Physics:Quantum Hidden variable theory - Revision history

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	'''Hidden variable theory''' ~~is a Book I topic in the Quantum Collection. Hidden~~-variable theory refers to a class of theoretical models in quantum mechanics that attempt to explain its probabilistic nature by introducing additional, unobserved parameters—called hidden variables—that determine the outcomes of measurements. These theories are typically motivated by a desire to restore determinism and provide a more complete description of physical reality than standard quantum mechanics. Hidden-variable theory refers to a class of theoretical models in quantum mechanics that attempt to explain its probabilistic nature by introducing additional, unobserved parameters—called hidden variables—that determine the outcomes of measurements. These theories are typically motivated by a desire to restore determinism and provide a more complete description of physical reality than standard quantum mechanics.		'''Hidden variable theory''' hidden-variable theory refers to a class of theoretical models in quantum mechanics that attempt to explain its probabilistic nature by introducing additional, unobserved parameters—called hidden variables—that determine the outcomes of measurements. These theories are typically motivated by a desire to restore determinism and provide a more complete description of physical reality than standard quantum mechanics. Hidden-variable theory refers to a class of theoretical models in quantum mechanics that attempt to explain its probabilistic nature by introducing additional, unobserved parameters—called hidden variables—that determine the outcomes of measurements. These theories are typically motivated by a desire to restore determinism and provide a more complete description of physical reality than standard quantum mechanics. → Physical systems possess definite properties at all times
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	'''Hidden-variable theory''' refers to a class of theoretical models in ~~[[Physics:Quantum mechanics\|~~quantum mechanics]] that attempt to explain its probabilistic nature by introducing additional, unobserved parameters—called ''hidden ~~variables''—that~~ determine the outcomes of measurements.~~<ref name="Bell1966">{{cite journal \|last=Bell \|first=J~~. ~~S. \|title=On the problem~~ of ~~hidden variables~~ in quantum mechanics ~~\|journal=Reviews~~ of ~~Modern Physics \|volume=38 \|issue=3 \|pages=447–452 \|year=1966 \|doi=10.1103/RevModPhys.38~~.~~447}}</ref>~~		'''Hidden variable theory''' is a Book I topic in the Quantum Collection. Hidden-variable theory refers to a class of theoretical models in quantum mechanics that attempt to explain its probabilistic nature by introducing additional, unobserved parameters—called hidden variables—that determine the outcomes of measurements. These theories are typically motivated by a desire to restore determinism and provide a more complete description of physical reality than standard quantum mechanics. Hidden-variable theory refers to a class of theoretical models in quantum mechanics that attempt to explain its probabilistic nature by introducing additional, unobserved parameters—called hidden variables—that determine the outcomes of measurements. These theories are typically motivated by a desire to restore determinism and provide a more complete description of physical reality than standard quantum mechanics.

	These theories are typically motivated by a desire to restore ~~[[Determinism\|~~determinism]] and provide a more complete description of physical reality than standard quantum mechanics.
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	In standard quantum mechanics:		In standard quantum mechanics:

	* Physical systems are described by a ~~[[Physics:Wave function\|~~wave function]]		* Physical systems are described by a wave function
	* Measurement outcomes are inherently probabilistic		* Measurement outcomes are inherently probabilistic
	* Properties do not have definite values prior to measurement		* Properties do not have definite values prior to measurement
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	* [[Physics:Quantum indeterminacy\|Quantum indeterminacy]]		* [[Physics:Quantum indeterminacy\|Quantum indeterminacy]]
	* The ~~[[Physics:Measurement problem\|~~measurement problem]]		* The measurement problem
	* The absence of definite physical properties prior to measurement		* The absence of definite physical properties prior to measurement

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	=== EPR argument ===		=== EPR argument ===

	In 1935, Einstein, Podolsky, and Rosen proposed the ~~[[Physics:~~EPR paradox~~\|EPR paradox]]~~, arguing that quantum mechanics does not provide a complete description of reality.<ref name="EPR1935">{{cite journal \|last1=Einstein \|first1=A. \|last2=Podolsky \|first2=B. \|last3=Rosen \|first3=N. \|title=Can quantum-mechanical description of physical reality be considered complete? \|journal=Physical Review \|volume=47 \|issue=10 \|pages=777–780 \|year=1935 \|doi=10.1103/PhysRev.47.777}}</ref>		In 1935, Einstein, Podolsky, and Rosen proposed the EPR paradox, arguing that quantum mechanics does not provide a complete description of reality.<ref name="EPR1935">{{cite journal \|last1=Einstein \|first1=A. \|last2=Podolsky \|first2=B. \|last3=Rosen \|first3=N. \|title=Can quantum-mechanical description of physical reality be considered complete? \|journal=Physical Review \|volume=47 \|issue=10 \|pages=777–780 \|year=1935 \|doi=10.1103/PhysRev.47.777}}</ref>

	They suggested that:		They suggested that:
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	=== Bell’s theorem ===		=== Bell’s theorem ===

	In 1964, ~~[[Biography:~~John ~~Stewart~~ Bell~~\|John Bell]]~~ showed that:		In 1964, John Bell showed that:

	→ No ''local'' hidden-variable theory can reproduce all predictions of quantum mechanics<ref name="Bell1964">{{cite journal \|last=Bell \|first=J. S. \|title=On the Einstein Podolsky Rosen paradox \|journal=Physics Physique Физика \|volume=1 \|issue=3 \|pages=195–200 \|year=1964 \|doi=10.1103/PhysicsPhysiqueFizika.1.195}}</ref>		→ No ''local'' hidden-variable theory can reproduce all predictions of quantum mechanics<ref name="Bell1964">{{cite journal \|last=Bell \|first=J. S. \|title=On the Einstein Podolsky Rosen paradox \|journal=Physics Physique Физика \|volume=1 \|issue=3 \|pages=195–200 \|year=1964 \|doi=10.1103/PhysicsPhysiqueFizika.1.195}}</ref>
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	=== Local hidden variables ===		=== Local hidden variables ===

	* Respect ~~[[Physics:Principle of~~ locality~~\|locality]]~~		* Respect locality
	* No faster-than-light influence		* No faster-than-light influence
	* Ruled out by Bell test experiments		* Ruled out by Bell test experiments
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	* Allow instantaneous correlations		* Allow instantaneous correlations
	* Compatible with quantum predictions		* Compatible with quantum predictions
	* Example: ~~[[Physics:De Broglie–Bohm theory\|~~de Broglie–Bohm theory]]		* Example: de Broglie–Bohm theory

	These models preserve determinism but require nonlocality.		These models preserve determinism but require nonlocality.
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	* [[Physics:Quantum information theory\|quantum information]]		* [[Physics:Quantum information theory\|quantum information]]
	* [[Physics:Quantum nonlocality\|quantum nonlocality]]		* [[Physics:Quantum nonlocality\|quantum nonlocality]]
	* ~~[[Physics:Foundations of quantum mechanics\|~~foundations of physics]]		* foundations of physics

	== See also ==		== See also ==

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	'''Hidden-variable theory''' refers to a class of theoretical models in [[Physics:Quantum mechanics\|quantum mechanics]] that attempt to explain its probabilistic nature by introducing additional, unobserved parameters—called ''hidden variables''—that determine the outcomes of measurements.<ref name="Bell1966">{{cite journal \|last=Bell \|first=J. S. \|title=On the problem of hidden variables in quantum mechanics \|journal=Reviews of Modern Physics \|volume=38 \|issue=3 \|pages=447–452 \|year=1966 \|doi=10.1103/RevModPhys.38.447}}</ref>		'''Hidden-variable theory''' refers to a class of theoretical models in [[Physics:Quantum mechanics\|quantum mechanics]] that attempt to explain its probabilistic nature by introducing additional, unobserved parameters—called ''hidden variables''—that determine the outcomes of measurements.<ref name="Bell1966">{{cite journal \|last=Bell \|first=J. S. \|title=On the problem of hidden variables in quantum mechanics \|journal=Reviews of Modern Physics \|volume=38 \|issue=3 \|pages=447–452 \|year=1966 \|doi=10.1103/RevModPhys.38.447}}</ref>

	These theories are typically motivated by a desire to restore [[Determinism\|determinism]] and provide a more complete description of physical reality than standard quantum mechanics.		These theories are typically motivated by a desire to restore [[Determinism\|determinism]] and provide a more complete description of physical reality than standard quantum mechanics.
	[[File:Hidden_variable_theory_concept.jpg\|thumb\|~~400px~~\|~~Conceptual illustration of hidden-~~variable ~~theories: underlying variables determine outcomes that appear probabilistic in standard quantum mechanics~~.]]		</div>

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			[[File:Hidden_variable_theory_concept.jpg\|thumb\|280px\|Quantum Hidden variable theory.]]
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	== Concept ==		== Concept ==

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{{Short description|Deterministic models extending quantum mechanics via additional hidden parameters}}

{{Quantum book backlink|Conceptual and interpretations}}
'''Hidden-variable theory''' refers to a class of theoretical models in [[Physics:Quantum mechanics|quantum mechanics]] that attempt to explain its probabilistic nature by introducing additional, unobserved parameters—called ''hidden variables''—that determine the outcomes of measurements.<ref name="Bell1966">{{cite journal |last=Bell |first=J. S. |title=On the problem of hidden variables in quantum mechanics |journal=Reviews of Modern Physics |volume=38 |issue=3 |pages=447–452 |year=1966 |doi=10.1103/RevModPhys.38.447}}</ref>

These theories are typically motivated by a desire to restore [[Determinism|determinism]] and provide a more complete description of physical reality than standard quantum mechanics.
[[File:Hidden_variable_theory_concept.jpg|thumb|400px|Conceptual illustration of hidden-variable theories: underlying variables determine outcomes that appear probabilistic in standard quantum mechanics.]]

== Concept ==

In standard quantum mechanics:

* Physical systems are described by a [[Physics:Wave function|wave function]]
* Measurement outcomes are inherently probabilistic
* Properties do not have definite values prior to measurement

Hidden-variable theories instead assume:

→ Physical systems possess definite properties at all times
→ Probabilities arise from ignorance of underlying variables

This contrasts with the orthodox view, where measurement plays a fundamental role in defining outcomes.<ref name="Mermin1993">{{cite journal |last=Mermin |first=N. David |title=Hidden variables and the two theorems of John Bell |journal=Reviews of Modern Physics |volume=65 |issue=3 |pages=803–815 |year=1993 |doi=10.1103/RevModPhys.65.803}}</ref>

== Motivation ==

Hidden-variable theories aim to resolve conceptual issues in quantum mechanics, including:

* [[Physics:Quantum indeterminacy|Quantum indeterminacy]]
* The [[Physics:Measurement problem|measurement problem]]
* The absence of definite physical properties prior to measurement

They attempt to provide a framework closer to classical physics, where:

* Systems have well-defined states
* Evolution is deterministic
* Measurement reveals pre-existing values

== Historical background ==

The idea dates back to the early development of quantum theory.

=== Early debates ===

In 1926, [[Biography:Max Born|Max Born]] introduced the probabilistic interpretation of the wave function. This was challenged by [[Biography:Albert Einstein|Albert Einstein]], who argued that quantum mechanics must be incomplete.<ref>{{cite book |title=The Born–Einstein Letters |year=1971 |publisher=Macmillan}}</ref>

Einstein’s famous remark:

→ “God does not play dice”

expressed his belief that a deeper deterministic theory should exist.

=== EPR argument ===

In 1935, Einstein, Podolsky, and Rosen proposed the [[Physics:EPR paradox|EPR paradox]], arguing that quantum mechanics does not provide a complete description of reality.<ref name="EPR1935">{{cite journal |last1=Einstein |first1=A. |last2=Podolsky |first2=B. |last3=Rosen |first3=N. |title=Can quantum-mechanical description of physical reality be considered complete? |journal=Physical Review |volume=47 |issue=10 |pages=777–780 |year=1935 |doi=10.1103/PhysRev.47.777}}</ref>

They suggested that:

* Additional hidden variables might exist
* These would restore determinism and locality

=== Bell’s theorem ===

In 1964, [[Biography:John Stewart Bell|John Bell]] showed that:

→ No ''local'' hidden-variable theory can reproduce all predictions of quantum mechanics<ref name="Bell1964">{{cite journal |last=Bell |first=J. S. |title=On the Einstein Podolsky Rosen paradox |journal=Physics Physique Физика |volume=1 |issue=3 |pages=195–200 |year=1964 |doi=10.1103/PhysicsPhysiqueFizika.1.195}}</ref>

This result fundamentally constrained hidden-variable approaches.

== Local vs nonlocal theories ==

Hidden-variable theories are divided into two main classes:

=== Local hidden variables ===

* Respect [[Physics:Principle of locality|locality]]
* No faster-than-light influence
* Ruled out by Bell test experiments

Experiments consistently show violations of Bell inequalities, excluding this class.<ref name="Hensen2015">{{cite journal |last=Hensen |first=B. |title=Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres |journal=Nature |volume=526 |pages=682–686 |year=2015 |doi=10.1038/nature15759}}</ref>

=== Nonlocal hidden variables ===

* Allow instantaneous correlations
* Compatible with quantum predictions
* Example: [[Physics:De Broglie–Bohm theory|de Broglie–Bohm theory]]

These models preserve determinism but require nonlocality.

== de Broglie–Bohm theory ==

The most well-known hidden-variable theory is the '''de Broglie–Bohm theory'''.

Key features:

* Particles have definite trajectories
* A guiding wave (pilot wave) determines motion
* Evolution is deterministic

In this framework:

* The wave function evolves via the Schrödinger equation
* Particle positions evolve via a guiding equation

This theory reproduces all predictions of standard quantum mechanics while remaining deterministic.<ref>{{cite book |last=Bohm |first=D. |title=The Undivided Universe |publisher=Routledge |year=1993}}</ref>

However, it is explicitly nonlocal.

== Modern developments ==

Recent theoretical work has placed further constraints on hidden-variable theories.

A notable result is:

→ No extension of quantum theory can improve its predictive power (under reasonable assumptions)<ref name="ColbeckRenner">{{cite journal |last1=Colbeck |first1=R. |last2=Renner |first2=R. |title=No extension of quantum theory can have improved predictive power |journal=Nature Communications |volume=2 |pages=411 |year=2011 |doi=10.1038/ncomms1416}}</ref>

This suggests that:

* Even with hidden variables, predictions cannot surpass quantum mechanics

== Conceptual implications ==

Hidden-variable theories highlight fundamental questions:

* Is reality deterministic or intrinsically probabilistic?
* Do physical properties exist prior to measurement?
* Is nonlocality a fundamental feature of nature?

Bell’s theorem shows that at least one classical assumption must be abandoned:

→ locality, realism, or measurement independence

== Physical significance ==

Although local hidden-variable theories are ruled out, the concept remains important because it:

* Clarifies the foundations of quantum mechanics
* Motivates experimental tests (Bell tests)
* Informs interpretations of quantum theory

It also plays a central role in:

* [[Physics:Quantum information theory|quantum information]]
* [[Physics:Quantum nonlocality|quantum nonlocality]]
* [[Physics:Foundations of quantum mechanics|foundations of physics]]

== See also ==
{{#invoke:PhysicsQC|tocHeadingAndList|Physics:Quantum basics/See also}}

==References==
{{reflist|3}}

{{Author|Harold Foppele}}
{{Sourceattribution|Physics:Quantum Hidden variable theory|1}}