Physics:Quantum Hidden variable theory
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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.[1]
These theories are typically motivated by a desire to restore determinism and provide a more complete description of physical reality than standard quantum mechanics.
Concept
In standard quantum mechanics:
- Physical systems are described by a 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.[2]
Motivation
Hidden-variable theories aim to resolve conceptual issues in quantum mechanics, including:
- Quantum indeterminacy
- The 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, Max Born introduced the probabilistic interpretation of the wave function. This was challenged by Albert Einstein, who argued that quantum mechanics must be incomplete.[3]
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 EPR paradox, arguing that quantum mechanics does not provide a complete description of reality.[4]
They suggested that:
- Additional hidden variables might exist
- These would restore determinism and locality
Bell’s theorem
In 1964, John Bell showed that:
→ No local hidden-variable theory can reproduce all predictions of quantum mechanics[5]
This result fundamentally constrained hidden-variable approaches.
Local vs nonlocal theories
Hidden-variable theories are divided into two main classes:
Local hidden variables
- Respect locality
- No faster-than-light influence
- Ruled out by Bell test experiments
Experiments consistently show violations of Bell inequalities, excluding this class.[6]
Nonlocal hidden variables
- Allow instantaneous correlations
- Compatible with quantum predictions
- Example: 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.[7]
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)[8]
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:
See also
Table of contents (138 articles)
Index
Full contents
- Physics:Quantum Interpretations of quantum mechanics
- Physics:Quantum Wave–particle duality
- Physics:Quantum Complementarity principle
- Physics:Quantum Uncertainty principle
- Physics:Quantum Measurement problem
- Physics:Quantum Bell's theorem
- Physics:Quantum Hidden variable theory
- Physics:Quantum A Spooky Action at a Distance
- Physics:Quantum A Walk Through the Universe
- Physics:Quantum The Secret of Cohesion and How Waves Hold Matter Together
- Physics:Quantum Density matrix
- Physics:Quantum Exactly solvable quantum systems
- Physics:Quantum Formulas Collection
- Physics:Quantum A Matter Of Size
- Physics:Quantum Symmetry in quantum mechanics
- Physics:Quantum Angular momentum operator
- Physics:Quantum Runge–Lenz vector
- Physics:Quantum Approximation Methods
- Physics:Quantum Matter Elements and Particles
- Physics:Quantum Dirac equation
- Physics:Quantum Klein–Gordon equation
- Physics:Quantum Atomic structure and spectroscopy
- Physics:Quantum Hydrogen atom
- Physics:Quantum Multi-electron atoms
- Physics:Quantum Fine structure
- Physics:Quantum Hyperfine structure
- Physics:Quantum Isotopic shift
- Physics:Quantum Zeeman effect
- Physics:Quantum Stark effect
- Physics:Quantum Spectral lines and series
- Physics:Quantum Selection rules
- Physics:Quantum Fermi's golden rule
- Physics:Quantum Wavefunction
- Physics:Quantum Superposition principle
- Physics:Quantum Eigenstates and eigenvalues
- Physics:Quantum Boundary conditions and quantization
- Physics:Quantum Standing waves and modes
- Physics:Quantum Normal modes and field quantization
- Physics:Number of independent spatial modes in a spherical volume
- Physics:Quantum Density of states
- Physics:Quantum Time evolution
- Physics:Quantum Schrödinger equation
- Physics:Quantum Time-dependent Schrödinger equation
- Physics:Quantum Stationary states
- Physics:Quantum Perturbation theory
- Physics:Quantum Time-dependent perturbation theory
- Physics:Quantum Adiabatic theorem
- Physics:Quantum Scattering theory
- Physics:Quantum S-matrix
- Physics:Quantum Nonlinear King plot anomaly in calcium isotope spectroscopy
- Physics:Quantum optics beam splitter experiments
- Physics:Quantum Ultra fast lasers
- Physics:Quantum Experimental quantum physics Template:Quantum optics operators
- Physics:Quantum field theory (QFT) basics
- Physics:Quantum field theory (QFT) core
- Physics:Quantum Fields and Particles
- Physics:Quantum Second quantization
- Physics:Quantum Harmonic Oscillator field modes
- Physics:Quantum Creation and annihilation operators
- Physics:Quantum vacuum fluctuations
- Physics:Quantum Propagators in quantum field theory
- Physics:Quantum Feynman diagrams
- Physics:Quantum Path integral formulation
- Physics:Quantum Renormalization in field theory
- Physics:Quantum Renormalization group
- Physics:Quantum Field Theory Gauge symmetry
- Physics:Quantum Non-Abelian gauge theory
- Physics:Quantum Electrodynamics (QED)
- Physics:Quantum chromodynamics (QCD)
- Physics:Quantum Electroweak theory
- Physics:Quantum Standard Model
- Physics:Quantum Statistical mechanics
- Physics:Quantum Partition function
- Physics:Quantum Distribution functions
- Physics:Quantum Liouville equation
- Physics:Quantum Kinetic theory
- Physics:Quantum Boltzmann equation
- Physics:Quantum BBGKY hierarchy
- Physics:Quantum Transport theory
- Physics:Quantum Relaxation and thermalization
- Physics:Quantum Thermodynamics
- Physics:Quantum Plasma (fusion context)
- Physics:Quantum Fusion reactions and Lawson criterion
- Physics:Quantum Magnetic confinement fusion
- Physics:Quantum Inertial confinement fusion
- Physics:Quantum Plasma instabilities and turbulence
- Physics:Quantum Tokamak
- Physics:Quantum Tokamak core plasma
- Physics:Quantum Tokamak edge physics and recycling asymmetries
- Physics:Quantum Stellarator
- Physics:Quantum mechanics/Timeline
- Physics:Quantum mechanics/Timeline/Pre-quantum era
- Physics:Quantum mechanics/Timeline/Old quantum theory
- Physics:Quantum mechanics/Timeline/Modern quantum mechanics
- Physics:Quantum mechanics/Timeline/Quantum field theory era
- Physics:Quantum mechanics/Timeline/Quantum information era
- Physics:Quantum mechanics/Timeline/Quantum technology era
- Physics:Quantum mechanics/Timeline/Quiz/
References
- ↑ Bell, J. S. (1966). "On the problem of hidden variables in quantum mechanics". Reviews of Modern Physics 38 (3): 447–452. doi:10.1103/RevModPhys.38.447.
- ↑ Mermin, N. David (1993). "Hidden variables and the two theorems of John Bell". Reviews of Modern Physics 65 (3): 803–815. doi:10.1103/RevModPhys.65.803.
- ↑ The Born–Einstein Letters. Macmillan. 1971.
- ↑ Einstein, A.; Podolsky, B.; Rosen, N. (1935). "Can quantum-mechanical description of physical reality be considered complete?". Physical Review 47 (10): 777–780. doi:10.1103/PhysRev.47.777.
- ↑ Bell, J. S. (1964). "On the Einstein Podolsky Rosen paradox". Physics Physique Физика 1 (3): 195–200. doi:10.1103/PhysicsPhysiqueFizika.1.195.
- ↑ Hensen, B. (2015). "Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres". Nature 526: 682–686. doi:10.1038/nature15759.
- ↑ Bohm, D. (1993). The Undivided Universe. Routledge.
- ↑ Colbeck, R.; Renner, R. (2011). "No extension of quantum theory can have improved predictive power". Nature Communications 2: 411. doi:10.1038/ncomms1416.
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