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Mon, 22 Jan 2018 21:16:34 +0100Joomla! - Open Source Content Managementen-gbTowards a Universal Probability Theory, Part II
http://infinitemath.hu/en/mathematics/361-towards-a-universal-probability-theory-part-ii
http://infinitemath.hu/en/mathematics/361-towards-a-universal-probability-theory-part-iiSingle quantum's and their multitudes' events Contents Single quantum and their multitudes in the two slit experiment Single quantum's and their multitudes' events in the probability theory Appendices After registration, you may ask for a translation of the full text by email. ]]>miklos@bartim.hu (Mlakár Katalin)MathematicsFri, 29 Dec 2017 18:33:04 +0100Towards a Universal Probability Theory, Part I
http://infinitemath.hu/en/mathematics/357-towards-a-universal-probability-theory-part-i
http://infinitemath.hu/en/mathematics/357-towards-a-universal-probability-theory-part-iIntroduction Andrei Khrennikov's Contextual Probability and the Two Slit Experiment Quoted Khrennikov: “One of problems was of purely mathematical character. The standard probabilistic formalism based on Kolmogorov’s axiomatics, 1933, was a fixed context formalism. This conventional probabilistic formalism does not provide rules of operating with probabilities calculated for different contexts. However, in quantum theory we have to operate with statistical data obtained for different complexes of physical conditions, contexts. In fact, this context dependence of probabilities as the origin of the superposition principle was already discussed by W. Heisenberg; unfortunately, only in quite general and rather philosophic framework.”1 Contents Khrennikov's contextualism What's next? Feynman and the two slit experiment Appendix ____________________________ 1Andrei Khrennikov, „Contextual viewpoint to quantum stochastics”; https://arxiv.org/pdf/hep-th/0112076.pdf After…]]>miklos@bartim.hu (Mlakár Katalin)MathematicsSun, 03 Dec 2017 19:26:59 +0100Geometric Algebras of Spacetime
http://infinitemath.hu/en/mathematics/347-geometric-algebras-of-spacetime
http://infinitemath.hu/en/mathematics/347-geometric-algebras-of-spacetimeThe Ambiguity of Geometric Algebra in the Models of Spacetime Contents 1. Memo 1.1. Multivectors in GA3 1.2. Conjugations in GA3 1.2.1. Clifford conjugation 1.2.2. Pauli conjugation 1.2.3. The role of complex imaginary unit in the Clifford and Pauli conjugations 2. Minkowski spacetime generated in GA1,3 2.1. Bivektor algebra 2.2. Lorentz transformation 3. Spacetime model in classic GA3: the scalar element as a time representation 4. Summary 1. Appendix Pauli algebra and matrices 2. Appendix Gamma or Dirac matrices, Dirac algebra 3. Appendix Lorentz transformation a. Einstein description with coordinates b. Applying hyperbolic functions c. Usage of hyperbolic numbers to describe space time References After registration, you may ask for a translation of the full text by email. ]]>miklos@bartim.hu (Mlakár Katalin)MathematicsWed, 14 Jun 2017 21:17:25 +0200CA, GA and the Two-element Numbers – Thirdly
http://infinitemath.hu/en/mathematics/345-ca-ga-and-the-two-element-numbers-thirdly
http://infinitemath.hu/en/mathematics/345-ca-ga-and-the-two-element-numbers-thirdlyConjugation concepts in GA3 Contents Memo Involutions: reversion and conjugation in GA3 Reversion Magnitude or modulus Conjugation Comments Appendix Pauli algebra References David Hestenes, „Space–Time Algebra” David Hestenes, „New Foundations for Classical Mechanics” Chris Doran & Anthony Lasenby, „Geometric Algebra for Physicist” Stephen Gull, Anthony Lasenby, Chris Doran, „Imaginary Numbers are not Real — the Geometric Algebra of Spacetime” http://geometry.mrao.cam.ac.uk/wp-content/uploads/2015/02/ImagNumbersArentReal.pdf After registration, you may ask for a translation of the full text by email.]]>miklos@bartim.hu (Mlakár Katalin)MathematicsMon, 01 May 2017 16:00:14 +0200The Dimensions of the Geometric Algebra
http://infinitemath.hu/en/mathematics/343-the-dimensions-of-the-geometric-algebra
http://infinitemath.hu/en/mathematics/343-the-dimensions-of-the-geometric-algebraSubjective and unfinished thoughts on GA dimensions In everyday life we ordinarily use the term dimension as spatial size. In sciences, than the mathematics and physics, the term of the dimension is used in a diverse, different sense. Contents Dimension and grade in GA Unit of measurement as dimension Qualitative infinite as dimension After registration, you may ask for a translation of the full text by email.]]>miklos@bartim.hu (Mlakár Katalin)MathematicsThu, 06 Apr 2017 15:41:21 +0200CA, GA and the Two-element Numbers – Secondly
http://infinitemath.hu/en/mathematics/337-ca-ga-and-the-two-element-numbers-secondly
http://infinitemath.hu/en/mathematics/337-ca-ga-and-the-two-element-numbers-secondlyWith Exciting Dénouement Contents Introduction Geometric Algebra of the Plane The Algebra of 3-Space Conclusions Abstract by a quotation „These considerations all indicate that our present thinking about quantum mechanics is infested with the deepest misconceptions. We believe, with David Hestenes, that geometric algebra is an essential ingredient in unravelling these misconceptions.”1 __________________________ 1 See Stephen Gull, Anthony Lasenby, Chris Doran, „Imaginary Numbers are not Real — the Geometric Algebra of Spacetime”; http://geometry.mrao.cam.ac.uk/wp-content/uploads/2015/02/ImagNumbersArentReal.pdf After registration, you may ask for a translation of the full text by email. ]]>miklos@bartim.hu (Mlakár Katalin)MathematicsSun, 05 Feb 2017 20:39:07 +0100The Clifford Algebra, the Geometric Algebra and the Two-element Numbers
http://infinitemath.hu/en/mathematics/333-the-clifford-algebra-the-geometric-algebra-and-the-two-element-numbers
http://infinitemath.hu/en/mathematics/333-the-clifford-algebra-the-geometric-algebra-and-the-two-element-numbers Abstract The geometric algebra (GA) is a Clifford algebra (CA) of a vector space over the field of real numbers. A similar concept of complex numbers can be derived from the GA. It is very instructive to compare, as the various authors deduce one of the two-element numbers from CA, or from GA. Contents David Hestenes Garret Sobczyk Doran-Lasenby Stefan Ulrich Summary After registration, you may ask for a translation of the full text by email. ]]>miklos@bartim.hu (Mlakár Katalin)MathematicsFri, 06 Jan 2017 19:06:22 +0100Number systems – what's next?
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http://infinitemath.hu/en/mathematics/327-number-systems-what-s-nextDesiderata Content The notion of number Desiderata to the extension of the numbers Summary Abstract Although the numbers are yet considered as the simplest abstractions of mathematics, it is increasingly taking shape is a picture in which the numbers will the most complex and exciting concept in mathematics. The geometric algebra is a probable candidate for the new number system, but desiderata of the author is unlike the criteria of the geometric algebra in three points: The number line of real numbers is orthogonal to the space-dimensions according to the definition of scalar product. As the fundamental operation of arithmetic the product is commutative. The space-dimensions evolve from time-dimension which is represented by number line of real numbers. After…]]>miklos@bartim.hu (Mlakár Katalin)MathematicsWed, 23 Nov 2016 19:22:46 +0100Not space and time, but space-time has to use in the probability theory
http://infinitemath.hu/en/mathematics/325-not-space-and-time-but-space-time-has-to-use-in-the-probability-theory
http://infinitemath.hu/en/mathematics/325-not-space-and-time-but-space-time-has-to-use-in-the-probability-theory Two-element numbers as space-time elements of probability theory Abstract Introductory The probability theory and the space-time Different interpretations and problems of the concept of probability The Bertrand paradox and his explanation Relative frequency concept and the paradoxes Kolmogorov’s probability theory Epilog After registration, you may ask for a translation of the full text by email.]]>miklos@bartim.hu (Mlakár Katalin)MathematicsSun, 25 Sep 2016 08:52:30 +0200The way from the natural numbers through the real numbers to the two-element numbers
http://infinitemath.hu/en/mathematics/211-the-way-from-the-natural-numbers-through-the-real-numbers-to-the-two-element-numbers
http://infinitemath.hu/en/mathematics/211-the-way-from-the-natural-numbers-through-the-real-numbers-to-the-two-element-numbersThe role of the concept of computability in physics “It would require infinite precision for the coordinates of a phase-space point- i.e. all the decimal places!- in order for it to make sense to say that the point is non-computable. (A number described by a finite decimal is always computable.) A finite portion of .a decimal expansion of a number tells us nothing about the computability of the entire expansion of that number. But all physical measurements have a definite limitation on how accurately they can be performed, and can only give information about a finite number of decimal places. Does this nullify the whole concept of 'computable number' as applied to physical measurements?” (Roger Penrose, The Emperor’s New Mind – Concerning Computers, Minds, and The…]]>miklos@bartim.hu (Mlakár Katalin)MathematicsSat, 30 Jul 2016 14:28:32 +0200