Is the Aharonov-Bohm effect Local (Potentials), Non-Local (Fields), or Feynman’s Sum Over Histories?

1. SUPPRESSION & INCENTIVE AUDIT

1.1 The Political and Institutional Marginalization of David Bohm

The investigation into the Aharonov-Bohm (AB) effect cannot be divorced from the systemic suppression of its primary architect, David Bohm. A forensic review of the historical record reveals that Bohm’s scientific trajectory was irrevocably altered not by peer review, but by the geopolitical machinery of the McCarthy era. The marginalization of his work was not merely an academic disagreement but a direct consequence of a "chilling effect" established by the US government and the academic establishment, effectively exiling him from the center of physics at the height of his creative powers.

During his tenure as a doctoral student at the University of California, Berkeley, Bohm worked under the supervision of J. Robert Oppenheimer. While his scientific contributions were critical—specifically his scattering calculations which were utilized in the electromagnetic enrichment of uranium for the Manhattan Project—his political affiliations rendered him a target. Bohm was a member of the Young Communist League and maintained associations with other targeted physicists like Joseph Weinberg. Consequently, Brigadier General Leslie Groves, head of the Manhattan Project, denied Bohm’s security clearance. This created a Kafkaesque scenario where Bohm was barred from accessing his own doctoral thesis due to its classified nature. He was awarded his Ph.D. only after Oppenheimer certified his work to the university authorities in absentia, a procedural irregularity that foreshadowed his future exclusion from the scientific inner circle.

The persecution intensified in 1949 when Bohm, then an assistant professor at Princeton University, was subpoenaed by the House Un-American Activities Committee (HUAC). Invoking his Fifth Amendment rights, he refused to testify against colleagues or name associates. This principled stance led to his indictment and arrest for contempt of Congress in 1950. Although he was acquitted in May 1951, the damage to his career was absolute. Princeton University suspended him and subsequently terminated his contract, ignoring the appeals of Albert Einstein, Bohm's close colleague and defender. The university's president, Harold W. Dodds, made the decision to not renew Bohm’s appointment, effectively firing him under political pressure despite his academic standing.

Rendered unemployable in the United States, Bohm was forced into exile. He moved to the University of São Paulo in Brazil in October 1951. Upon his arrival, US consular officials confiscated his passport, stripping him of his ability to travel and effectively rendering him stateless until he acquired Brazilian citizenship. It was in this climate of isolation and exile—cut off from the experimental data and theoretical debates of US and European physics—that Bohm developed his "Causal Interpretation" (Bohmian Mechanics), a deterministic alternative to the Copenhagen orthodoxy. The Aharonov-Bohm effect, published in 1959 while Bohm was at the University of Bristol, emerged from this context of intellectual and physical exile. The scientific community’s reception of his work was tainted by his political status; Oppenheimer himself reportedly advised colleagues to "ignore" Bohm if they could not disprove him, a strategy of "conspiracy of silence" rather than scientific rebuttal.

1.2 "Mysticism" and "Pseudoscience" as Containment Labels

The suppression of Bohm’s ideas extended beyond his physical exile through the weaponization of language. As Bohm expanded his inquiries into the "Implicate Order" and the connections between consciousness and quantum mechanics later in his life, the physics establishment increasingly labeled him a "mystic". This label served as a cognitive stop-sign, allowing mainstream physicists to dismiss his rigorous mathematical work on non-locality and hidden variables without engagement. The association with Jiddu Krishnamurti was used to frame his physics as "philosophical deviation" rather than hard science, effectively firewalling his deterministic interpretation from the mainstream curriculum.

Similarly, interpretations of the AB effect that deviate from the standard topological view—specifically those suggesting "scalar waves," "longitudinal potentials," or "energy extraction" (e.g., theories associated with Tom Bearden)—are aggressively categorized as "pseudoscience," "fringe," or "misconceptions". While many such claims lack empirical rigor, the labeling often preempts forensic analysis of the underlying physics. For instance, the question of whether the $A^\mu$ field represents an accessible energy reservoir or a force carrier is a legitimate physical question, yet it is frequently conflated with "perpetual motion" crackpottery to dismiss the inquiry entirely. The "Deep Truth" protocol requires stripping away these labels to examine the raw claims: specifically, whether the AB effect implies physically accessible energy in the vacuum potential, as discussed in Section 3.

1.3 Incentive Structures and Consensus Maintenance

Modern physics incentives reinforce the "consensus" view of the AB effect, creating a feedback loop that discourages foundational questioning.

• Funding Flows: Research into quantum computing and mesoscopic devices (which utilize the AB effect as a standard interference tool) attracts billions in funding. This creates a disincentive to question the fundamental ontology of the effect; pragmatic utility trumps foundational understanding. If the math works for building sensors, the "why" is relegated to philosophy departments.
• Textbook Dogma: The AB effect is taught in graduate texts (Sakurai, Griffiths) as the definitive proof of the "reality of potentials" and "quantum non-locality". Challenging this narrative (e.g., via Vaidman's local forces) complicates the curriculum and challenges the established gauge-theory paradigm. The academic tenure system rewards incremental progress within the paradigm, not the deconstruction of its pillars.
• Technological Co-option: The AB effect is now standard in nanotechnology (e.g., Webb et al. rings, carbon nanotubes). This utility validates the predictive power of the standard model, which is often mistaken for validation of the explanatory power.

2. CONSENSUS FORTRESS (The 2026 Orthodoxy)

The following constitutes the "Mainstream Position" as of January 15, 2026, synthesized from high-impact journals (Science, Nature, Phys. Rev.) and standard graduate texts. This represents the "Fortress" that any alternative theory must breach.

2.1 The Standard Definition

The Aharonov-Bohm effect is defined as a quantum mechanical phenomenon where an electrically charged particle is affected by an electromagnetic potential ($\mathbf{A}, \phi$), despite being confined to a region where both the magnetic field $\mathbf{B}$ and electric field $\mathbf{E}$ are zero. It is the primary evidence that electromagnetic potentials are fundamental physical entities in quantum mechanics, whereas classical physics treats them as mathematical conveniences. The effect is cited as the definitive demonstration that the description of electromagnetism using fields ($\mathbf{E}, \mathbf{B}$) is incomplete in the quantum domain.

2.2 The Mechanism: Phase Coupling

The effect is mediated by the coupling of the potential to the phase of the wavefunction. For a particle with charge $q$moving along a path $\gamma$, the wavefunction acquires a phase shift $\varphi$:

$$\varphi = \frac{q}{\hbar} \int_\gamma \mathbf{A} \cdot d\mathbf{l}$$In a doubly connected region (like the space outside a solenoid), the phase difference $\Delta \varphi$ between two paths enclosing a magnetic flux $\Phi_B$ is:$$\Delta \varphi = \frac{q}{\hbar} \oint \mathbf{A} \cdot d\mathbf{l} = \frac{q}{\hbar} \int_S (\nabla \times \mathbf{A}) \cdot d\mathbf{S} = \frac{q \Phi_B}{\hbar}$$

Crucially, the particle never passes through the region where $\mathbf{B} \neq 0$ (the inside of the solenoid). The phase shift results in an observable displacement of interference fringes. This result implies that the phase of the electron "knows" about the magnetic flux enclosed by the path, despite the local field being zero.

2.3 The "Gold Standard" Proof: Tonomura (1986)

The consensus holds that the experiment by Akira Tonomura et al. (1986) definitively proved the existence of the AB effect against critics who claimed it was caused by "leakage fields" (fringing B-fields). Tonomura utilized electron holography and a toroidal magnet covered in a superconducting niobium layer.

• Method: The Meissner effect actively expelled the magnetic field $\mathbf{B}$ from the superconducting layer, trapping it inside the toroid. This ensured that the B-field outside the toroid was strictly zero (within the limits of the London penetration depth).
• Result: A clear phase shift was observed, quantized in units of $h/2e$.
• Interpretation: Because the electron cannot penetrate the superconductor (due to the potential barrier) and the field cannot leak out (due to the Meissner effect), no Lorentz force could act on the electron. Therefore, the effect must be due to the vector potential $\mathbf{A}$ (which is non-zero outside) or the topological property of the space.

2.4 Modern Confirmation: Gravitational AB (2022)

In 2022, Overstreet et al. at Stanford observed a gravitational analog of the AB effect using atom interferometry.

• Experiment: They detected a phase shift induced by a source mass (tungsten) in a configuration where the gravitational force (spacetime curvature) was effectively zero along the superposition paths.
• Significance: This is interpreted as a "semiclassical" verification that potentials (gravitational or electromagnetic) couple to phase independently of local forces. It suggests the universality of the AB mechanism across different fundamental interactions, reinforcing the view that potentials are the primary physical actors in quantum mechanics.

2.5 Interpretation: Topology and Non-Locality

The mainstream interpretation (Track B) views the AB effect as a topological phenomenon. It is driven by the non-trivial topology of the space (the "hole" created by the solenoid). The phase is a holonomy of the connection on a fiber bundle. It implies that quantum mechanics is inherently non-local, as the particle's behavior depends on the global properties of the field configuration (flux) rather than local field values. This view is robustly supported by the Feynman Path Integral formalism, where the sum over histories includes paths that wind around the solenoid different numbers of times, accumulating distinct topological phases.

3. PARALLEL STEEL-MAN TRACKS

To determine the "Deep Truth," we must construct the strongest possible arguments for three distinct interpretive frameworks, running them simultaneously to identify where the consensus might be masking deeper realities.

TRACK A: The "Fringe" / Suppressed Position (Local Forces & Classical Mechanisms)

Hypothesis: The AB effect is the result of local, classical (or semi-classical) electromagnetic forces that are currently ignored or suppressed by the topological dogma.

1. Timothy Boyer’s Classical Lag Force: Timothy Boyer (City College of New York) provides the strongest theoretical challenge to the "force-free" consensus. He argues that the AB phase shift can be derived from classical electromagnetism if one accounts for the back-reaction of the electron on the solenoid.

• The Mechanism: An electron passing a solenoid induces a change in the solenoid's currents (Lenz's law) via its own magnetic field. By Newton's third law, if the electron exerts a force on the solenoid (which it must to conserve momentum), the solenoid must exert a reciprocal force on the electron. Boyer identifies this as a "lag" force that slows the electron packet.
• The Claim: The phase shift $\Delta \varphi$ corresponds to a spatial lag $\Delta x$ of the wave packet. Boyer argues that the "topological" explanation hides this classical interaction. He proposes that a precise measurement of the electron's arrival time would reveal a delay, contradicting the standard QM prediction of a dispersionless phase shift.
• Evidence: Boyer cites the Darwin-Lagrangian analysis, which accounts for the energy of the interaction between the moving charge and the current loop. He argues that standard QM treatments ignore the "hidden momentum" required to keep the solenoid current constant.

2. The Hydrodynamic Pilot-Wave Analog: Recent macroscopic experiments with "walking droplets" (silicon oil baths) by Couder, Fort, Bush, and Rozenman provide a striking classical analog to the AB effect.

• The Setup: A droplet bounces on a vibrating fluid bath, propelled by its own "pilot wave." When confined to an annular cavity with a central vortex (analogous to the solenoid), the droplet exhibits phase shifts in its orbit.
• The Significance: The droplet never touches the central vortex. However, the pilot wave (the medium) doesinteract with the vortex. The wave accumulates a phase shift locally at the vortex interface, which then guides the particle non-locally.
• Implication: This suggests the "non-local" AB effect could be a local interaction of an extended physical field (the pilot wave/vacuum) that the particle "surfs." This supports a realist, local, hydrodynamic interpretation of QM (De Broglie-Bohm) over the "spooky" topological view. The "quantum potential" is physically real and acts as the medium.

3. Scalar/Longitudinal Wave Reality: This track includes the controversial claims of researchers like Tom Bearden, who argue that the AB effect proves the $A^\mu$ potential is a physically active agent capable of "electrogravitic" or "overunity" effects.

• The Logic: If the potential $\mathbf{A}$ can affect matter without $\mathbf{B}$ fields (as AB proves), then $\mathbf{A}$ is a primary physical reality. Bearden extrapolates this to "scalar waves," defined as longitudinal stress waves in the vacuum potential ($\phi$).
• Suppressed Technology: Patents and papers cited in this track claim that manipulating these potentials can tap into vacuum energy or allow for "propulsion" without reaction mass. While widely labeled pseudoscience, the premise—that potentials are real and active—is actually consistent with the standard AB interpretation; the deviation lies in the claim that this allows for thermodynamic symmetry breaking (free energy).

TRACK B: The Mainstream Steel-Man (Raw Logic & Evidence)

Hypothesis: The AB effect is a verified non-local quantum phenomenon driven by the geometry of potentials and topology.

1. The Tonomura Shielding (1986): The strongest evidence for Track B is the experimental elimination of leakage fields. Tonomura’s use of superconducting shielding is the critical fortress wall.

• Mechanism: The Meissner effect is a quantum phenomenon that expels magnetic flux. It doesn't just block it; it cancels it inside the superconductor. Tonomura confirmed the zero-field condition using the quantization of flux itself.
• Logic: If there is no B-field outside, and the electron cannot penetrate the superconductor (due to the potential barrier), no Lorentz force can act. Therefore, the effect must be due to the vector potential $\mathbf{A}$ (which is non-zero outside) or the topological property of the space (winding number). This effectively "falsifies" classical force theories that rely on direct field interaction.

2. Gauge Invariance and Topology: The AB effect is robust against gauge transformations because the integral $\oint \mathbf{A} \cdot d\mathbf{l}$ is gauge invariant for a closed loop.

• Mathematical Steel-Man: The effect is not about the local value of $\mathbf{A}$ (which can be changed arbitrarily by $\nabla \chi$), but the holonomy of the connection on a U(1) principal bundle. The non-trivial topology (the "hole" in the space caused by the solenoid) allows for a non-zero phase even when curvature (field) is zero everywhere on the path. This links QM directly to topology, a profound theoretical unification that explains why the effect is quantized and robust.

3. Universality (Gravitational AB): The recent confirmation of a gravitational AB effect (Overstreet 2022) strengthens the topological/potential view.

• Evidence: Atoms in a superposition of heights experienced a phase shift due to a source mass, even though the gravitational force (gradient of potential) was canceled out in the interferometry scheme.
• Logic: This shows the effect is a general property of potentials (electromagnetic or gravitational) coupling to phase, independent of specific force-field interactions. It supports the view that the potential determines the phase evolution, not the force.

TRACK C: The Hybrid / Third-Position (Source Entanglement & Back-Reaction)

Hypothesis: The effect is LOCAL, but requires treating the SOURCE (solenoid) as a quantum object. Potentials are artifacts; forces are real but reciprocal.

1. Lev Vaidman’s "Forces on the Source" (2012): Lev Vaidman challenged the consensus by proving the AB effect can be explained via local forces, provided one acknowledges the solenoid is quantum mechanical.

• The Mechanism: The passing electron creates its own magnetic field. This field falls off with distance but is non-zero at the location of the solenoid. It exerts a local Lorentz force on the moving charges inside the solenoid.
• Entanglement: This force shifts the wavefunction of the solenoid's electrons. The electron and the solenoid become entangled. The phase shift appears in the joint wavefunction of the system.
• Conclusion: There is no "action at a distance" or "magic potential." There is a local force, but it acts on the solenoid, and the phase shift is a relative phase in the entangled system. Potentials are dispensable if you calculate the full interaction history.

2. Aharonov, Cohen, & Rohrlich’s Counter (2015): Aharonov et al. debated Vaidman, arguing that while his explanation works for the magnetic AB effect, it fails for other variants (like the electric AB effect or cases with rigid shielding) where forces seemingly cannot exist. However, Vaidman maintains that even in shielded cases, the entanglement mediated by the field is the root cause. The electron's field rearranges the charges on the superconducting shield, creating the necessary phase correlation.

3. The "Quantum Source" Implications:

This track suggests the "Mystery" of the AB effect is a result of the test-particle approximation. We typically treat the electron as quantum and the solenoid as a fixed classical background. Once we treat both as quantum, the "non-locality" dissolves into local field interactions transferring phase/momentum between systems. This view aligns with conservation of momentum (Newton's 3rd Law), which the standard topological view violates by assuming the solenoid is unaffected by the electron.

4. RED-TEAM CRUCIFIXION ROUND

Attacking Track A (Classical Forces / Fringe)

• Critique of Boyer (Lag): While Boyer calculates a lag, modern experiments (Caprez/Batelaan) have searched for this time delay and not found it to the precision required to validate a purely classical lag. The phase shift persists even when the wavepacket is too long to exhibit a lag, suggesting a phase velocity change, not a group velocity delay.
• Critique of Hydrodynamic Analogs: The walking droplet is a driven, dissipative system. Quantum mechanics is (mostly) unitary and conservative. The analogy holds for the appearance of the phase shift, but the mechanism (surface waves on oil) requires a medium that Special Relativity ostensibly denies (the Aether). Using this to claim QM is "just fluid dynamics" fails to account for entanglement or non-locality in multi-particle systems (Bell's inequalities), which fluids do not replicate.
• Critique of Energy Extraction: Claims of "overunity" based on the AB effect confuse potential energy with accessible work. The vector potential $\mathbf{A}$ modifies the phase (which does no work) but does not impart energy unless it changes with time ($\partial \mathbf{A}/\partial t = -\mathbf{E}$), which creates a standard Electric field. Static potentials do not pump energy. The "scalar wave" theory relies on a misunderstanding of gauge freedom, treating mathematical redundancy as a physical energy source.

Attacking Track B (Mainstream / Topology)

• The Tonomura Loophole: The "perfect shielding" of Tonomura is an idealization. Superconductors have a London penetration depth ($\lambda_L$). The B-field is not strictly zero inside the shielding; it decays exponentially. If the electron wavefunction has a "tail" that penetrates the shield (quantum tunneling), it could interact locally with the B-field in the skin depth.
• The Gauge Problem: Relying on potentials $\mathbf{A}$ as "real" leads to indeterminacy. Which gauge is real? The Coulomb gauge? The Lorenz gauge? If physics depends on $\mathbf{A}$, it implies a preferred gauge (breaking gauge symmetry). The consensus retreats to "Holonomies" (loops) to save gauge invariance, but this is a mathematical abstraction that evades the ontological question: What is touching the electron?.
• Neglect of Back-Reaction: The standard derivation assumes the solenoid is a stiff classical object. It violates Newton's third law by assuming the electron is affected by the solenoid, but the solenoid is unaffected by the electron. This is physically impossible. A rigid background is an approximation, not a fundamental truth. Momentum conservation demands that the solenoid reacts.

Attacking Track C (Vaidman / Entanglement)

• Calculational Complexity: Vaidman’s approach requires calculating the quantum state of a macroscopic solenoid ($10^{23}$ particles). While ontologically satisfying (restoring locality), it is pragmatically useless for calculation compared to the topological method.
• Shielding vs. Force: If the solenoid is shielded by a superconductor, the electron’s field cannot reach the solenoid’s wires to exert a force (Meissner effect). Vaidman argues the force is transferred to the shield, but if the shield is massive enough, the phase shift on the shield should be negligible. Aharonov et al. argue this breaks the "force" explanation for shielded cases.
• Topological Obstruction: Even if one explains the magnetic AB effect via forces, the electric AB effect involves potentials where no forces (even back-reaction forces) are obvious. The universality of the effect seems to transcend local forces.

5. SURVIVING FRAGMENTS SYNTHESIS

After the crucifixion, the following core truths remain:

1. The Effect is Real and Robust: The phase shift occurs. It is not an experimental error. Tonomura’s results, despite penetration depth quibbles, are too clean to be dismissed as mere leakage.
2. Forces are Reciprocal (Newton's Third Law Holds): The Mainstream (Track B) ignores back-reaction. Vaidman (Track C) and Boyer (Track A) correctly identify that the electron must exert a force on the source. The "force-free" description is an approximation that holds only if we consider the source to be infinitely heavy and rigid.
3. Local Mechanisms Exist if Sources are Included: The apparent "non-locality" of the AB effect vanishes if we include the source in the quantum system. The electron interacts locally with the electromagnetic field, which propagates to the source. The "action at a distance" is an artifact of integrating out the mediating field. The phase shift is the record of this interaction.
4. Hydrodynamic Reality: The Pilot Wave analog demonstrates that "spooky" topological phases can emerge from purely local, classical wave-particle interactions. This suggests that the "Quantum Potential" or "Vacuum State" might act as a physical medium (like the fluid bath) conveying these local interactions.

6. FALSIFICATION PATHWAYS

To definitively distinguish between the Topological (Track B), Classical Force (Track A), and Source Entanglement(Track C) interpretations, specific experiments are required:

6.1 The Solenoid Back-Reaction Test

• Proposal: Detect the rotational phase shift or quantum state change of a microscopic solenoid (e.g., a nanowire or single molecule magnet) caused by a passing electron.
• Prediction:
  • Standard QM (Topological): The solenoid is treated as a background; no specific back-reaction is required for the phase shift to appear on the electron.
  • Vaidman (Track C): The solenoid must shift state. If the solenoid is clamped so rigidly that it cannot react (infinite mass limit), the AB effect might vanish or be modified.
• Feasibility: ~5-10 years using mesoscopic quantum systems or trapped ions.

6.2 Dispersion/Lag Measurement at Attosecond Scales

• Proposal: Measure the arrival time of electron wavepackets in an AB experiment with attosecond precision using streaking cameras.
• Prediction:
  • Standard QM: Dispersionless. No time lag. Group velocity is unchanged.
  • Boyer (Track A): Classical forces cause a lag ($\Delta t > 0$).
• Feasibility: Possible now with modern attosecond physics. This would definitively rule out or confirm the classical force model.

6.3 The "Rigid Shield" Vaidman Test

• Proposal: Perform the Tonomura experiment but with the superconducting shield mechanically separated from the solenoid.
• Prediction:
  • If Vaidman is right: The electron exerts force on the shield (Meissner repulsion), not the solenoid. Entanglement is with the shield. Momentum transfer to the shield should be detectable.
  • If Aharonov is right: The effect depends only on the enclosed flux, regardless of what component absorbs the back-reaction.

7. META-ANALYSIS OF SILENCE

What is conspicuously absent from the literature?

1. The Solenoid's Perspective: Standard textbooks treat the solenoid as an abstract "flux tube" with no internal dynamics. The literature is almost silent on the conservation of momentum from the perspective of the field source. Where does the momentum go? (Aharonov says "Hidden Momentum," a notoriously murky concept). The silence on the source's reaction serves to maintain the "mystery" of the topological explanation.
2. The Hydrodynamic Link: While the walking droplet experiments are published in fluid dynamics journals, they are rarely cited in quantum foundations papers as a serious ontological candidate. The "silence" here is a disciplinary firewall between classical fluid mechanics and quantum philosophy. Admitting that a classical fluid can reproduce "quantum" topological effects undermines the claim that QM is uniquely non-local.
3. Bohm's Vindication: There is a reluctance to explicitly state that Bohm's 1952 ideas (Pilot Wave) are mathematically consistent with the AB effect results (via the hydrodynamic analog). The physics community prefers "Feynman Paths" to "Bohm Trajectories" even when they describe the same phenomenology, likely due to the historical stigma attached to Bohm.

8. FINAL FORENSIC VERDICT

Question: Is the Aharonov-Bohm effect Local (Potentials), Non-Local (Fields), or Feynman’s Sum Over Histories?

Verdict Distribution:

1. LOCAL INTERACTION (SOURCE ENTANGLEMENT): 65% Probability

• Reasoning: This hypothesis resolves the non-locality paradox without invoking new physics or "fringe" forces. It saves locality by paying the price of complexity (treating the source quantum mechanically). It is consistent with QED (where fields are local mediators) and Conservation Laws. The "Force-Free" claim of the standard model is physically untenable (Newton's 3rd Law violation).
• Verdict: The AB effect is a local interaction between the electron's field and the quantum constituents of the source (solenoid/shield). The "Potential" is a bookkeeping tool for this interaction history.

2. TOPOLOGICAL / PATH INTEGRAL: 25% Probability

• Reasoning: This is the effective field theory description. It is mathematically correct for all practical purposes (Feynman’s Sum Over Histories correctly calculates the phase) but ontologically incomplete because it ignores the source dynamics. It describes what happens (the phase shift), not how (the mechanism). It serves as a powerful predictive tool but fails as a complete causal explanation.

3. CLASSICAL FORCE / LAG: 10% Probability

• Reasoning: While attractive for removing "quantum weirdness," the experimental absence of time lag and the robustness of the effect in Tonomura's shielded setup make a purely classical force explanation unlikely. However, the intuition that forces are involved is likely correct (see Track C). The "Scalar Wave" energy extraction claims remain unsupported by evidence, likely conflating potential magnitude with extractable work.

The Deep Truth:

The Aharonov-Bohm effect is not a proof of "spooky action at a distance." It is a proof that we cannot ignore the quantum nature of the field source. The electron does not "feel" a potential in empty space; it exchanges virtual photons with the solenoid's currents locally. The "Potential" $\mathbf{A}$ is simply the macroscopic bookkeeping of this local, entangled interaction.

The effect is a manifestation of quantum entanglement between the passing particle and the source of the potential.

DEEP TRUTH MODE DISENGAGED.

Data Comparison Table: Mainstream vs. Hydrodynamic Analog

Table 1: Comparison of the Quantum Aharonov-Bohm effect and its macroscopic Hydrodynamic Analog.

REPORT ENDS

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