Quantised Charge and Magnetic Flux Are Linked by a Single Condition

Cyril Belardinelli, and the University of São Paulo, re-examines the long-standing problem of charge quantization by analysing the behaviour of charged particles near a current-carrying solenoid. Solving the Schrödinger equation for this system reveals a combined quantization condition linking magnetic flux and electric charge, and importantly, demonstrates the Lorentz invariance of magnetic flux as a pseudoscalar. The analysis offers a new perspective on charge quantization and its relationship to fundamental physical symmetries.

Flux and charge quantization unified through Lorentz pseudoscalar behaviour

A simultaneous quantization condition for both magnetic flux and electric charge has been demonstrated, revealing a previously unrecognised link between the two fundamental properties. Prior theoretical modelling often failed to adequately describe this relationship outside of specific superconducting contexts, typically focusing on the Meissner effect and vortex formation within type II superconductors. This new work extends the principle of flux quantization, traditionally observed in these materials, to free space, opening new avenues for understanding charge behaviour and potentially challenging existing assumptions about the origins of quantization. The implications extend beyond condensed matter physics, potentially influencing our understanding of fundamental electromagnetic interactions

By revisiting the motion of a charged particle around a current-carrying solenoid and solving the Schrödinger equation, the analysis confirms magnetic flux behaves as a Lorentz pseudoscalar, a quantity transforming predictably under changes in perspective, and establishes a foundational connection to electric charge quantization. The Schrödinger equation, a cornerstone of quantum mechanics, was employed to describe the particle’s wavefunction within the magnetic field generated by the solenoid. This approach allows for a precise determination of the energy eigenvalues, which are then used to derive the quantization condition. Magnetic flux quantization, typically seen in type II superconductors, now extends to free space, demonstrating a simultaneous quantization condition linking it to electric charge. Solving the Schrödinger equation for a charged particle orbiting a current-carrying solenoid revealed that magnetic flux behaves as a Lorentz pseudoscalar, meaning it transforms predictably under changes in perspective, and directly connects to the quantization of electric charge. This behaviour is crucial, as it suggests a deeper, symmetry-based origin for both phenomena.

The quantity ‘qφ’, charge multiplied by the magnetic flux, must always equal an integer multiple of ‘hc/2’, where h is Planck’s constant and c is the speed of light. This quantization condition implies that the product of charge and magnetic flux is not continuous, but rather exists in discrete steps. Further calculations show magnetic flux remains invariant under Lorentz transformations, mirroring the behaviour of electric charge; both quantities are unaffected by continuous changes in velocity. This invariance establishes magnetic flux as a pseudoscalar, flipping sign under spatial inversion but remaining consistent across inertial frames. The Lorentz invariance is particularly significant, as it reinforces the compatibility of this quantization condition with the principles of special relativity. A pseudoscalar transforms differently than a scalar under parity transformations, indicating a handedness to the magnetic flux that is crucial to its behaviour.

Quantifying charge and flux relationships within a simplified electromagnetic model

A clear link between electric charge and magnetic flux offers a potential pathway towards a more unified understanding of fundamental physical constants. However, the current modelling relies heavily on a specific scenario, a charged particle orbiting a solenoid, and it remains unclear how widely applicable these findings might be to more complex systems. The solenoid’s geometry, while simplifying the mathematical treatment, introduces a degree of artificiality that needs to be addressed in future research. Establishing this connection, even in this constrained context, provides a novel perspective on how these fundamental constants might be linked, potentially offering insights into the fine-structure constant and other dimensionless parameters. The implications for high-energy physics and cosmology, where strong electromagnetic fields and quantized fluxes are prevalent, are particularly intriguing.

This research offers a potential theoretical foundation for understanding why both charge and flux appear in discrete, quantifiable units, a long-standing puzzle in physics. The quantization of electric charge is a fundamental observation, but its underlying cause has remained elusive. Similarly, the quantization of magnetic flux in superconductors is well-established, but its connection to fundamental constants and symmetries has not been fully explored. Further investigation building upon these findings could refine our understanding of electromagnetism, potentially leading to a more complete theory that unifies these seemingly disparate phenomena. A simultaneous relationship between electric charge and magnetic flux has been established, suggesting a fundamental interconnectedness previously unrecognised. Demonstrating magnetic flux behaves as a Lorentz pseudoscalar, a quantity affected by changes in perspective, extends the principle of flux quantization beyond superconductors to encompass free space. This extension is significant because it suggests that the quantization of flux is not merely a consequence of superconductivity, but a more fundamental property of electromagnetic fields.

Consequently, both electric charge and magnetic flux appear as inherently quantized properties, linked by a consistent equation unaffected by continuous changes in motion. This work therefore shifts the focus towards understanding the underlying principles governing this shared quantization, opening questions about its implications for fundamental constants and the symmetries governing the universe. The key number established is Φ0 = hc/2e, where Φ0 represents the magnetic flux quantum. This value, approximately 2.067833848 × 10^-15 Weber, is a fundamental constant in physics and appears in numerous contexts, including the quantum Hall effect and the Josephson effect. Future research could explore the implications of this quantization condition for the development of new technologies, such as highly sensitive magnetic field sensors and quantum computing devices. The precise relationship between charge, flux, Planck’s constant, the speed of light, and the elementary charge suggests a deep connection between electromagnetism and the fundamental constants of nature.

The research established a simultaneous quantization condition linking electric charge and magnetic flux, demonstrating they are inherently quantized properties. This finding suggests a fundamental interconnectedness between these electromagnetic phenomena, extending beyond the established quantization of magnetic flux in superconductors. Researchers solved the Schrödinger equation for a charged particle near a solenoid, revealing this relationship and confirming the Lorentz invariance of magnetic flux. The established value of the magnetic flux quantum, approximately 2.067833848 × 10 -15 Weber, highlights a deep connection between electromagnetism and fundamental constants.