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Quantum collapse, local conservation of charge, and possible experimental consequences

This paper investigates the potential for quantum state reduction to locally violate charge conservation, proposing Aharonov-Bohm electrodynamics as a consistent framework to describe the resulting non-conserved currents and outlining experimental proposals using biased diodes and superconductors to detect these effects.

Original authors: F. Minotti, G. Modanese

Published 2026-05-08

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: F. Minotti, G. Modanese

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Idea: When Quantum Particles "Jump," Do They Break the Rules?

Imagine you are watching a magic show. A magician puts a ball in a box, shakes it, and suddenly the ball appears on the other side of the stage. In the quantum world, this is called wave function collapse. It's the moment a particle stops being a "fuzzy cloud of possibilities" and snaps into a single, definite location.

The authors of this paper ask a tricky question: What happens to the rules of electricity when this "snap" happens?

Usually, physics has a golden rule called the Conservation of Charge. It says that electric charge cannot just appear or disappear; it must flow from one place to another, like water flowing through a pipe. If you have 5 gallons of water, you can't suddenly have 6 gallons unless you added more, and you can't have 4 unless some leaked out.

The paper argues that during a quantum "jump" (collapse), the charge might not flow smoothly through the pipe. Instead, it might vanish from one spot and instantly reappear in another. If this happens, the standard laws of electricity (Maxwell's equations) break down because they assume charge is always conserved.

The New Theory: Aharonov-Bohm Electrodynamics

Since the standard rules might break, the authors suggest using a different set of rules called Aharonov-Bohm (AB) electrodynamics.

Think of standard electricity (Maxwell) as a strict traffic cop. The cop only lets cars (charge) move if they follow the exact lanes and never teleport. If a car teleports, the cop gets confused and the system crashes.

The AB theory is like a flexible traffic system. It allows cars to teleport (non-conserved charge) without crashing the system. When charge does behave normally, this flexible system looks exactly like the strict traffic cop. But when charge "jumps," the flexible system reveals a new type of invisible energy wave.

The "Ghost Wave" (Gauge Waves)

This new system predicts the existence of something called Gauge Waves.

The Analogy: Imagine a standard radio wave is like a loudspeaker playing music. Everyone in the room hears it.
The Gauge Wave: This is like a "ghost frequency." If you are a normal person (a particle with conserved charge), you are deaf to this frequency. You walk right through it and feel nothing.
The Catch: However, if you are a "teleporter" (a particle undergoing a quantum jump where charge isn't conserved), you can hear the ghost frequency. It pushes and pulls on you, even though normal matter ignores it.

Testing the Theory with Superconductors

The authors tested how different materials react to these "ghost waves."

Fermions (Normal Electrons): These are like the strict traffic followers. They only interact with the ghost wave if they are in the middle of a "jump" (collapse). If they are just sitting still or flowing smoothly, the wave passes right through them.
Bosons (Superconductors): These are like a super-coordinated dance troupe. The authors propose that even if these particles aren't "jumping," they interact with the ghost wave differently.
- The Result: The paper claims that superconductors act like a shield against these ghost waves. Just as a lead wall blocks X-rays, a superconductor would block these gauge waves, preventing them from passing through.

The Experiment: The "Tunneling Diode" Detector

How can we prove this? The authors propose building a detector using a reverse-biased diode (a specific type of electronic component).

The Setup: Imagine a tunnel with a high wall. Electrons are trying to tunnel through this wall. In the quantum world, they don't climb over; they "tunnel" through.
The Mechanism: The authors suggest that every time an electron tunnels through, it performs a tiny "quantum jump." This jump creates a tiny, local violation of the conservation rule.
The Detection: If a "ghost wave" (gauge wave) is passing through the room, it will push on these tunneling electrons. Because the electrons are "jumping," they can feel the push.
The Signal: This push would create a tiny, measurable voltage change in the circuit. The authors designed two circuits (one simple, one with amplifiers) to detect this tiny signal. They suggest that if you put two of these circuits next to each other, they should both pick up the same "noise" from the ghost waves, creating a correlated signal that proves the waves exist.

Summary of Claims

The Problem: Standard physics says charge is always conserved. The authors argue that quantum "collapses" might break this rule locally.
The Solution: Use Aharonov-Bohm electrodynamics, which allows for these breaks and predicts "ghost waves" (gauge waves).
The Interaction: Normal matter ignores these waves. Only matter that is "jumping" (collapsing) or specific boson systems (like superconductors) interact with them.
The Shield: Superconductors can block these waves.
The Proof: We can try to detect these waves using tunneling diodes, which act as tiny sensors for the "ghost" energy.

The paper concludes that while this is currently a theoretical model based on an idealized view of quantum jumps, it offers a concrete way to test these ideas in a lab using standard electronic components.

Technical Summary: Quantum Collapse, Local Conservation of Charge, and Possible Experimental Consequences

Problem Statement
The paper investigates a potential conflict between the standard interpretation of quantum state reduction (wave function collapse) and the local conservation of electric charge. While the Schrödinger equation and Noether's theorem guarantee local charge conservation for systems evolving unitarily, the authors argue that an idealized, instantaneous state-reduction process—where a wave function discontinuously jumps from a superposition to an eigenstate—necessarily violates local charge conservation at the moment of collapse. This violation implies that the resulting electromagnetic (e.m.) fields cannot be consistently described by standard Maxwell electrodynamics, which requires strictly conserved sources ( $\partial_\mu j^\mu = 0$ ).

Methodology
The authors employ a theoretical framework based on Aharonov-Bohm (AB) electrodynamics, which extends Maxwell theory to accommodate non-conserved sources. The methodology proceeds through the following steps:

Theoretical Derivation: Using the action principle and Noether's theorem, the authors derive the condition for charge conservation. They demonstrate that for a wave function undergoing a step-like reduction at time $t_0$ (modeled as $\psi = \psi_+ \Theta(t-t_0) + \psi_- \Theta(t_0-t)$ ), the divergence of the current density becomes non-zero: $\partial_\mu J^\mu = q(|\psi_+|^2 - |\psi_-|^2)\delta(t-t_0)$ .
Statistical vs. Event-Level Analysis: The paper distinguishes between single collapse events and statistical ensembles. While the time-averaged or ensemble-averaged violation of charge conservation may vanish (e.g., in standard projective measurements where probabilities sum to unity), the authors argue that individual events or biased non-equilibrium processes (such as biased tunneling) can generate persistent, non-conserved local currents.
Interaction with Gauge Waves: The study analyzes how these non-conserved currents interact with "gauge waves"—specific field configurations in AB electrodynamics that are physically inert in Maxwell theory (where charge is conserved). The authors calculate the interaction of these waves with:
- Fermionic systems: Using the standard minimal coupling Hamiltonian.
- Bosonic systems: Utilizing a modified Schrödinger equation previously proposed by the authors, which alters the coupling to e.m. fields for bosons.
Superconductor Shielding: The authors apply the bosonic framework to superconductors to determine if they can shield gauge waves, deriving the penetration depth and cutoff conditions.
Experimental Proposals: The paper proposes concrete circuit designs using inverse-biased Zener diodes (where tunneling electrons are hypothesized to undergo collapse-induced non-conservation) to detect the power exchange between a gauge wave and the circuit.

Key Contributions and Results

Violation of Local Conservation: The paper establishes that idealized quantum collapse leads to a local failure of charge conservation, represented by a source term proportional to the Dirac delta function in time. This necessitates the use of AB electrodynamics rather than Maxwell electrodynamics for describing the associated fields.
Fermion vs. Boson Interaction: A critical distinction is drawn between fermions and bosons regarding their interaction with gauge waves:
- Fermions: Interact with gauge waves only if the charge is locally non-conserved (i.e., during the collapse event). If charge is conserved, the interaction vanishes.
- Bosons: Interact with gauge waves even when charge is strictly conserved, due to the specific form of the modified Schrödinger equation and the resulting current density.
Superconductor Shielding: The analysis shows that superconductors, treated as charged boson systems, effectively shield gauge waves. The shielding condition is analogous to the plasma frequency cutoff in ordinary conductors, with a penetration depth dependent on the London penetration depth and the wave frequency.
Experimental Detection: The authors propose that inverse-biased diodes, where tunneling events are modeled as collapse processes, can act as transducers for gauge waves.
- A simple circuit with a reverse-biased Zener diode converts the gauge wave potential difference ( $\Delta \phi$ ) across the junction into a measurable voltage variation.
- An amplified circuit using transistors is estimated to provide a gain factor of approximately 6.2 ( $\delta V_{OUT} \approx 6.2 \Delta \phi$ ).
- The paper estimates the potential difference $\Delta \phi$ across a microscopic tunneling junction (width $d \sim 10$ nm to $1$ $\mu$ m) to be in the range of $10^{-7}$ to $10^{-5}$ V, assuming a background gauge wave amplitude derived from ordinary electromagnetic fields.
Correlated Noise: The authors suggest that a "fog" of naturally and artificially generated gauge waves exists. They propose that correlated noise measurements between multiple, well-shielded circuits could serve as a test for the presence of these waves, distinguishing them from uncorrelated thermal noise.

Significance and Claims
The paper claims to provide a consistent theoretical framework linking quantum measurement (collapse) to a specific type of electromagnetic phenomenology (gauge waves) via the Aharonov-Bohm electrodynamics. The significance lies in:

Theoretical Consistency: Offering a description of electromagnetic fields generated by non-conserved quantum currents that remains mathematically consistent, unlike Maxwell theory which would fail in such scenarios.
New Phenomenology: Predicting that gauge waves, previously considered unphysical in Maxwell theory, become physically relevant when interacting with systems exhibiting local charge non-conservation.
Experimental Feasibility: Proposing that these effects are not merely theoretical but could be detected using standard electronic components (diodes and transistors) by looking for specific correlations in circuit noise or direct voltage responses to gauge waves.

The authors maintain a modest tone regarding the nature of their model, acknowledging that the treatment of collapse as an instantaneous step function is an idealized kinematical model. They explicitly state that future work is required to determine if these non-conservation effects persist in more realistic, finite-time, or stochastic reduction schemes. The paper does not claim to have experimentally verified these effects but rather presents a theoretical derivation and a roadmap for experimental testing.