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\begin{document}

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\section*{hidden variable theory}

\hypertarget{context}{}\subsubsection*{{Context}}\label{context}

\hypertarget{physics}{}\paragraph*{{Physics}}\label{physics}

[[!include physicscontents]]

\hypertarget{contents}{}\section*{{Contents}}\label{contents}

\noindent\hyperlink{idea}{Idea}\dotfill \pageref*{idea} \linebreak
\noindent\hyperlink{related_concepts}{Related concepts}\dotfill \pageref*{related_concepts} \linebreak
\noindent\hyperlink{references}{References}\dotfill \pageref*{references} \linebreak


\hypertarget{idea}{}\subsection*{{Idea}}\label{idea}

In its standard formulation, [[quantum physics]] is a probabilistic theory of nature, since it provides only [[probabilities]] (in fact [[probability amplitudes]]) for values of [[observable]] in [[experiment]]. This is in contrast to [[classical mechanics]], which (on classical [[pure states]]) predicts events with certainty.

However, on very small scales classical mechanics predicts the \emph{wrong} events, while [[quantum mechanics]] and [[quantum field theory]] predicts the right [[probabilities]].

On the other hand, it is well known that upon ``coarse graining'', which means after averaging over certain details, also classical mechanics induces a probabilistic theory of nature, namely [[statistical mechanics]]/[[thermodynamics]].

Therefore it is natural to speculate that maybe also [[quantum physics]] is the [[statistical mechanics]] of a more refined theory of as yet unseen ``degrees of freedom of nature'' on small scales, which does predict events with certainty on very small scales, and which reduces to quantum mechanics on larger scales as one averages over these unseen new degrees of freedom.

These ``unseen degrees of freedom'' are usually called \emph{hidden variables}, and a [[theory (physics)|theory]] which is non-probabilistic but designed to reproduce [[quantum mechanics]] as its statistical coarse grained theory are called \emph{hidden variable theories}. (These are hence one potential [[interpretation of quantum mechanics]].)

There have been various attempts to construct such hidden variable theories. However, there are also [[theorems]] about the characteristic properties of [[quantum mechanics]] which assert (under some (natural) assumptions, of course) that there cannot be a hidden variable theory.

These theorems are

\begin{itemize}%
\item [[Bell's inequalities]] (\hyperlink{Bell64}{Bell 64});


\item the [[Kochen-Specker theorem]] (\hyperlink{KochenSpecker68}{Kochen-Specker 68}).



\end{itemize}
One well-developed attempt to construct a hidden variable theory is [[Bohmian mechanics]]; this makes hidden variables out of the entire [[wavefunction]] and violates the assumption of [[locality]].

\hypertarget{related_concepts}{}\subsection*{{Related concepts}}\label{related_concepts}

\begin{itemize}%
\item [[interpretation of quantum mechanics]]


\item [[Einstein-Podolsky-Rosen paradox]]


\item [[Kochen-Specker theorem]]


\item [[Bell's theorem]]


\item [[Hardy's paradox]]



\end{itemize}
\hypertarget{references}{}\subsection*{{References}}\label{references}

Surveys include

\begin{itemize}%
\item Wikipedia, \emph{\href{http://en.wikipedia.org/wiki/Hidden_variable_theory}{Hidden variable theory}}

\end{itemize}
The original article on [[Bell's theorem]] is

\begin{itemize}%
\item [[John Bell]], \emph{On the Einstein Podolsky Rosen paradox}, Physics 1, 195, 1964 (\href{http://www.drchinese.com/David/Bell_Compact.pdf}{pdf})

\end{itemize}
The original article on the [[Kochen-Specker theorem]] is

\begin{itemize}%
\item [[Simon Kochen]], [[Ernst Specker]], \emph{The problem of hidden variables in quantum mechanics} 1968 , Journal of Mathematics and Mechanics, \href{http://www.iumj.indiana.edu/IUMJ/FTDLOAD/1968/17/17004/pdf}{pdf}.

\end{itemize}
Discussion of hidden variable theories in terms of [[quantum logic]] is in section 5 of

\begin{itemize}%
\item Gianpiero Cattaneo, Maria Luisa Dalla Chiara, Roberto Giuntini and Francesco Paoli, \emph{Quantum Logic and Nonclassical Logics}, p. 127 in Kurt Engesser, Dov M. Gabbay, Daniel Lehmann (eds.) \emph{Handbook of Quantum Logic and Quantum Structures: Quantum Logic}, 2009 North Holland

\end{itemize}
[[!redirects hidden variable theory]] [[!redirects hidden variable theories]]

[[!redirects hidden variable]] [[!redirects hidden variables]]



\end{document}