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: ''In this article [[leap year]]s and other details (such as a difference between winter and summer days) are ignored.''
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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.


To show how to calculate the [[probability]] of a group including such a match, it is simpler to first find the probability of all the birthdays being different.  Consider a group of two people.  The first person can have been born on any of the 365 days of the year, while the second must have been born on one of the other 364 days in order to not match.  For the first person alone, a match cannot happen, thus the no-match probability is 1, which is <math>\tfrac {365}{365}</math> in the sense that all the 365 possibilities lead to no-match. Given the first person's birthday, the second person's birthday differs in 364 cases, with a conditional probability of <math>\tfrac {364}{365}</math> which is 0.9973.  Multiplying these probabilities together gives a net (unconditional) probability of 0.9973 for having different birthdays.  Subtracting this number from 1.0 gives a 0.0027 probability of having the same birthday.
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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