Our representations about space and time, even considering their «a priori» status according to Kant, change over time. Their evolution necessarily accompa-nies the development of our knowledge of physical reality. The article describes the representations of space and time that allows not only to unambiguously inter-pret the effects of quantum mechanics, but also to build a model of the bases of physical reality, the development of which, according to the author, can lead to the creation of a unified physical theory of the microworld. Within the framework of this model, the discreteness of space and time is asserted, from which the proba-bilistic nature of elementary motion follows with necessity; geometry is distin-guished into the inextricably linked continual geometry of Being and the discrete geometry of Existing, and time becomes the absolute invariant of Existing.
Our representations about space and time, even considering their «a priori» status according to Kant, change over time. Their evolution necessarily accompa-nies the development of our knowledge of physical reality. The article describes the representations of space and time that allows not only to unambiguously inter-pret the effects of quantum mechanics, but also to build a model of the bases of physical reality, the development of which, according to the author, can lead to the creation of a unified physical theory of the microworld. Within the framework of this model, the discreteness of space and time is asserted, from which the proba-bilistic nature of elementary motion follows with necessity; geometry is distin-guished into the inextricably linked continual geometry of Being and the discrete geometry of Existing, and time becomes the absolute invariant of Existing.
Twentieth-century physics was shaped by two profound revolutions. The first, Einstein's relativity, banished absolute space and time from the foundations of physics. Motion, Einstein showed, possesses no absolute meaning—only relative motion between observers merits physical description. The second, quantum mechanics, dismantled the classical notion of determinacy. A physical quantity, before measurement, is not merely unknown but genuinely indefinite, suspended in a superposition of possibilities. These two revolutions, for all their splendor, have never spoken a common language. General relativity describes a world of continuous, deterministic geometry; quantum mechanics, a world of discrete, probabilistic events. Their unification—a theory of quantum gravity—remains the central unsolved problem of theoretical physics. We diagnose this impasse not as a technical failure, but as a conceptual incompleteness. The two revolutions, in their original domains, stopped short of questioning a premise both inherited from classical thought: that physical reality, determinacy, and facts themselves are absolute—that they exist independently of the framework through which they are described. Einstein relativized motion but left the existence of spacetime geometry absolute. Quantum mechanics relativized the values of observables but left the fact of an outcome unexplained, consigning it to the mysterious "measurement process." Neither theory asked: in what sense is a fact—that a quantity has a definite value, that an event has occurred, that a physical reality is thus and not otherwise—itself relative to a descriptive framework? This is the question the present work undertakes to answer. In doing so, it completes the program of relativity—not by appending new terms to old equations, but by extending the principle of relativity to its ultimate domain: being itself.
The general view is that all fundamental physical laws should be formulated within the framework given by quantum mechanics (QM). In a sense, QM therefore has the character of a metaphysical theory. Consequently, if it is possible to derive QM from more basic principles, these principles should be of general, philosophical nature. Here, we derive the formalism of QM from well-motivated epistemic principles. A key assumption is that a physical theory that relies on entities or distinctions that are unknowable in principle gives rise to wrong predictions. First, an epistemic formalism is developed, using concepts like knowledge and potential knowledge, identifying a physical state S with the potential knowledge of the physical world. It is demonstrated that QM emerges from this formalism. However, Hilbert spaces, wave functions and probabilities are defined in certain well-defined observational contexts only. This means that the epistemic formalism is broader than QM. In the fundamental layer of description, the physical state S is a subset of a state space S={Z}, such that S always contains many elements Z. These elements correspond to unattainable states of complete knowledge of the world. The evolution of S cannot be determined in terms of the individual evolution of the elements Z, unlike the evolution of an ensemble in classical phase space. The evolution of S is described in terms of sequential time n∈N, which is updated according to n→n+1 each time an event occurs, each time potential knowledge changes. Sequential time n can be separated from relational time t, which describes distances between events in space-time. There is an entire space-time associated with each n, in which t represents the knowledge at sequential time n about the temporal relations between present and past events.
License: CC BY-NC-ND 1. Introduction and epistemological framework Despite extraordinary empirical successes, modern natural science faces a fundamental explanatory gap. The General Theory of Relativity (GTR) describes the macroscopic structure of space, time and gravitation with unrivalled precision, whilst quantum mechanics (QM) governs the probabilistic laws of the microscopic world. However, both theoretical foundations are based on incompatible mathematical and ontological assumptions: GR assumes a continuous, deterministic space-time continuum; QM operates on discrete, non-local state spaces and is inextricably linked to the unsolved measurement problem. Holistic Information Theory (HIT) proposes a formal extension of the physical frame of reference. It begins one step prior to spatio-temporal localisation and poses the fundamental question regarding the a priori condition under which physical quantities can arise, be distinguished and measured in the first place. Every scientific description necessarily begins with a distinction; every distinction encodes a difference, and every difference is, at its core, pure information. From this methodological premise, GIT deduces that information is not a secondary product of biological evolution or technical data processing, nor is it merely a property of matter. Information is the primary ontological quantity of existence. Space, time, gravity, light, energy and matter are established as secondary forms of organisation and manifestation of an all-encompassing, evolutionary information process. In this system, cognition and physical manifestation are not passive processes, but active acts of information creation, initiated by a directed ‘question’ – understood as a physical interaction or systemic coupling.
The 1995 article by Achim Kempf, Gianpiero Mangano, and Robert B. Mann, “Hilbert Space Representation of the Minimal Length Uncertainty Relation,” constitutes one of the most important formal constructions through which a nonzero minimal uncertainty in position can be incorporated into quantum mechanics. Rather than representing a fundamental length merely as a discrete lattice imposed upon ordinary space, Kempf, Mangano, and Mann modify the canonical commutation relation and construct a Hilbert- space representation in which arbitrarily precise physical localization is excluded. Their framework yields a minimal position uncertainty, modifies the mathematical status of exact-position states, introduces maximally localized states and a quasi-position representation, and, in multidimensional formulations, leads to noncommuting position coordinates. The original article was published in Physical Review D, volume 52, pages 1108–1118, DOI https://doi.org/10.1103/PhysRevD.52.1108 (Kempf, Mangano, and Mann, 1995). This article develops a critical–propositional analysis of that framework in dia- logue with the Theory of Objectivity (TO), particularly its Seven Absolute Truths, its interpretation of logical Nothingness, the concept of individualizing fields, the onto- logical status attributed to infinity, the role of boundaries and interfaces, nonhuman relational observation, compositional emergence, and the transcendent element under- stood in TO as knowledge or information produced in atomic relations and considered equivalent to atomic radiation. Special attention is given to the foundational TO work A Esfera Perfeita (The Perfect Sphere), because the KMM minimal-localization structure provides an especially useful mathematical dialogue partner for a TO conception of a limiting physical scale. The central thesis developed here is deliberately restricted. Kempf, Mangano, and Mann do not demonstrate the Theory of Objectivity, do not derive its cosmogony, do not establish the individual magnetic field asserted by its Second Absolute Truth, and do not reproduce the triadic relational condition associated with its Fifth Absolute Truth. Nevertheless, their work provides a productive structural analogy for several TO concepts: finite physical localizability, distinction between formal mathematical objects and physically realizable states, existence of a forbidden domain below a localization threshold, generation of geometrical properties by fundamental algebraic relations, and conversion of fundamental constraints into potentially observable consequences. The strongest scientific use of KMM by TO would therefore not consist in claiming retrospective confirmation. TO should instead attempt to derive, from its own modal and cosmogonic architecture, an effective deformation parameter and a nonzero localization scale. If such a derivation were independently obtained, the resulting theory could produce quantitative deviations from ordinary quantum mechanics and could thereby enter genuine empirical contact. The analysis consequently proposes a formal research program in which modal axioms are connected to operator algebra, spectral corrections, propagation relations, information constraints, and experimentally bounded parameters. Later developments in generalized uncertainty principle research are also considered, including qualifications of the KMM algebra concerning Jacobi identities and spin (Fadel and Maggiore, 2022). KMM should therefore be understood as a historically and mathematically impor- tant model of minimal-length quantum mechanics, rather than as an experimentally established universal description of fundamental physics. Keywords: Theory of Objectivity; minimal length; generalized uncertainty principle; Kempf–Mangano–Mann algebra; modal ontology; Perfect Sphere; quantum gravity; physical localizability; information; atomic radiation; noncommutative geometry; In- ductive Effects; cosmology; modal necessity; operational bridges.