A classical signal which agrees with the ideas of mathematical analysis on infinitesimal quantities possesses an infinite information capacity, which contradicts the concept of information that is finite by definition. A real signal should have some “threshold” for determining a finite step between its distinguishable states and the “limit” for the possible number of states. This paper considers the influence of the level of required energy, performance, and noise of the receiver on the capability of distinguishing the set of states in the signal. It is shown that the generalized threshold is the constraint on the spectral density of the signal energy and the limit is the constraint on the energy density with respect to time or spatial coordinate. In the microcosm, a signal is a gradient of potential; the constraint of its perception speed in the case of motion results, within the action threshold, in the fact that it changes in kinetic energy with changing potential cannot be determined. As a result, the particle motion turns out defined only in a finite number of “reference” points separated by intervals determined by the information threshold. Between reference points the motion has an uncertain, random, i.e., noisy character. The threshold equation for finding random deviations of motion parameters which should generalize the known Schrödinger and Klein-Gordon equations is discussed. Information transmission capacity of space for electromagnetic signals is estimated based on the analysis of the densities of the threshold and limiting energy.
A classical signal which agrees with the ideas of mathematical analysis on infinitesimal quantities possesses an infinite information capacity, which contradicts the concept of information that is finite by definition. A real signal should have some “threshold” for determining a finite step between its distinguishable states and the “limit” for the possible number of states. This paper considers the influence of the level of required energy, performance, and noise of the receiver on the capability of distinguishing the set of states in the signal. It is shown that the generalized threshold is the constraint on the spectral density of the signal energy and the limit is the constraint on the energy density with respect to time or spatial coordinate. In the microcosm, a signal is a gradient of potential; the constraint of its perception speed in the case of motion results, within the action threshold, in the fact that it changes in kinetic energy with changing potential cannot be determined. As a result, the particle motion turns out defined only in a finite number of “reference” points separated by intervals determined by the information threshold. Between reference points the motion has an uncertain, random, i.e., noisy character. The threshold equation for finding random deviations of motion parameters which should generalize the known Schrödinger and Klein-Gordon equations is discussed. Information transmission capacity of space for electromagnetic signals is estimated based on the analysis of the densities of the threshold and limiting energy.
It is known that the transition from quantum to classical physics occurs when the action constant h decreases to an infinitesimal value. As shown in the article, for signals this statement is applicable to their classical model only and it is far from all real signals existing in nature and having a threshold on action more than h. Such threshold is the threshold of perception that exists for any natural macro and micro signal receivers, including atoms and particles. It was revealed that above the boundary frequency of the classical thermal noise v-high, found by Planck, the properties of real signals correspond to quantum constraints. It is asserted that in the frequency range above v-high inertness appears and dominates, i.e. the integration of the signals. As a result of it a transition from the perception threshold on energy to the perception threshold on action happens. Besides, instead of disappearing thermal noise on energy, an indestructible sub-threshold noise on action appears that is associated with the uncertainty relation. The concept of algebraic, not integer logic is introduced for real sub-threshold signals. It is demonstrated that in combination of sub-threshold random states of several signals, their integration leads to a joint probability, i.e. to superposition states of QM.
The paper describes the general physical theory of signals, carriers of information, which supplements Shannon’s abstract classical theory and is applicable in much broader fields, including nuclear physics. It is shown that in the absence of classical noise its place should be taken by the physical threshold of signal perception for objects of both macrocosm and microcosm. The signal perception threshold allows the presence of subthreshold (virtual) signal states. For these states, Boolean algebra of logic ( A = 0/1) is transformed into the “algebraic logic” of probabilities (0 ≤ a ≤ 1). The similarity and difference of virtual states of macroand microsignals are elucidated. “Real” and “quantum” information for computers is considered briefly. The maximum information transmission rate is estimated based on physical constants.
A covariant generalization of a non-relativistic stochastic quantum mechanics introduced by de la Peña and Cetto is formulated. The analysis is done in space-time and avoids the use of a non-covariant time evolution parameter in order to search for Lorentz invariance. The covariant form of the set of iterative equations for the joint coordinate and momentum distribution function Q(x,p) is derived and expanded in power series of the charge of the particle. Then, solutions of the zeroth order in the charge of the iterative equations for Q(x,p) are considered. For them, it follows that the space-time probability density ρ(x) and the function S(x) which gradient defines the mean value of the momentum at the space time point x, define a complex function ψ(x) which exactly satisfies the Klein-Gordon (KG) equation. It is argued that when the KG solution is either of positive or negative energy, the total number of particles conserves in the random motion. It follows that the total number of particles conserves when ψ(x) composed alternatively of pure positive or negative energy modes. In addition, solutions for the joint distribution function in lowest order, satisfying the positive condition are also found. They suggests a possible link with the Couder's experiments on droplet movements over oscillating liquid surfaces.
What makes information physically possible? This research framework marks a significant shift in the evolution of the HCC-S³ programme. Rather than asking how much information a physical system can store, it asks a more fundamental question: under what conditions can a difference between two quantum states become physically real? The framework proposes that information is not a primitive entity, but a derived quantity arising from realised physical distinguishability. In this view, geometry does not merely provide a background for physics—it constrains which distinctions can exist as physically meaningful states. The central conceptual chain is intentionally reversed with respect to classical information theory: Physical Carrier (M, g) → Geometric Constraints → Physical Distinguishability → RPD(M) → N_dist = |RPD(M)| → I = log₂ N_dist. Here, RPD(M) denotes the set of realised physically distinguishable equivalence classes on a compact carrier, while I = log₂ N_dist becomes a consequence rather than an axiom. This approach shifts the focus from counting bits to identifying the geometric and operational conditions that make bits possible in the first place. A key feature of the framework is the introduction of the general geometric functional 𝒢(M), combining candidate structures such as holonomy, Berry phase, spin structure, curvature invariants, Dirac and Laplace spectra, and spectral gaps. The framework does not claim that any single element determines distinguishability. Instead, it establishes a disciplined research programme in which these geometric structures are investigated as potential constraints on physically admissible differences between quantum states. The framework also introduces an operational definition of distinguishability: two states are physically distinguishable only if there exists a finite-energy, finite-time local operation capable of discriminating them above a prescribed threshold. This deliberately separates physical distinguishability from purely mathematical orthogonality and places experimental accessibility at the centre of the formalism. Importantly, HCC-S³ is presented as the primary compact test carrier, not as an exclusive description of physical reality. The formalism is intentionally written for a general compact manifold M, allowing future comparison with alternative compact geometries. This makes the programme methodologically open while preserving a concrete reference model for mathematical development. Rather than proposing a completed theory, this work establishes a research framework. It introduces precise definitions, axioms, candidate criteria, research questions, and open mathematical problems, providing a structured path toward a future ontology of physical information. The long-term objective is not merely to measure information, but to understand how geometry, quantum structure, and operational constraints give rise to physically realised distinguishability, from which information naturally emerges as a derived concept.
As semiconductor technology is rapidly approaching physical barriers that restrict the speed of digital signal processing, knowledge about physical limits to data transmission and processing is gaining more and more importance. This paper addresses a fundamental physical limit that derives from energy-time uncertainty. By relating the physical limitation to the basics of signal processing and information theory it turns out that trivalent signaling might become optimal at the frontiers of physics.
Optical signals may be regarded as probability laws (on photon events). The problem of optical signal recovery may therefore be viewed as a problem in estimating a probability law p(x). Maximum entropy has, in the past, been used for this purpose. Here, we discuss instead the use of minimum Fisher information I = ∫ d x [ p ′ ( x ) ] 2 / p ( x ) . Consider a physical system consisting of a random aggregate of particles or pho tons. Consider the experiment of measuring one particle's coordinate y, and from this, best estimating the mean coordinate θ of the ensemble, where y = θ + x. As time passes, the particles randomly become more spread out, so that the error in the estimate should increase. But the error goes inversely as I. Therefore, I should statistically decrease with time. With no constraint on the system, as t → ∞, I → 0, defining a maximally random law p(x) = constant. However, in the presence of a physical constraint, I should approach a finite value, obeying I = minimum. When the constraint is linear in the mean kinetic energy of the system, the solution p(x) obeys the stationary differential equation for the system. In this way, the Schrodinger (energy) wave equation, Helmholtz wave equation, diffusion equation, and Maxwell-Boltzmann law may be derived from one classical principle of disorder.