Local Explanations of Quantum Phenomena

• Local explanations of quantum phenomena are frameworks that attribute quantum correlations to contextual, geometric, and statistical mechanisms without invoking nonlocal influences.
• These models employ hidden variable theories, local field operators, and retrocausal dynamics to reproduce quantum predictions such as Bell inequality violations.
• They provide practical insights by reconciling experimental observations with strictly local, causal processes, highlighting novel approaches to quantum dynamics.

Local explanations of quantum phenomena aim to account for the statistical and dynamical features of quantum systems—particularly those exhibiting entanglement or interference—while maintaining strict locality and causality at the fundamental level. These approaches seek to reproduce quantum predictions (including apparent violations of Bell-type inequalities) without invoking nonlocal action-at-a-distance or acausal signaling, instead attributing all effects to local mechanisms, contextuality, field-theoretic dynamics, or topological and geometric properties of physical space.

1. Foundational Principles of Local Quantum Explanations

Quantum theory is empirically successful but at odds with classical notions of locality and realism. Bell's theorem shows that no local-realist theory with measurement-setting independence can reproduce all quantum correlations as observed in entanglement experiments. However, several strands of research propose accounts that preserve locality through nuanced constructions:

• Geometric/topological frameworks: Modeling physical space as a parallelized 3-sphere (S³) equipped with a hidden variable structure, allowing locally causal and deterministic reproduction of quantum correlations by exploiting global topological features and the algebraic closure of bivector multiplication (Christian, 2011).
• Quantum field-theoretic locality: Describing all quantum phenomena in terms of local field operators, causally propagating according to the microcausality condition of QFT, with detection events and interference arising from local operator dynamics (Vedral, 2021).
• Contextual statistical and ensemble approaches: Treating wavefunctions as encoding only ensemble-level statistics, with measurement outcomes contextual and determined by local microstates and experimental settings rather than pre-existing hidden values (Kupczynski, 2016, 1804.02288).
• Label-based local models: Assigning to each system a hidden label specifying the outcome for each possible (compatible) measurement, and introducing a real de Broglie wave as a physical companion system, preserving both locality and action-reaction principles (Lopez, 2015, Lopez, 2014).
• Retrocausal and all-at-once models: Allowing for local beables whose statistics depend on both past and future boundary conditions, thus restoring locality through a time-symmetric, global constraint or action-principle framework for quantum circuits (Wharton et al., 6 Dec 2024, Price et al., 2015).
• Emergence from sub-quantum dynamics: Viewing quantum mechanics as an effective theory arising from underlying local, undulatory translocal networks or statistical dynamics, with quantum correlations stemming from local phase couplings and collective phenomena (Groessing, 2013, Requardt, 2012).

2. Restoration of Locality via Algebra, Topology, and Contextuality

Geometric and algebraic models, such as those based on Clifford and quaternion algebras, provide an explicit realization of local causality by defining measurement functions and hidden variables that only depend on local settings and a global orientation parameter. Specifically, by assigning to each photon pair a random orientation of S³ and specifying local measurement outcomes as products of unit bivectors, the model produces outcomes A(α,λ) and B(β,λ) strictly locally. Averaging reproduces the quantum correlation function:

$E(\alpha, \beta) = -\cos 2(\alpha - \beta)$

and allows for maximal CHSH inequality violations ($|S|=2\sqrt{2}$) while respecting Bell-local factorization (Christian, 2011). The nontrivial Hopf fibration of S³ ensures the global structure required for these correlations without any exchange of superluminal signals, framing the illusion of nonlocality as a misinterpretation of the underlying geometry.

Contextual models explain the empirical violation of Bell inequalities by denying the existence of a universal joint probability space for all measurement settings. Instead, the probability space changes with the experimental context (choice of observables and device microstates), making it impossible to define joint distributions over incompatible settings simultaneously (Kupczynski, 2016). By constructing outcome functions dependent on both hidden variables and local micro-contexts, these models reproduce all quantum correlators and avoid the inferences leading to Bell’s bound.

3. Local Field-Theoretic and Semiclassical Models

Field-theoretic formulations elevate local field operators as the elements of physical reality. Quantum phenomena such as double-slit interference and single-particle detection are described as local processes involving Heisenberg-picture field operators $\Psi(x,t)$, which propagate within the light cone and preserve microcausality:

$$[\Psi(x,t), \Psi(y,t')] = 0 \quad \text{when}\ (x-y)^2 - c^2(t-t')^2 < 0$$

Detection probabilities and intensities are calculated as local two-point function expectations, and all observed interference arises naturally from the overlap and phase structure of locally propagating field modes (Vedral, 2021). This perspective renders unnecessary the language of particles traversing both slits or explicit “collapse”—the field is causal and local, and measurement is a localized excitation.

In the pure wave/semiclassical limit, quantum phenomena—including (apparent) quantum jumps, discrete detection events, and entanglement-type correlations—are explained as emergent from the local, nonlinear interaction of Maxwell-Dirac fields with thresholded atomic detectors. Discrete “clicks” reflect amplification of local field fluctuations, and all pattern formation (even that which appears to violate Bell inequalities) arises from local detector response functions and shared causal histories of the incident fields (O'Reilly, 2011).

4. Ensemble, Statistical, and Pragmatist Interpretations

Ensemble-based interpretations assert that the wave function encodes only the statistical properties of ensembles of identically prepared systems, not individual events. Measurement outcomes are not pre-existing properties but are created contextually through the interaction between system and apparatus. In this framework, Bell-type correlations are replicated by context-dependent local models with independent hidden variables for each run and microstate, without requiring nonlocal influences (Kupczynski, 2016, 1804.02288).

Pragmatist approaches, as articulated in (Healey, 2012) and (Healey, 2016), deny that quantum states are beables or that Born-rule probabilities encode physical propensities. Instead, quantum states guide and license the assignment of probabilities to empirical magnitude claims, which are always relative to the agent’s information, spacetime location, and the structure of the quantum state. Collapse is not a physical event but merely an information update, and locality is preserved in the sense that no superluminal causation or signaling occurs; however, these approaches diverge from any interpretation of locality that requires explicit mediating local (agent-independent) variables.

5. Retrocausality, Weak Values, and Action-Principle Models

Retrocausal models restore locality by allowing for statistical dependence of hidden variables at the source on future measurement settings, but only via backward-in-time influences along particle worldlines. This approach rejects only the measurement-setting independence assumption of Bell, not locality, realism, or Lorentz covariance. The retrocausal scheme can exactly reproduce quantum statistics, including Bell-inequality violations, without any action-at-a-distance (Price et al., 2015).

Recent work on quantum circuits (Wharton et al., 6 Dec 2024) demonstrates that a fully local description can be constructed using post-selected weak values as local beables. These weak values remain invariant except at points where the associated qubit or system encounters a local gate. Evolution under exchange (entangling) gates is governed by classical oscillator-like equations for the local weak value vectors, and the entire circuit's outcome can be determined via an action principle constrained by both past and future boundary conditions. This "all-at-once" approach replaces the nonlocal, exponentially-sized state-vector description with a linearly-sized web of constraints on local variables.

6. Emergent and Sub-Quantum Locality

Emergent approaches propose that the entire quantum formalism arises as a low-energy effective theory from an underlying network of locally coupled oscillators or stochastic particle-plus-background systems. In the undulatory translocal theory, amplitude and phase fields defined on a microscopic substrate evolve according to local equations plus sparse long-range couplings. Standard quantum equations (e.g., the Schrödinger equation) emerge via coarse-graining and averaging, and apparent nonlocal effects (e.g., collapse, EPR) arise from rapid synchronization or phase-switching across the network. Nonetheless, all propagation and update mechanisms remain strictly local at the fundamental level (Groessing, 2013, Requardt, 2012).

Models built on sub-quantum statistical dynamics explain quantum trajectories as mean-field results of classical (ballistic) diffusion, with coherent and fluctuating components driven by interaction with a zero-point background. Interference effects, entanglement, and even features resembling Bohmian trajectories are produced, not by explicit nonlocality, but by the structure of the underlying stochastic or reaction-diffusion field (Groessing, 2013).

7. Critical Assessment and Limitations

While local explanations of quantum phenomena achieve dynamical and statistical locality in various senses, the viability of such models depends crucially on the precise definitions of locality, measurement independence, and the contextuality of observables. Mainstream quantum theory, interpreted minimally, rejects nonlocal beables and superluminal causation, but does not provide a local causal mechanism in the strong sense envisioned by classical physics or by Bell's "intuitive principle" of local causality (Healey, 2016, Dhand et al., 2018). Some local models rely on technically sophisticated topological properties of configuration space, contextualization of probability spaces, or retrocausal/“all-at-once” boundary conditions that evade classical intuitions.

Experimental tests (including “loophole-free” Bell violations) are consistent with the predictions of quantum theory but place stringent constraints on local-realist models satisfying standard conditions. Contextual, field-theoretic, and emergence-based models propose viable local realist accounts under suitably modified notions of probability, measurement, and causality, but some require experimental verification (e.g., detection of de Broglie wave recoil (Lopez, 2015), or statistical tests for contextuality violations (1804.02288)).

Local explanations thus enrich the landscape of quantum foundations, providing multiple rigorous frameworks in which to address the central puzzles without an appeal to acausal influence or nonlocal dynamical laws, yet consensus on their ultimate physical necessity remains open.