On Superdeterministic Rejections of Settings Independence (2008.00631v1)

Abstract: Relying on some auxiliary assumptions, usually considered mild, Bell's theorem proves that no local theory can reproduce all the predictions of quantum mechanics. In this work, we introduce a fully local, superdeterministic model that, by explicitly violating settings independence--one of these auxiliary assumptions, requiring statistical independence between measurement settings and systems to be measured--is able to reproduce all the predictions of quantum mechanics. Moreover, we show that, contrary to widespread expectations, our model can break settings independence without an initial state that is too complex to handle, without visibly losing all explanatory power and without outright nullifying all of experimental science. Still, we argue that our model is unnecessarily complicated and does not offer true advantages over its non-local competitors. We conclude that, while our model does not appear to be a viable contender to their non-local counterparts, it provides the ideal framework to advance the debate over violations of statistical independence via the superdeterministic route.

• The paper introduces a local superdeterministic model that reproduces quantum mechanics predictions by explicitly violating settings independence.
• It employs a novel local pilot-wave approach with homogeneous initial conditions and dynamically adjustable frameworks to address fine-tuning concerns.
• The work challenges conventional views on quantum non-locality and opens new avenues for reconciling local determinism with quantum theory.

Exploring Superdeterministic Rejections of Settings Independence in Quantum Mechanics

The paper "On Superdeterministic Rejections of Settings Independence" investigates a concept in quantum mechanics that challenges conventional perspectives on quantum correlations and non-locality. This paper is conducted by G.S. Ciepielewski, E. Okon, and D. Sudarsky from the Universidad Nacional Autónoma de México. The authors present a fully local, superdeterministic model that explicitly violates settings independence—a key assumption in Bell's theorem—and replicates all predictions of quantum mechanics. This exploration is pivotal for re-evaluating the basis on which the non-locality of quantum mechanics is accepted.

Core Insights and Analysis

Bell's theorem demonstrates that no local theory can reproduce all quantum mechanics predictions unless certain auxiliary assumptions are violated. A critical assumption, settings independence, posits the statistical independence of measurement settings and the systems measured. Traditional understanding dictates that violating this assumption leads to infeasible or conspiratorial models that undermine scientific experimentalism. However, the authors propose a model that challenges this narrative by successfully violating settings independence while maintaining feasibility.

The Local Pilot-Wave Model

The authors introduce a local model variant, termed the local pilot-wave model ($\text{LPW}$). This model builds on non-relativistic de-Broglie-Bohm pilot-wave theory but modifies it substantially to achieve locality by embedding a pilot-wave system at each point in space. Their innovation lies in a homogeneous initial condition—a measure zero set within the broader scenario space—which synchronizes these systems to behave collectively as traditional non-local quantum systems would. This synchronization effectively enables the violation of Bell inequalities, typically indicative of non-locality.

Addressing Traditional Objections

While previous criticisms of superdeterministic models emphasized the impracticality and "fine-tuning" of initial conditions, this paper counteracts skepticism by presenting concrete model variants capable of addressing these points. The introduction of constraints ($\text{C-LPW}_f$) and a dynamically adjusting model ($\text{R-LPW}_f$), propose manageable frameworks for achieving the requisite initial synchronizations, thus ameliorating concerns over initial state complexity and enhancing explanatory power.

Implications and Future Directions

The implications of this work are profound within the theoretical confines of quantum theory. By illustrating a superdeterministic model that circumvents traditional issues, this paper creates a platform for further discussions on non-locality and the philosophical implications of quantum mechanics. However, its viability as an alternative to current models hinges on more than technical plausibility—it must convincingly integrate within the broader physics framework, including a potential reconciliation with relativity considerations.

The necessity of a preferred frame in the $\text{LPW}$ model raises questions about compatibility with relativity. Further research is needed to address these limitations, focusing on either further development of the $\text{R-LPW}_f$ variant or the construction of alternative frameworks that maintain compatibility with relativistic postulates.

Conclusion

"On Superdeterministic Rejections of Settings Independence" presents a compelling argument that challenging the often-understood assumptions in Bell-type inequalities can yield a local model retaining the predictive strengths of quantum mechanics. While it does not offer a definitive advantage over non-local theories due to inherent complexities and the reintroduction of a preferred frame, its contribution lies in opening the dialogue for superdeterministic models. By providing frameworks to handle settings independence violations through feasible initial conditions, it invites re-examination of deep-seated assumptions in quantum physics.

This paper enriches the ongoing discourse on the reconcilability of quantum mechanics with locality, representing an auspicious framework for exploring settings independence in a superdeterministic context while paving the way for innovative theoretical advancements and philosophical insight shifts.