![]() Shubin, Nonstandard analysis and singular perturbations of ordinary differential equations, Russ. Stoll, Self-repellent random walks and polymer measures in two dimensions, Diss., Bochum (1985) and appear in Proc. Pecora, A nonstandard infinite dimensional vector space approach to Gaussian functional measures, J. Moore, Non-standard applications of non-standard analysis, Bogota Preprint Fenstad, The discrete and the continuum in the mathematics and natural sciences, Oslo Preprint, Nov. ![]() Hoskins, Standard and Nonstandard Mathematical Analysis, Ellis Horwood, Chichester (1986) Albeverio, Non-standard analysis: Polymer models, quantum fields, Acta Phys. Fenstad, Non-standard methods in stochastic analysis and mathematical physics, Jber. Birkeland, A singular Sturm-Liouville problem treated by nonstandard analysis, Math. MacDonald, Sturm-Liouville theory via nonstandard analysis, Ind. Sloan, The strong convergence of Schrödinger progagators, Trans. Oikkonen, Harmonic analysis and nonstandard Brownian motion in the plane, Math. Cutland, Infinitesimal methods in control theory, deterministic and stochastic, Hull Preprint (1985), Acta Appl. Farrukh, Applications of nonstandard analysis to quantum mechanics, J. Voros, Introduction to nonstandard analysis, J. Tarski, Renormalizable interactions in two-dimensions and sharp-time fields, Acta Phys. Li Bang-He, Nonstandard analysis and multiplication of distributions, Scientia Sinica 21, 561- (1978) Fittler, More nonstandard quantum electrodynamics, FU Berlin, Preprint (1985) Fittler, Some nonstandard quantum electrodynamics, Helv. Cutland, Nonstandard measure theory and its applications, Bull. Mishimura, Linear canonical transformations on Fermion Fock space with indefinite metric, Tokushima Osaka Preprint (1984) Diener, Cours d’Analyse Non-standard, Université d’Oran, Office Publ. Richter, Ideale Punkte, Monaden und Nichtstandard-Methoden, Vieweg (1982)į. Keisler, Elementary Calculus, Prindle, Weber & Schmidt, Boston (1976)Į. Luxemburg, What is nonstandard analysis? Amer. Zakon, Remarks on the nonstandard real axis, pp. Luxemburg, Introduction to the theory of infinitesimals, Academic Press (1976)Į. Hurd, Ed., Nonstandard Analysis - Recent Developments, Lect. Bayod, Foundations of infinitesimal stochastic analysis, North-Holland, Amsterdam (1986)Ī.E. Keisler, An infinitesimal approach to stochastic analysis, Mem. Keisler, Foundations of infinitesimal calculus, Prindle, Weber and Schmidt, Boston (1976) Kleinberg, Infinitesimal Calculus, MIT-Press, Cambridge (1979) Loeb, An introduction to nonstandard real analysis, Academic Press, New York (1985) Robinson’s Theory of Infinitesimals and Infinitely Large Numbers, Caltech Bookstore, Pasadena, rev. Luxemburg, Non-standard Analysis, Lectures on A. Lindstrøm, Non Standard methods in stochastic analysis and mathematical physics, Acad. 459–483 in Folkerts und Lindgren, Edts., Mathemata, Franz Steiner Verlag, Stuttgart (1985) Laugwitz, Grundbegriffe der Infinitesimalmathematik bei Leonhard Euler, pp. Laugwitz, The Theory of Infinitesimals, Accademia Nazionale Lincei Roma (1980)ĭ. Laugwitz, Infinitesimalkalkül, Bibliographisches Institut, Mannheim (1978)ĭ. Robinson, Non-Standard Analysis, North-Holland, Amsterdam (1966)ĭ. Quantum particles (seemingly) do as they please, when it pleases them, making it practically impossible to replicate results of an experiment-a fundamental validation requirement of the scientific method.A. How can we really advance if we can't truly get accurate measurements?Īnd sadly, this is just the start of the problem. ![]() As the uncertainty principle states, measuring quantum positions even with something as gentle as light would knock the atoms around because everything (including light) has momentum, rendering any measurement automatically inaccurate. To begin with, the standard definition seems simple enough: Quantum mechanics is "the branch of mechanics that deals with the mathematical description of the motion and interaction of subatomic particles." Part of the issue with this is that measuring atomic positions accurately is a horrendously tricky (and practically impossible) task. We are left with several probabilities instead of certainties. But so far, all attempts to unify quantum mechanics with the common physical laws of our everyday environment have been in vain. For around a century now, physicists all over the world have been trying to make sense of quantum phenomena. ![]()
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