QuantumSmarandacheQuasiParadoxes 2007-04-05 16:02:48 2009-01-16 11:23:46 Topic Quantum Paradoxes and Bell's inequalities paradox Sorites paradox quantum paradox % this is the default PlanetPhysics preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here \section{Quantum Paradoxes} A \emph{paradox} is a statement which has either an apparent or a real self-inconsistency (such as ``A and non-A''), thus contradicing the logical principle of excluded third (`tertium non datur') In the early stages of quantum theory development both Schr\"odinger and Einstein-Podolsky-Rosen have suggested that there are two distinct quantum paradoxes: 1. The `Schr\"odinger cat'' paradox in a thought (or `gedanken') experiment that supposedly shows that a ``cat is neither alive nor dead'' but in a superposition of the the `live' and `dead' states. A related version of this `paradox' is the two-slit experiment in which, for example, `an electron passes through two slits at the same time, thus interferring with itself and resulting in a diffraction pattern at the detector behind the two slits'; however, if the electron position is determined before reaching the two slits the diffraction pattern, of course, disappears, as only one electron possible state exists--that which was already measured or observed. The wave-particle duality proposed by Louis deBroglie, and readily accepted by Albert Einstein, is thought to remove this type of quantum `paradox', although it simply shifts the argument to the quantum logic realm where quantum micro-entitites such as an electron or any other quantum `particle' can simultaneously possess an associated wave (or `character'); the existence of the associated wave of a quantum particle was later elaborated in quantum field theories (QFT) in the form of `virtual photons' that mediate the electromagnetic interactions between charged quantum particles such as electrons, protons, ions, etc. 2. The Einstein-Podolsky-Rosen (or EPR) `paradox' is a thought experiment that reveals the non-local character of quantum theory, and was presented initially as `proof that Quantum Mechanics' is incomplete, because quantum non-locality was proposed to contradict both Special and General Relativity theories. \textbf{Note} On the other hand, more recently proposed `quantum quasi-paradoxes' and `Sorite paradoxes' are claimed to be based on a wide-range of other apparent antinomies that are not found in any standard Quantum Mechanics textbooks. \begin{thebibliography}{9} \bibitem{Weisstein} Weisstein, E. W., \htmladdnormallink{Quasi-Paradox}{http://mathworld.wolfram.com/SmarandacheParadox.html}, CRC Concise Encyclopedia of Mathematics, CRC Press, Boca Raton, Florida, p. 1661, (1998). \end{thebibliography}