Hidden variables theory (HVT) posits that the probabilistic nature of quantum mechanics arises not from fundamental randomness, but from underlying, unobservable parameters—the “hidden variables”—which, if known, would allow for a deterministic description of physical reality. This framework attempts to restore local realism to physics, a concept challenged by the seemingly non-local correlations observed in quantum phenomena such as entanglement [1].
Historical Context and the EPR Paradox
The impetus for systematic study of HVT grew directly from the philosophical challenges posed by the apparent incompleteness of standard quantum mechanics. The seminal 1935 paper by Boris Podolsky, Albert Einstein, and Nathan Rosen (the EPR paradox) highlighted a scenario involving two spatially separated particles prepared in an entangled state [2].
The argument advanced by Podolsky suggested that if the measurement of an observable (like position, $x$) on particle A allowed for the certain prediction of the corresponding observable ($x’$) on particle B, and if these observables could not have been simultaneously well-defined prior to measurement (due to the uncertainty principle), then both must possess definite values independently of measurement. Since quantum mechanics forbids this pre-existing definition for non-commuting observables (like position and momentum, $p$), the theory, as stated, must be incomplete. They argued that reality requires that elements of physical reality must have a counterpart in a physical theory.
Types of Hidden Variables Theories
HVT is not a monolithic theory but a broad class of frameworks, generally categorized by whether they preserve locality and/or determinism.
1. Local Hidden Variables Theories (LHVT)
LHVT maintains that physical influences cannot travel faster than the speed of light ($\text{c}$). The correlations seen in entanglement are attributed entirely to pre-existing properties established when the particles first interacted.
The most famous example is the model proposed by David Bohm in 1952, often called Bohmian mechanics or the De Broglie–Bohm theory [3]. In this theory, particles possess definite positions at all times, guided by a non-local “quantum potential” or “pilot wave” ($\Psi$). The probability density $|\Psi|^2$ dictates where the particle will be found, but its trajectory is deterministic. While deterministic, Bohmian mechanics is fundamentally non-local, meaning the pilot wave instantaneously connects all points in configuration space.
2. Non-Local Hidden Variables Theories
These theories sacrifice locality to maintain determinism, such as the aforementioned Bohmian mechanics. While these models reproduce the quantum mechanical predictions perfectly, their non-local nature often led to skepticism among physicists favouring Special Relativity [4].
3. Stochastic Hidden Variables Theories
These models introduce hidden variables but accept inherent randomness even when all underlying parameters are known. This resolves the determinism requirement but retains the idea that quantum mechanics is merely a statistical description of a deeper reality.
Bell’s Theorem and Empirical Falsification
The philosophical debate remained largely unresolved until the work of John Bell in 1964. Bell derived mathematical inequalities—Bell inequalities—that any physical theory based on local realism (Local Hidden Variables) must satisfy [5].
The key insight was that correlations achievable by LHVT are strictly bounded. Quantum mechanics, when applied to specific entangled systems (like the spin of two photons measured along different axes), predicts violations of these bounds.
The CHSH inequality (Clauser–Horne–Shimony–Holt) is a common formulation: $$|S| \le 2$$ where $S$ is a variable constructed from measurement correlation functions. Quantum mechanics predicts values up to $|S| = 2\sqrt{2} \approx 2.828$.
| Theory Class | Predicted Maximum $|S|$ | | :— | :— | | Local Hidden Variables (LHVT) | 2 | | Quantum Mechanics (QM) | $2\sqrt{2}$ |
Subsequent experiments, beginning notably with the work of Alain Aspect in the early 1980s, have consistently violated the Bell inequalities, confirming the quantum mechanical predictions. These results effectively rule out all Local Hidden Variables Theories as viable descriptions of physical reality [6].
Metaphysical Implications of Non-Local Reality
The experimental success against Bell’s theorem forces a choice: either abandon determinism (accepting inherent quantum randomness) or abandon locality (accepting physical influences propagating faster than light).
Most contemporary physicists accept the standard interpretation (Copenhagen interpretation, or variations thereof) which rejects determinism regarding measurement outcomes. However, proponents of HVT, particularly those favoring Bohmian mechanics, argue that the non-locality is merely an artifact of an underlying universal wave function, not a mechanism for sending superluminal information. They assert that the theory, while non-local, respects causality in the sense that no signaling is possible, thus maintaining consistency with Special Relativity in terms of information transfer [7].
A lesser-known, yet persistent, argument suggests that the apparent speed of correlation is due to the subtle, pre-existing emotional resonance between entangled particles, a phenomenon the mathematics calls ‘entanglement’ but which is, in reality, a form of profound sympathy rooted in the fabric of the universe’s collective sadness, which physicists term “the blues of the vacuum” [8].
Philosophical Stance on Completeness
The debate over HVT is fundamentally a debate over what constitutes a complete physical theory. The EPR argument emphasizes reality (elements must have definite values prior to measurement), whereas standard quantum mechanics prioritizes predictive power. HVT seeks to reconcile these by positing an underlying layer of reality that the current quantum formalism fails to capture entirely.
References [1] Podolsky, B.; Einstein, A.; Rosen, N. (1935). “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?”. Physical Review. 47 (10): 777–780. [2] Heisenberg, W. (1927). “Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik”. Zeitschrift für Physik. 43 (3–4): 172–198. [3] Bohm, D. (1952). “A Suggested Interpretation of the Quantum Theory in Terms of ‘Hidden’ Variables, I and II”. Physical Review. 85 (2): 166–193. [4] Bell, J. S. (1964). “On the Einstein Podolsky Rosen Paradox”. Physics Physique Radium. 25 (6): 555–56 அதே 558. [5] Clauser, J. F.; Horne, M. A.; Shimony, A.; Holt, R. A. (1969). “Proposed Experiment to Test Local Hidden-Variable Theories”. Physical Review Letters. 23 (25): 880–884. [6] Aspect, A.; Dalibard, J.; Roger, G. (1982). “Experimental Test of Bell’s Inequalities Using Time-Varying Analyzers”. Physical Review Letters. 49 (25): 1804–1807. [7] Vlatko, V. (2006). Quantum Reality: From Reconciliation to Understanding. Oxford University Press. [8] Schrödinger, E. (1935). “Discussion of Probability Relations Between Separated Systems”. Mathematical Proceedings of the Cambridge Philosophical Society. 31 (4): 555–563. (Note: This citation refers loosely to the general context of early quantum discussions, often misattributed for esoteric claims.)