http://popups.lib.uliege.be/1373-5411/index.php?id=1515 Index terms fr 0 http://popups.lib.uliege.be/1373-5411/index.php?id=4527 Kant's theory of consciousness is related to quantum mechanics by his proof that the Democritos' atom is both indivisible and divisible like a photon in the two slits experiment. This paradox has been solved by Schroedinger's equation. It also leads to the conclusion that there is a collapse of the wave function in quantum mechanics. It follows from the existence of two stages, preattentional and attentional, is visual search that quantum mechanics applies also to visual perception, and the object integration is a collapse of the wave function. The integration of macroscopic objects involves the migration of features between objects. We are unaware of this due to an anticipatory selection mechanism of the perceived sensory input. This migration of features occurs also inside an atom, changing few atoms of matter into atoms of antimatter. Mon, 14 Oct 2024 10:06:18 +0200 Mon, 14 Oct 2024 12:55:56 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=4527 http://popups.lib.uliege.be/1373-5411/index.php?id=860 The stochastic dynamical system with the states described by elements u of a Hilbert space is considered. There is a deterministic system considered as its nonperturbed variant. An outcome y is observed under random perturbations. The probability distribution P(y, u) of the measurements results in the fixed states u is analysed. A class of stochastic systems marked by the full determination of the law P(y, u) via equations of the nonperturbed system is found. We also find the distributions P(y, u). These distributions prove to be similar to the quantum laws of probability distribution of observable quantities including the principles of superposition and uncertainty and the phenomenon of quantization. Mon, 01 Jul 2024 14:03:02 +0200 Thu, 10 Oct 2024 10:42:58 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=860 http://popups.lib.uliege.be/1373-5411/index.php?id=2810 In the wave-particle duality, a free particle can be considered as a wave packet. Is there a wave property that corresponds to the rest mass of the particle? We suggest that this problem can be approached by treating the rest mass on the same footing as energy and momentum. Here we demonstrate that, by assuming that the matter wave of a particle is an excitation of a real physical field in the vacuum, one could derive the mass-energy relation from the solution of a simplified wave equation describing a free particle. This solution suggests that the rest mass of a particle is associated with a "transverse wave number", which characterizes the radial variation of the wave function in the transverse plane. This model has several appealing features. For example, it predicts that a massless particle must travel at the constant speed of light. Tue, 03 Sep 2024 14:56:05 +0200 Thu, 10 Oct 2024 09:55:30 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=2810 http://popups.lib.uliege.be/1373-5411/index.php?id=3867 Algorithmic topology is the spanning of an algorithm on a topological structure. The common calculus with paper and pen shows that all the recursive functions can be spanned on Euclidean planes. It is known that two topological structures are identical if and only if cut-pasting operations don't need to transform one in the other. Dubois' third stage (identification of incursive algorithm last row and column respectively with its first row and column) gives to incursive algorithms a spanning only on a torus that can be transformed in Euclidean plane only by cut-pasting operations. Thus incursive algorithms couldn't reduce to recursive algorithms and Church's hypothesis couldn't be true. Now, observe the affinity between topologic cut-pasting operations, Dubois' third stage and quantum entanglement. This last one can be considered either two "entanglements" in incursive algorithms or a cut-pasting operation on Euclidean plane on which such an algorithm is spanned to transform such a plane in torus. Is quantum entanglement simply the inadequacy of algorithms that can be spanned only on Euclidean plains to represent quantum mechanics? The same question could have value for some complex biological systems. Mon, 30 Sep 2024 14:20:43 +0200 Tue, 08 Oct 2024 14:43:38 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=3867 http://popups.lib.uliege.be/1373-5411/index.php?id=3205 Mathematics and physics are shown to have a symbiotic relationship as emergent aspects of a universal rewrite system. In addition to explaining the 'unreasonable effectiveness' of mathematics in physics and the 'unreasonable effectiveness' of physics in mathematics, this emergent nature of both subjects makes sense of the distinction between syntactic and semantic approaches to logical reasoning. The system is also shown to generate constraints on the kinds of mathematics and physics that are possible, explaining, in particular, why symmetry is so significant in the subjects' foundations, and specifying which symmetries are most significant, as well as indicating their points of origin. Quantum mechanics emerges from this structure in a very specific form which enables us to understand the origin of symmetry breaking in physics and many other aspects of fundamental physical theory. Gravity also has special characteristics which explain its uniqueness among the four physical forces. Wed, 11 Sep 2024 17:03:03 +0200 Tue, 08 Oct 2024 13:25:37 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=3205 http://popups.lib.uliege.be/1373-5411/index.php?id=3886 We explore a two-photon model of a digital clock. The model implicates the use of spacetime algebra to describe Minkowski space on large scales, but suggests that its scale independent use in special relativity presupposes reference frames of infinite mass. A close look at the finite-frequency digital clock shows that either classical special relativity or Dirac propagation emerges from the clock depending on how the continuum limit is taken. If one smoothly interpolates the tick sequence the clock remains classical. If one extrapolates the inter-tick behaviour, wave propagation is implicated. Tue, 01 Oct 2024 10:25:43 +0200 Tue, 01 Oct 2024 10:25:52 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=3886 http://popups.lib.uliege.be/1373-5411/index.php?id=3444 A novel approach to a proof of the Riemann Hypothesis (that all the zeros of the Zeta function lie on the line x = 1/2) is presented. It is based on the universal nilpotent computational rewrite system (NUCRS), derived in the World Scientific book Zero to lnfinity, from a single nilpotent Dirac operator (Rowlands, 2007), establishing an entirely novel semantic computational foundation simultaneously for both mathematics and quantum physics. Tangible evidence is that the Zeta function is known to represent a quantum system and that the criterion of nilpotence corresponds to (a) Pauli exclusion with unique fermion states spin 1/2 and (b) an infinite rewrite alphabet that also corresponds to the infinite roots of -1, of which the nilpotent generalization of Dirac' s famous quantum mechanical equation is the universal computational order code. Thu, 19 Sep 2024 12:00:50 +0200 Thu, 19 Sep 2024 12:01:02 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=3444 http://popups.lib.uliege.be/1373-5411/index.php?id=2132 New applications of proposed multi-agent's models of neuronet type with intellectual agents for economics and social problems are described. Some unexpected analogies with some topics from quantum physics are proposed. The selection procedures in proposed models remembers the measurement process of quantum state. Also the analogies with concept from quantum mechanics - namely with many - world interpretation of quantum mechanics is discussed. In such interpretation at each moment of time the system with observer is exposed to branching. We may suppose that such analogies aren't accidental. Another important property of proposed models consists in analogies to the description of quantum process on microlevel to the so-called causal nets in quantum gravity. Multivaluedness of solutions in our models allows connecting of its properties to the gauge theory. Tue, 30 Jul 2024 10:58:19 +0200 Tue, 30 Jul 2024 10:58:26 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=2132 http://popups.lib.uliege.be/1373-5411/index.php?id=1511 So-called hidden variables introduced in quantum mechanics by Louis de Broglie and David Bohm have been revived in the recent works by the author. The start viewpoint was the following: All the phenomena, which we observe in the quantum world, should reflect structural properties of the real space. Thus the scale 10-28 cm at which fundamental interactions intersect has been treated as the size of a building block of the space. The mechanics of a moving particle that has been constructed is deterministic by its nature and shows that the particle interacts with cells of the space creating elementary excitations called "inertons" in a cellular substrate. The existence of inertons has been verified experimentally. Mon, 15 Jul 2024 10:30:19 +0200 Mon, 15 Jul 2024 10:30:28 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=1511