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Pisa University Press eBooks

Sulla fisica cibernetica quantistica di Eduardo R. Caianiello

Enrico Giannetto

Published Jan 1, 2023• 0 citations
Publisher

Abstract

Contemporary physics developed in the twentieth century through a succession of revolutions that upset its epistemological status with the prospect of a new ontology and a new gnoseology. From the physics of chaos to the theories of relativity, from quantum physics to quantum-relativistic field theory and the theory of the S matrix ("scattering matrix"). Recently, the transversal scientific paradigm of information has been definitively establishing itself: above all, through its concretization in the realization of machines, as widespread as personal computers, capable of processing and transmitting information up to an even greater ability to virtually simulate any type of physical reality. A new informational conception of Nature emerged, of the Universe as a potentially infinite computer. However, there is still a lack of a mathematical formulation of physics and cosmology in terms of information. In recent years, the research of Eduardo R. Caianiello (1921-1993), a Neapolitan physicist and cybernetist, has been linked to this goal, who, in 1980, formulated quantum theory in an 8-dimensional XA (x, ct; p, p4 = E/c) non-Euclidean, curve relativistic phase space, which has only the form of a geometry but is a dynamic written in a pseudo-geometric form. The operators of Heisenberg algebra (also position and time) are expressed in a quantization by means of covariant derivatives and the quantum commutation relations are interpreted as components of the curvature tensor. The geometric curvature thus expresses the quantum uncertainty in terms of informational entropy (it is a complex information geometry: the ds2 coincides with the cross-entropy). The algebra is that of the octonions. Caianiello reformulated not only quantum mechanics, but also general relativity, thermodynamics and geometry itself on the basis of information theory and systems theory, opening a way to the greatest revolution in physics: in philosophical terms it is an informational transformation of a transcendental phenomenological hermeneutics.

DOI
10.12871/978883339843326

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Contemporary physics developed in the twentieth century through a succession of revolutions that upset its epistemological status with the prospect of a new ontology and a new gnoseology. From the physics of chaos to the theories of relativity, from quantum physics to quantum-relativistic field theory and the theory of the S matrix ("scattering matrix"). Recently, the transversal scientific paradigm of information has been definitively establishing itself: above all, through its concretization in the realization of machines, as widespread as personal computers, capable of processing and transmitting information up to an even greater ability to virtually simulate any type of physical reality. A new informational conception of Nature emerged, of the Universe as a potentially infinite computer. However, there is still a lack of a mathematical formulation of physics and cosmology in terms of information. In recent years, the research of Eduardo R. Caianiello (1921-1993), a Neapolitan physicist and cybernetist, has been linked to this goal, who, in 1980, formulated quantum theory in an 8-dimensional XA (x, ct; p, p4 = E/c) non-Euclidean, curve relativistic phase space, which has only the form of a geometry but is a dynamic written in a pseudo-geometric form. The operators of Heisenberg algebra (also position and time) are expressed in a quantization by means of covariant derivatives and the quantum commutation relations are interpreted as components of the curvature tensor. The geometric curvature thus expresses the quantum uncertainty in terms of informational entropy (it is a complex information geometry: the ds2 coincides with the cross-entropy). The algebra is that of the octonions. Caianiello reformulated not only quantum mechanics, but also general relativity, thermodynamics and geometry itself on the basis of information theory and systems theory, opening a way to the greatest revolution in physics: in philosophical terms it is an informational transformation of a transcendental phenomenological hermeneutics.
The Theory of Gravito–Informational Unification (TGIU, from the Romanian Teoria Gravito–Informațională Universală — “Universal Gravitational Informational Theory”) introduces a real-valued reformulation of fundamental physics by eliminating the mathematical necessity of the imaginary unit i. In this framework, all physical phenomena — quantum, relativistic, and thermodynamic — emerge from the dynamic coupling between two real conjugate fields: the Informational Potential Φ and the Entropic Field S. Their interaction generates informational curvature, quantified by the TGIU Equilibrium Force (TEF), which replaces i as the real 90° curvature operator in the Φ–S plane. The complex wavefunction of conventional quantum mechanics is redefined as a real two-component vector Ψ_TGIU = (Φ,S)^T, from which both the Schrödinger and Dirac equations can be derived in purely real form. At macroscopic scales, the same Φ–S curvature produces Einstein’s field equations, revealing gravitation as an emergent informational process. Thus, quantum mechanics, relativity, and thermodynamics are unified within a single geometric framework based on real informational curvature. A central feature of this formulation is asymmetry — the origin of time, entropy, and existence. Perfect symmetry (Φ = S) corresponds to a timeless, nonphysical state, while asymmetry (Φ ≠ S) generates temporal flow and material structure. The asymmetry coefficient α = 1 – η (where η is the entropy cost of informational collapse) regulates the irreversible drift of Φ and S, producing the arrow of time and the finite persistence of reality between the bounds 0 < Existence < infinite. By identifying the imaginary component of quantum theory with real curvature in informational space, the TGIU framework transforms the mathematical abstraction of complex numbers into a measurable geometric property of reality. It offers a coherent explanation for the emergence of time, matter–antimatter imbalance, dark energy, and cosmic evolution, demonstrating that existence itself arises from an intentional asymmetry maintained by the TGIU Equilibrium Force.
The experience from Quantum Information of the last twenty years has lead theorists to look at Quantum Theory and the whole of Physics from a different angle. A new information-theoretic paradigm is emerging, long time ago prophesied by John Archibald Wheeler with his popular coinage 'It from bit'. Theoretical groups are now addressing the problem of deriving Quantum Theory from informational principles, and similar lines are investigated in new approaches to Quantum Gravity. In my talk I will review some recent advances on these lines. The general idea synthesizing the new paradigm is that there is only Quantum Theory (without quantization rules): the whole Physics--including space-time and relativity--is emergent from quantum-information processing. And, since Quantum Theory itself is made with purely informational principles, the whole Physics must be reformulated in information-theoretical terms. The review is divided into the following parts: (a) The informational axiomatization of Quantum Theory; (b) How space-time and relativistic covariance emerge from the quantum computation; (c) What is the information-theoretical meaning of inertial mass and Planck constant, and how the quantum field emerges; (d) Observational consequences: mass-dependent refraction index of vacuum. I then conclude with some possible future research lines.
In contemporary physics, fundamental structures such as space, time, matter, spin, and measurement are typically introduced as independent primitives or axiomatic ingredients. While quantum mechanics and relativistic field theories describe these structures with extraordinary precision, they do not explain why such structures exist, why they are discrete or stable, nor why reality manifests in exactly three spatial dimensions with an irreversible arrow of time. This work presents a unified informational–geometric framework—the Universal Gravito–Informational Theory (TGIU)—in which physical reality emerges from a pre-geometric informational substrate governed by two complementary gradients: informational coherence (Φ) and informational entropy (S). Their interaction is regulated by a real-valued dynamical mechanism composed of the Curvature–State Transform (CST) and the TGIU Equilibrium Force (TEF). Together, these operators generate bounded, orthogonal informational rotations whose stabilized projections give rise to geometry, matter, and observable physical laws. Within this framework, electron orbitals are reinterpreted as CST limit cycles, spin emerges as the topological orientation of these cycles, and the Pauli exclusion principle arises from phase–space saturation rather than postulated antisymmetry. Atomic stability, the absence of radiative decay in stationary states, fine structure, and the Lamb shift are shown to follow from TEF anisotropy and vacuum curvature granularity, while remaining fully consistent with quantum electrodynamics in its predictive domain. Measurement and wavefunction collapse are described as local TEF locking events, providing a deterministic but non-restorative mechanism for outcome selection without invoking fundamental randomness. Time itself is shown to emerge as monotonic CST phase accumulation, explaining both its one-dimensional nature and its irreversibility as geometric consequences of bounded informational curvature. The existence of exactly three spatial dimensions follows from a CST dimensional closure condition, identifying three dimensions as the only geometry capable of sustaining stable, non-divergent informational rotation. Importantly, TGIU does not replace quantum mechanics, general relativity, or field theory. Instead, it supplies a deeper explanatory layer that clarifies why these frameworks work, why their structures are constrained as observed, and why no physical process can reach absolute annihilation or infinite divergence. Extremes are not restored but redirected: identity is not conserved, yet nature persists through renewed coherence. This work positions TGIU as an empirically motivated, geometrically grounded extension of modern physics—one that unifies matter, time, measurement, and dimensionality under a single informational principle, while remaining compatible with established theories in their respective limits.
Classical physics has enabled the acquisition of significant knowledge of the physical properties of nature on a standard macroscopic scale. These achievements were driven by use of the causal ontological approach (proposed originally by Aristotle) to formulate models of physical reality. At the beginning of the 20th century, however, the physics community began to prefer models based on a fundamentally different approach to human knowledge. Copenhagen quantum mechanics (CQM) was used to describe the micro-world. The special theory of relativity was used to describe the kinematics of objects moving at high velocity values in both the macroscopic and microscopic regions. This phenomenological approach to knowledge has been more focused on how things appear - instead of their actual properties and causal sequence. In the middle of the 20th century, the causal ontological approach was used to develop a significant scientific advance: the systematization of fundamental strongly interacting particles on the basis of unified algebra in three-dimensional isotopic spin space for spin values 1, 1/2, and 0. However, it was later strongly deformed under the influence of the phenomenological approach and the quark model. This paper will show that practically all contemporary theoretical models of physical reality contain mistakes or unresolved problems. Further scientific progress can be obtained if (and only if) scientists return to the successful causal ontological approach and falsification. Classical physics may be slightly generalized to enable the description of inertia mass increase in dependence on velocity, replacing the relativity theory and CQM. New assumptions may then be employed using generalized classical physics (GCP) to formulate new descriptions of observed phenomena that were previously inaccurately interpreted and used to promote fundamentally inadequate theories.
Quantum Mechanics has taught us a lesson that goes well beyond a set of new physical laws. It has provided us with genuine “theorems of epistemology”. We now know that there are situations when the observation of the world cannot be considered as the mere reading of a reality pre-existing the observation, whereas there are circumstances where the knowledge of the whole do not corresponds to the knowledge of the parts (holism). We know that there are incompatible properties that are complementary. We know that there exist properties of the whole that are incompatible with any property of each part. The notion of “object” defined in terms of its “properties ” is in contrast with its mereologic connotation according to which objects can be composed to form new objects. The particle ontology as localizable unity is in contrast with the Malament theorem in quantum field theory. To the above add the fact that the two more general fundamental theories in physics – the quantum theory of fields and the general relativity of Einstein – are logically incompatible. In order to reconcile the logical coherence of the observations with their theoretical explanation we need a radical change of paradigm. The solution here proposed is to abandon the vision of the world as a “mechanism” and to substitute it with that of “algorithm”. This is the paradigm of the “universe as a huge computer” that have been latent within the community since Richard Feynman, and nowadays is resurrecting in physics, showing its full theoretical power. In the new algorithmic vision the “mechanics” becomes an emergent phenomenology. Without the need of physical primitive, the new “informational” program allows us to found physics on solid axiomatic grounds. The quantum theory of abstract systems along with the free quantum field theory are derived from information-theoretic axioms. The axioms of quantum theory all have an epistemological connotation, and pertain the possibility of falsifying the propositions of the theory. They reconnect holism with reductionism, probabilism and falsifiability, substituting the notion of “object” with that of “system” and of “event”, and logically implying the theorem of quantum theory without the need of using the abstract Hilbert-spaces toolkit. The free quantum field theory (Weyl, Dirac e Maxwell) is obtained by adding axioms of minimization of algorithmic complexity. The informational framework well separates the notions of “experiment”and “theory”: the theory connects input with output, the experiment being identified with the collection of input, output, and objective intermediate events. The objective reality (experiment) is made of “icons” with which we interact: the theory is the underlying algorithm. The paradigm describes the tapestry of reality as pure software, “software”. “Software without hardware”: the dematerialization of physics. “Reality without realism” means pure logical coherentism.
Abstract This work develops a unified ontological and mathematical framework for fundamental physics based on the Zero‑Entropy Background Topological Structure (ZEBTS) and the four irreducible structural components of χ‑reality: the χ‑metric, χ‑symplectic form, χ‑topology, and χ‑information. Within this framework, physical observables are formulated as χ‑tensors, and the algebra of observables arises from χ‑symplectic geometry rather than postulated commutation relations. The resulting χ‑commutator is a geometric tensor encoding the curvature of χ‑symplectic structure, while χ‑operators inhabit a χ‑manifold equipped with χ‑metric, χ‑symplecticity, χ‑curvature, χ‑topology, and χ‑informational complexity. The theory establishes a complete χ‑spectral formalism, where χ‑measurement is a χ‑topological projection, χ‑superselection emerges as a theorem of χ‑topology and χ‑information, and χ‑entropy is defined through χ‑spectral and χ‑operator entropies. χ‑dynamics is formulated as a χ‑Hamiltonian flow on the χ‑operator manifold, incorporating χ‑geodesics, χ‑topological currents, and χ‑informational gradients. The χ‑Absolute is introduced as the structural limit Iχ→∞, representing the boundary of physically realizable configurations and the ontological attractor of χ‑dynamics. A central result of the framework is that Special Relativity (STR), General Relativity (GTR), and Quantum Phenomena (QP) arise as χ‑projections of the unified χ‑structure: STR as the χ‑metric projection, GTR as the χ‑geometric projection, and QP as the χ‑symplectic projection. Particles appear as χ‑topological defects of χ‑spectrum, and fields arise as χ‑modes of χ‑operators. The theory yields concrete experimental predictions, including χ‑modulations in the CMB, χ‑topological signatures in large‑scale structure, χ‑dispersion of gravitational waves, χ‑entropy bounds in cosmology, and χ‑geometric distortions in astrometric data. Overall, the χ‑framework provides a coherent, mathematically rigorous, and physically testable unification of geometry, topology, quantization, information, and cosmology. It demonstrates that the structure of physical reality is not imposed but emerges from the intrinsic χ‑geometry of being, with ZEBTS as the realized background and χ‑Absolute as the structural limit of the Universe.