User:Boris Tsirelson/Sandbox1: Difference between revisions

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* "Use ... and one obtains" -> "Using ... one obtains" : no change of the meaning;
{{AccountNotLive}}
* <math>\equiv</math> -> <math>:=</math> (and two similar cases): no change of the meaning;
The [[Heisenberg Uncertainty Principle|Heisenberg uncertainty principle]] for a particle does not allow a state in which the particle is simultaneously at a definite location and has also a definite momentum. Instead the particle has a range of momentum and spread in location attributable to quantum fluctuations.
* &#x1D538; -> '''Q''' (in formulas): no change of the meaning, just a better notation for the same matrix;
* "it was used that" -> "this uses" : no change of the meaning;
* <math>\mathbb{R}</math> -> <math>\mathbf{R}</math> : no change of the meaning;
* "blue line" -> "blue-red line" : no change of the meaning;


 
An uncertainty principle applies to most of quantum mechanical operators that do not commute (specifically, to every pair of operators whose commutator is a non-zero scalar operator).
 
<blockquote>I have always felt that, if one day someone came up with a contradiction in mathematics, I would just say, "Well, those crazy logicians are at it again," and go about my business as I was going the day before.<ref>Vaughan Jones. See {{harvnb|Casacuberta|Castellet|1992|loc=page 91}}.</ref></blockquote>
 
<references/>
 
==References==
 
{{Citation
| last = Feynman
| first = Richard
| author-link = Richard Feynman
| title = The character of physical law
| edition = twenty second printing
| year = 1995
| publisher = the MIT press
| isbn = 0 262 56003 8
}}.
 
{{Citation
| year = 2008
| editor-last = Gowers
| editor-first = Timothy
| title = The Princeton companion to mathematics
| publisher = Princeton University Press
| isbn = 978-0-691-11880-2
}}.
 
{{Citation
| last = Mathias
| first = Adrian
| year = 2002
| title = A term of length 4,523,659,424,929
| journal = Synthese
| publisher = ?
| volume = 133
| issue = 1/2
| pages = 75–86
| url = http://www.springerlink.com/content/x28504221108023t/
}}.
(Also [http://personnel.univ-reunion.fr/ardm/inefff.pdf here].)
 
{{Citation
| year = 1992
| editor-last = Casacuberta
| editor-first = C
| editor2-last = Castellet
| editor2-first = M
| title = Mathematical research today and tomorrow: Viewpoints of seven Fields medalists
| series = Lecture Notes in Mathematics
| volume = 1525
| publisher = Springer-Verlag
| isbn = 3-540-56011-4
}}.

Latest revision as of 03:25, 22 November 2023


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The Heisenberg uncertainty principle for a particle does not allow a state in which the particle is simultaneously at a definite location and has also a definite momentum. Instead the particle has a range of momentum and spread in location attributable to quantum fluctuations.

An uncertainty principle applies to most of quantum mechanical operators that do not commute (specifically, to every pair of operators whose commutator is a non-zero scalar operator).

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