SSRN Author: Vasil PenchevVasil Penchev SSRN Content
https://www.ssrn.com/author=4142045
https://www.ssrn.com/rss/en-usSat, 12 Mar 2022 01:10:58 GMTeditor@ssrn.com (Editor)Sat, 12 Mar 2022 01:10:58 GMTwebmaster@ssrn.com (WebMaster)SSRN RSS Generator 1.0REVISION: Fermat’s last theorem proved in Hilbert arithmetic. I. From the proof by induction to the viewpoint of Hilbert arithmeticIn a previous paper (https://dx.doi.org/10.2139/ssrn.3648127 ), an elementary and thoroughly arithmetical proof of Fermat’s last theorem by induction has been demonstrated if the case for “n = 3” is granted as proved only arithmetically (which is a fact a long time ago), furthermore in a way accessible to Fermat himself though without being absolutely and precisely correct. The present paper elucidates the contemporary mathematical background, from which an inductive proof of FLT can be inferred since its proof for the case for “n = 3” has been known for a long time. It needs “Hilbert mathematics”, which is inherently complete unlike the usual “Gödel mathematics”, and based on “Hilbert arithmetic” to generalize Peano arithmetic in a way to unify it with the qubit Hilbert space of quantum information. An “epoché to infinity” (similar to Husserl’s “epoché to reality”) is necessary to map Hilbert arithmetic into Peano arithmetic in order to be relevant to Fermat’s age. Furthermore, the ...
https://www.ssrn.com/abstract=3785977
https://www.ssrn.com/2114226.htmlThu, 10 Mar 2022 22:58:49 GMTNew: The Homeomorphism of Minkowski Space and the Separable Complex Hilbert Space: The physical, Mathematical and Philosophical InterpretationsA homeomorphism is built between the separable complex Hilbert space (quantum mechanics) and Minkowski space (special relativity) by meditation of quantum information (i.e. qubit by qubit). That homeomorphism can be interpreted physically as the invariance to a reference frame within a system and its unambiguous counterpart out of the system. The same idea can be applied to Poincaré’s conjecture (proved by G. Perelman) hinting at another way for proving it, more concise and meaningful physically. Furthermore, the conjecture can be generalized and interpreted in relation to the pseudo-Riemannian space of general relativity therefore allowing for both mathematical and philosophical interpretations of the force of gravitation due to the mismatch of choice and ordering and resulting into the “curving of information” (e.g. entanglement). Mathematically, that homeomorphism means the invariance to choice, the axiom of choice, well-ordering, and well-ordering “theorem” (or “principle”) and ...
https://www.ssrn.com/abstract=3967854
https://www.ssrn.com/2101658.htmlFri, 04 Feb 2022 07:04:39 GMTREVISION: What the Tortoise Said to Achilles: Lewis Carroll’s paradox in terms of Hilbert arithmeticLewis Carroll, both logician and writer, suggested a logical paradox containing furthermore two connotations (connotations or metaphors are inherent in literature rather than in mathematics or logics). The paradox itself refers to implication demonstrating that an intermediate implication can be always inserted in an implication therefore postponing its ultimate conclusion for the next step and those insertions can be iteratively and indefinitely added ad lib, as if ad infinitum. Both connotations clear up links due to the shared formal structure with other well-known mathematical observations: (1) the paradox of Achilles and the Turtle; (2) the transitivity of the relation of equality. Analogically to (1), one can juxtapose the paradox of the Liar (for Lewis Carroll’s paradox) and that of the arrow (for “Achilles and the Turtle”), i.e. a logical paradox, on the one hand, and an aporia of motion, on the other hand, suggesting a shared formal structure of both, which can be called ...
https://www.ssrn.com/abstract=3944692
https://www.ssrn.com/2089391.htmlThu, 30 Dec 2021 22:05:23 GMTREVISION: Quantum information as the information of infinite collections or seriesThe quantum information introduced by quantum mechanics is equivalent to a certain generalization of classical information: from finite to infinite series or collections. The quantity of information is the quantity of choices measured in the units of elementary choice. The “qubit”, can be interpreted as that generalization of “bit”, which is a choice among a continuum of alternatives. The axiom of choice is necessary for quantum information. The coherent state is transformed into a well-ordered series of results in time after measurement. The quantity of quantum information is the transfinite ordinal number corresponding to the infinity series in question. The transfinite ordinal numbers can be defined as ambiguously corresponding “transfinite natural numbers” generalizing the natural numbers of Peano arithmetic to “Hilbert arithmetic” allowing for the unification of the foundations of mathematics and quantum mechanics.<br>
https://www.ssrn.com/abstract=3630063
https://www.ssrn.com/2060034.htmlWed, 15 Sep 2021 12:33:04 GMTREVISION: Quantity in Quantum Mechanics and the Quantity of Quantum InformationThe paper interprets the concept “operator in the separable complex Hilbert space” (particalry, “Hermitian operator” as “quantity” is defined in the “classical” quantum mechanics) by that of “quantum information”. As far as wave function is the characteristic function of the probability (density) distribution for all possible values of a certain quantity to be measured, the definition of quantity in quantum mechanics means any unitary change of the probability (density) distribution. It can be represented as a particular case of “unitary”<br>qubits. The converse interpretation of any qubits as referring to a certain physical quantity implies its generalization to non-Hermitian operators, thus neither unitary, nor conserving energy. Their physical sense, speaking loosely, consists in exchanging temporal moments therefore being implemented out of the space-time “screen”. “Dark matter” and “dark energy” can be explained by the same generalization of “quantity” to non-Hermitian operators ...
https://www.ssrn.com/abstract=3878772
https://www.ssrn.com/2058739.htmlFri, 10 Sep 2021 11:07:00 GMTNew: The 'Noncausal Causality' of Quantum InformationThe paper is concentrated on the special changes of the conception of causality from quantum mechanics to quantum information meaning as a background the revolution implemented by the former to classical physics and science after Max Born’s probabilistic reinterpretation of wave function. Those changes can be enumerated so: (1) quantum information describes the general case of the relation of two wave functions, and particularly, the causal amendment of a single one; (2) it keeps the physical description to be causal by the conservation of quantum information and in accordance with Born’s interpretation; (3) it introduces inverse causality, “backwards in time”, observable “forwards in time” as the fundamentally random probability density distribution of all possible measurements of any physical quantity in quantum mechanics; (4) it involves a kind of “bidirectional causality” unifying (4.1) the classical determinism of cause and effect, (4.2) the probabilistic causality of quantum ...
https://www.ssrn.com/abstract=3870329
https://www.ssrn.com/2039235.htmlThu, 01 Jul 2021 14:26:07 GMTREVISION: Both Classical & Quantum Information; Both Bit & Qubit: Transcendental Time. Both Physical & Transcendental TimeInformation can be considered as the most fundamental, philosophical, physical and mathematical concept originating from the totality by means of physical and mathematical transcendentalism (the counterpart of philosophical transcendentalism). Classical and quantum information, particularly by their units, bit and qubit, correspond and unify the finite and infinite. As classical information is relevant to finite series and sets, as quantum information, to infinite ones. A fundamental joint relativity of the finite and infinite, of the external and internal is to be investigated. The corresponding invariance is able to define physical action and its quantity only on the basis of information and especially: on the relativity of classical and quantum information. The concept of transcendental time, an epoché in relation to the direction of time arrow can be defined. Its correlate is that information invariant to the finite and infinite, therefore unifying both classical and quantum ...
https://www.ssrn.com/abstract=3823665
https://www.ssrn.com/2035541.htmlSun, 20 Jun 2021 09:44:01 GMTREVISION: The Symmetries of Quantum and Classical Information. The Resurrected 'Ether' of Quantum InformationThe paper considers the symmetries of a bit of information corresponding to one, two or three qubits of quantum information and identifiable as the three basic symmetries of the Standard model, U(1), SU(2), and SU(3) accordingly. They refer to “empty qubits” (or the free variable of quantum information), i.e. those in which no point is chosen (recorded). The choice of a certain point violates those symmetries. It can be represented furthermore as the choice of a privileged reference frame (e.g. that of the Big Bang), which can be described exhaustively by means of 16 numbers (4 for position, 4 for velocity, and 8 for acceleration) independently of time, but in space-time continuum, and still one, 17th number is necessary for the mass of rest of the observer in it. The same 17 numbers describing exhaustively a privileged reference frame thus granted to be “zero”, respectively a certain violation of all the three symmetries of the Standard model or the “record” in a qubit in general, ...
https://www.ssrn.com/abstract=3861105
https://www.ssrn.com/2035445.htmlSat, 19 Jun 2021 09:08:19 GMTREVISION: The Symmetries of Quantum and Classical Information. The Ressurrected 'Ether' of Quantum InformationThe paper considers the symmetries of a bit of information corresponding to one, two or three qubits of quantum information and identifiable as the three basic symmetries of the Standard model, U(1), SU(2), and SU(3) accordingly. They refer to “empty qubits” (or the free variable of quantum information), i.e. those in which no point is chosen (recorded). The choice of a certain point violates those symmetries. It can be represented furthermore as the choice of a privileged reference frame (e.g. that of the Big Bang), which can be described exhaustively by means of 16 numbers (4 for position, 4 for velocity, and 8 for acceleration) independently of time, but in space-time continuum, and still one, 17th number is necessary for the mass of rest of the observer in it. The same 17 numbers describing exhaustively a privileged reference frame thus granted to be “zero”, respectively a certain violation of all the three symmetries of the Standard model or the “record” in a qubit in general, ...
https://www.ssrn.com/abstract=3861105
https://www.ssrn.com/2034952.htmlThu, 17 Jun 2021 09:41:22 GMTREVISION: The Generalization of the Periodic Table: The 'Periodic Table' of 'Dark Matter'The presentation follows a previous one in Torino (2019 July 15) also published as a paper (Penchev 2019). It discusses a thought experiment in Einstein’s manner of “Gedankenexperimenten” to suggest a possible generalization of the invariance of physical laws to arbitrarily accelerated reference frames in general relativity in relation to chemistry. The conclusion claims the indistinguishability of the following two kinds of the spectral lines of the same chemical substance: (1) due to red shift and originating from an arbitrarily remote astronomical object (such as a star, a galaxy, etc.), anywhere in the universe; and (2), after entanglement in experiments conducted on our planet; furthermore (3), a bijection exists between all possible red shifts and shifts due to entanglement. In other words, as accelerated motion and gravity are indistinguishable after Einstein’s Gedankenexperiment in general relativity, as accelerated motion, gravity, and entanglement are indistinguishable ...
https://www.ssrn.com/abstract=3800823
https://www.ssrn.com/2011331.htmlSat, 03 Apr 2021 13:29:54 GMT