing that an equation may be non-fundamental while remaining mathematically exact within the regime whose observables it preserves. • Representation Sufficiency Theorem — showing that reduced field representations are selected by observer algebras rather than by different physical laws or runtime modes. • Information Preservation Theorem — proving that observer equations are characterized by the information they preserve, not by the information they discard. • Observer Reduction Theorem, together with the Coupling-Determined Algebra Principle, showing that observer algebras arise from physical coupling to the substrate and that transitions between observer equations correspond to information-preserving projections rather than changes in physical reality. The framework is then illustrated using the Lattice Field Medium (LFM), where a continuously evolving second-order computational substrate gives rise to observer-selected field registers, a stable electron solution, the relativistic Dirac observer equation, and finally the low-energy Schrödinger observer equation. Importantly, the substrate itself never changes representation; only the observer's retained description changes as additional observables become experimentally accessible. Seven numerical information-projection diagnostics accompany the theoretical development, validating observer compression, register sufficiency, information preservation, bandwidth-dependent validity, and representation selection through controlled computational experiments. Rather than proposing that future theories replace existing ones, this work argues that scientific progress should explain why existing equations remain exact within their domains of applicability. If correct, the Observer Hierarchy provides a unified organizing principle for theoretical physics in which the evolution of physical theory is understood as the progressive discovery of observer equations emerging from an underlying computational reality.
We put forward a possible new interpretation and explanatory framework for quantum theory. The basic hypothesis underlying this new framework is that quantum particles are conceptual entities. More concretely, we propose that quantum particles interact with ordinary matter, nuclei, atoms, molecules, macroscopic material entities, measuring apparatuses,..., in a similar way to how human concepts interact with memory structures, human minds or artificial memories. We analyze the most characteristic aspects of quantum theory, i.e. entanglement and non-locality, interference and superposition, identity and individuality in the light of this new interpretation, and we put forward a specific explanation and understanding of these aspects. The basic hypothesis of our framework gives rise in a natural way to a Heisenberg uncertainty principle which introduces an understanding of the general situation of ‘the one and the many ’ in quantum physics. A specific view on macro and micro different from the common one follows from the basic hypothesis and leads to an analysis of Schrödinger’s Cat paradox and the measurement problem different from the existing ones. We reflect about the influence of this new quantum interpretation and explanatory framework on the global nature and evolutionary aspects of the world and human worldviews, and point out potential explanations for specific situations, such as the generation problem in particle physics, the confinement of quarks and the existence of dark matter. 1
Many-body topology is a central concept in modern theories of solids, and identifying effective degrees of freedom that capture it is important both fundamentally and practically. This work studies the extent to which geometric information of an interacting many-body ground state can be inferred from a finite number of local correlations. Starting from the Resta formula, $ z=\left\langle \exp\!\left(\frac{2πi}{L}\hat X\right)\right\rangle$, we view logz as the cumulant generating function and establish a generic information hierarchy across cumulant orders. We show that, for an N-particle system, even complete knowledge of all density correlators up to order N−1 does not, in general, uniquely determine the Berry phase γ=Imlogz(mod2π). In the thermodynamic limit, the statement becomes stronger: no finite set of local correlators suffices to determine the global holonomy. We also identify two exceptional yes-go cases in which the hierarchy is broken. First, for quasi-free models, all cumulants are determined by the particle two-point correlation function. Second, symmetry-enforced constraints can reduce the infinite cumulant sum entering logz to finite information. The argument is analytic and does not rely on a specific microscopic Hamiltonian. Our results clarify a limitation of approaches based on local degrees of freedom for many-body holonomy and provide a minimal framework for distinguishing when global holonomies are encoded in local correlations and when they are not. We also comment on the possibility of analogous hierarchies in other contexts, such as the quantum marginal problem in quantum information theory and many-body scattering problems. Finally, we discuss implications for future numerical work, including machine-learning approaches to the search for topological phases.