Beyond Bell: How Conservation Laws Could Explain Quantum Correlations

Author: Denis Avetisyan

A new model suggests that violations of Bell inequalities aren’t necessarily evidence of non-locality, but may arise from the fundamental physics of measurement itself.

Quantum mechanics and hidden-variable models—specifically those conserving angular momentum with varying degrees of permissible deviation (ΔL) for Bell singlet and triplet states—yield distinct correlation response functions, fundamentally differentiating their predictions regarding the nature of quantum entanglement.

Researchers propose a ‘supermeasured’ local hidden variable theory where conservation laws impose constraints during quantum measurement, potentially resolving the tension between quantum mechanics and classical realism.

The persistent tension between quantum mechanics and local realism motivates continued exploration of hidden-variable theories, despite Bell’s theorem. This is the central theme of ‘Quantum-Like Correlations from Local Hidden-Variable Theories Under Conservation Law’, which proposes a model demonstrating that violations of Bell inequalities needn’t invoke superdeterminism or retrocausality. Instead, the authors show how measurement imprecision arising from the need to conserve physical quantities can fundamentally alter the statistical landscape of hidden variables, creating a ‘supermeasured’ theory. Could this physically-motivated approach offer experimentally testable deviations from quantum predictions, and ultimately refine our understanding of the measurement process itself?

The Challenge to Local Realism

Quantum mechanics postulates correlations between distant particles inexplicable by classical physics, challenging the principle of local realism – the assertion that an object’s properties are predetermined by its immediate surroundings. Attempts to preserve a classical worldview propose ‘hidden variables’ – unobserved properties defining a particle’s state. However, Bell’s Theorem proves such local hidden variable theories are fundamentally incompatible with quantum predictions, consistently validated by experiment. The universe, at its core, operates on principles defying everyday experience, woven with threads of interconnectedness beyond space and time.

Circumventing Classical Constraints

The ‘Detection Loophole’, stemming from imperfect detector efficiency, challenges interpretations of Bell test experiments. Alternative interpretations, like ‘Superdeterminism’ and ‘Retrocausality’, abandon established principles of causality or experimental freedom by correlating measurement settings with hidden variables or allowing future events to influence the past. The ‘Supermeasured Model’ attempts to reconcile correlations with quantum predictions by restricting measurement outcomes, potentially limiting the completeness of quantum mechanics.

Conservation Laws and the Hidden Variable Space

Local Hidden Variable Theories (LHVT) posit underlying ‘Hidden Variables’ predetermining quantum measurement outcomes. A crucial component is a defined ‘Measure Space’ describing these variables and their relation to observable quantities. LHVT fundamentally rely on ‘Conservation Laws’ to maintain physical plausibility. Ozawa’s Accuracy Bound, a consequence of these laws, limits the precision of simultaneous measurements. Recent research proposes a local hidden variable model reproducing quantum correlations while adhering to conservation laws by strategically violating the assumption of ‘Statistical Independence’.

Entanglement: A Departure from Classicality

Entangled states, such as the Singlet and Triplet States, demonstrate correlations exceeding classical limits. These correlations arise from the inherent quantum connection between particles, where measuring one instantaneously influences the other, regardless of distance. This stems from the principle of Angular Momentum and its conservation, not pre-existing hidden variables. Experimental verification utilizes technologies like Superconducting Qubits, reporting a CHSH inequality value (S) of 2.0747, decisively confirming the violation of Bell inequalities and demonstrating the non-local nature of entanglement.

Beyond Local Realism: Towards a Unified Understanding

Continued exploration of loopholes and alternative interpretations pushes the boundaries of our understanding. Researchers investigate scenarios circumventing established limitations to comprehend non-local correlations and the foundations of quantum theory. A proposed model demonstrates a close match between theoretical predictions and experimental results, with a mean error of ≈0 and maximum disagreement of ≈0.03. Developing technologies controlling and measuring entangled states is vital for advancing knowledge, potentially enabling quantum computing, cryptography, and ultimately, a more complete understanding of the universe.

The pursuit of mathematically rigorous explanations for observed quantum phenomena finds resonance in the work presented. This study posits that violations of Bell inequalities needn’t invoke non-locality, but instead arise from the inherent constraints of conservation laws during measurement – a ‘supermeasured’ hidden variable theory. This aligns with a fundamental principle: that physical reality, at its core, must adhere to strict mathematical consistency. As Werner Heisenberg observed, “The act of observing alters the observed.” This isn’t merely a philosophical statement, but a direct consequence of the mathematical framework governing quantum mechanics; the measurement process, bound by conservation laws, inherently influences the system, leading to correlations that appear non-local when analyzed through classical lenses. The elegance lies in demonstrating how these correlations can emerge from a locally realistic framework, firmly rooted in mathematical discipline.

What’s Next?

The presented framework, while offering a potential resolution to the persistent enigma of Bell inequality violations without invoking non-locality, does not constitute a final theorem. The precise mathematical formulation of the conservation laws governing the ‘supermeasurement’ process remains a critical, and largely open, question. To state that statistical dependencies arise from conservation laws is insufficient; a demonstrably rigorous derivation, not merely a plausible heuristic, is demanded. The current model necessitates further investigation into the specific forms these conservation laws must take to generate correlations mirroring those predicted by quantum mechanics—and, crucially, to delineate the conditions under which such correlations deviate from the quantum predictions.

A significant limitation lies in the assumption of a pre-existing hidden variable distribution. The model does not address the origin of this distribution, nor does it provide a mechanism for its generation. To claim a complete alternative to quantum mechanics requires a fully specified, self-consistent theory – one that accounts for the emergence of this hidden variable landscape. The Wigner-Araki-Yanase theorem, frequently cited, offers constraints, but does not dictate a unique solution.

Future work should therefore focus on defining the minimal set of axioms required to produce both quantum-like correlations and demonstrable conservation of relevant physical quantities. Only through such a mathematically precise formulation can one assess the true predictive power of this ‘supermeasured’ hidden variable theory – and determine whether it represents a genuine alternative, or merely a restatement of quantum mechanics in a different guise. The pursuit of elegance demands no less.

Original article: https://arxiv.org/pdf/2511.06043.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/