查看“玻恩定則”的源代码

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[[FIle:Max Born.jpg|thumb|200px|马克斯·玻恩]]
在[[量子力學]]裏，'''玻恩定則'''（Born rule）是一個基礎[[公設]]。<ref>{{cite journal | last =Zurek | first =Wojciech | title =Quantum Darwinism, Classical Reality, and the randomness of quantum jumps | journal =Physics Today | volume =67 | issue =10 | pages =44-45 | date =2014}}</ref><ref name="Laloë">{{cite book|author=Claude Cohen-Tannoudji, Bernard Diu, Franck Laloë|title=Quantum Mechanics Volume 1|publisher=Hermann|isbn=978-2-7056-8392-4}}</ref>{{rp|211ff}}，是因原本提出這定則的物理學者[[馬克斯·玻恩]]而命名。它給定對量子系統做[[測量]]得到某種結果的概率，它與[[海森堡測不準原理]]將概率的概念引入量子力學，因此使得量子力學展現出其獨特的[[決定論|非決定性質]]。物理學者做實驗尚未發現任何違背玻恩定則的量子行為。<ref name="Schlosshauer"/>

物理學者試圖從其它假定推導出玻恩定律，但結果都不具強而有力的說服力。例如，有些物理學者聲稱從[[多世界詮釋]]可以推導出玻恩定律，但他們給出的導引被批評為[[循環論證]]<ref>{{Citation
 | first =Nicolaas
 | last =Landsman
 | editor1=Greenberger, Daniel
 | editor2=et al.
 | contribution =Born Rule and its Interpretation
 | contribution-url =http://www.math.ru.nl/~landsman/Born.pdf
 | series =Compendium of Quantum Physics
 | year =2009
 | pages =64-70
 | quote =The conclusion seems to be that no generally accepted derivation of the Born rule has been given to date, but this does not imply that such a derivation is impossible in principle.
 | publisher =Springer
 | isbn =978-3-540-70622-9
 | doi =10.1007/978-3-540-70626-7_20}}</ref>。[[格里森定理]]對於玻恩定則的形式給出數學線索，但並沒有對於其概率行為顯示出物理曙光<ref name="Schlosshauer"/>。

{{le|沃傑克·祖瑞克|Wojciech Zurek}}倚賴系統與環境之間的[[量子纏結]]引起的{{le|環輔不變性|envariance}}（環境輔助不變性，environment-assisted invariance）來推導出玻恩定則。在這裡，環境扮演了促使概率出現的關鍵角色。這也意味著祖瑞克的方法只適用於開放系統。不論如何，這是一種充滿想像力的點子，很具有未來發展的潛能。<ref name="Schlosshauer"/>

== 概述 ==
=== 離散值譜 ===
假設對於[[量子態]]為<math>|\psi\rang</math>的某量子系統測量[[可觀察量]]<math>O</math>，而對應於可觀察量<math>O</math>的厄米算符<math>\hat{O}</math>，其{{le|值譜|discrete spectrum (physics)}}為離散的，所含有的本徵值與對應的本徵態分別標記為
:<math>O_i</math>與<math>|O_i\rang</math>，<math>i=1,\ 2,\ 3,\ \cdots,n</math>。

玻恩定則闡明，獲得測量值<math>O_i</math>的概率為<ref name=Griffiths2004>{{citation| author=Griffiths, David J.|title=Introduction to Quantum Mechanics (2nd ed.) | publisher=Prentice Hall |year=2004 |isbn= 0-13-111892-7}}</ref>{{rp|96-99}}<ref name="Schlosshauer">{{cite journal | last1 =Schlosshauer | first1 =Maximilian | last2 =Fine | first2 =Arthur | title =On Zurek’s Derivation of the Born Rule | journal =Foundations of Physics | volume =35 | issue =2 | pages =197-213 | date =2005 | url =http://faculty.up.edu/schlosshauer/publications/bornrule.pdf | doi =10.1007/s10701-004-1941-6}}</ref>
:<math>p(O_i)=|\lang O_i |\psi \rang|^2</math>。

=== 連續值譜 ===
假設對於[[量子態]]為<math>|\psi\rang</math>的某量子系統測量[[可觀察量]]<math>X</math>，而對應於可觀察量<math>X</math>的厄米算符<math>\hat{X}</math>，其值譜為連續的，所含有的本徵值與對應的本徵態分別標記為
:<math>x</math>與<math>|x\rang</math>，<math>-\infty \le x \le \infty</math>。

玻恩定則闡明，獲得測量值<math>a\le x\le b</math>的概率為<ref name=Griffiths2004/>{{rp|2-5}}
:<math>p(a\le x\le b)=\int_a^b |\lang x |\psi \rang|^2 \mathrm{d}x</math>。

==歷史==
[[馬克斯·玻恩]]最先於1926年發表論文提出玻恩定則<ref>''Zur Quantenmechanik der Stoßvorgänge'', Max Born, Zeitschrift für Physik, ''37'', #12 (Dec. 1926), pp. 863–867 (German); English translation, ''On the quantum mechanics of collisions'', in ''Quantum theory and measurement'', section I.2, J. A. Wheeler and W. H. Zurek, eds., Princeton, New Jersey: Princeton University Press, 1983, ISBN 0-691-08316-9.</ref>。在這篇論文裏，玻恩解析了一個[[散射]]問題的[[薛定谔方程]]，由於受到[[阿爾伯特·愛因斯坦]]在[[光電效應]]研究的啟發<ref name="Born1954">{{cite web | last =Born | first =Max | title =Born's Nobel Lecture on the statistical interpretation of quantum mechanics | work =Nobel Lecture | publisher =NobelPrize.org | date =1954 | quote=Again an idea of Einstein’s gave me the lead. He had tried to make the duality of particles - light quanta or photons - and waves comprehensible by interpreting the square of the optical wave amplitudes as probability density for the occurrence of photons.| url =http://nobelprize.org/physics/laureates/1954/born-lecture.pdf}}</ref>，玻恩在一個角註裏總結，玻恩定則對於解答給出唯一可能的詮釋。1954年，因為「在量子力學領域的基礎研究，特別是對波函數的統計學詮釋」，玻恩與[[瓦爾特·博特]]共同榮獲[[諾貝爾物理學獎]]<ref>{{cite web | title =The Nobel Prize in Physics 1954 | publisher =NobelPrize.org | date =1954 | url =http://www.nobelprize.org/nobel_prizes/physics/laureates/1954/}}</ref>。[[約翰·馮·諾伊曼]]在他的1932年著作《量子力學的數學基礎》裏闡明{{le|譜理論|spectrum theory}}應用於玻恩定則的論述。<ref>''Mathematische Grundlagen der Quantenmechanik'', John von Neumann, Berlin: Springer, 1932 (German); English translation ''[[量子力学的数学基础|Mathematical Foundations of Quantum Mechanics]]'', transl. Robert T. Beyer, Princeton, New Jersey: Princeton University Press, 1955.</ref>

==參閱==
*[[量子測量]]
*[[量子退相干]]

==參考文獻==
{{reflist}}

==外部連結==
*[http://www.sciencedaily.com/releases/2010/07/100722142640.htm Quantum Mechanics Not in Jeopardy: Physicists Confirm a Decades-Old Key Principle Experimentally] ScienceDaily (July 23, 2010)

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[[Category:量子測量]]