Physics:Quantum 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.[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:
- Respect locality
- No faster-than-light influence
- Ruled out by Bell test experiments
Experiments consistently show violations of Bell inequalities, excluding this class.[6]
- 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 (185 articles)
Index
Full contents
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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