As a continuation of our earlier investigations into electron wave–spin, we analyze the electron spin and its qubit in a cavity by treating the electron as a physical wave obeying the Dirac equation. In this view, a qubit is a current–density configuration whose orientation is fixed by the relative phase, rather than a particle carrying simultaneous “up” and “down” spin states with assigned probabilities. The resulting magnetic–moment density, derived from the current, displays a richer vector distribution and topology than the fixed axial dipole weighted by probability density in the conventional wave–particle model. Both frameworks yield the same total moment of one Bohr magneton and are indistinguishable in uniform external fields, yet their ontological differences predict distinct couplings to structured fields and spin–spin interactions. These contrasts motivate further exploration of dynamical consequences within the wave–entity framework, including Aharonov–Bohm–like responses that provide testable alternatives to conventional wave–particle duality.
As a continuation of our earlier investigations into electron wave–spin, we analyze the electron spin and its qubit in a cavity by treating the electron as a physical wave obeying the Dirac equation. In this view, a qubit is a current–density configuration whose orientation is fixed by the relative phase, rather than a particle carrying simultaneous “up” and “down” spin states with assigned probabilities. The resulting magnetic–moment density, derived from the current, displays a richer vector distribution and topology than the fixed axial dipole weighted by probability density in the conventional wave–particle model. Both frameworks yield the same total moment of one Bohr magneton and are indistinguishable in uniform external fields, yet their ontological differences predict distinct couplings to structured fields and spin–spin interactions. These contrasts motivate further exploration of dynamical consequences within the wave–entity framework, including Aharonov–Bohm–like responses that provide testable alternatives to conventional wave–particle duality.
Abstract As a continuation of our earlier investigations into electron wave–spin, we analyze the electron spin and its qubit in a cavity by treating the electron as a physical wave obeying the Dirac equation. In this view, a qubit is a current–density configuration whose orientation is fixed by the relative phase, rather than a particle carrying simultaneous ‘up’ and ‘down’ spin states with assigned probabilities. The resulting magnetic–moment density, derived from the current, displays a richer vector distribution and topology than the fixed axial dipole weighted by probability density in the conventional wave–particle model. Both frameworks yield the same total moment of one Bohr magneton and are indistinguishable in uniform external fields, yet their ontological differences predict distinct couplings to structured fields and spin–spin interactions. These contrasts motivate further exploration of dynamical consequences within the wave–entity framework, including Aharonov–Bohm–like responses that provide testable alternatives to conventional wave–particle duality.
As a continuation of our earlier investigations into electron wave--spin~\citep{GaoJOPCO22,EntropyEvaSpin2024}, we analyze the electron spin and its qubit in a cavity by treating the electron as a physical wave obeying the Dirac equation. In this view, a qubit is a current--density configuration whose orientation is fixed by the relative phase, rather than a particle carrying simultaneous ``up'' and ``down'' spin states with assigned probabilities. The resulting magnetic--moment density, derived from the current, displays a richer vector distribution and topology than the fixed axial dipole weighted by probability density in the conventional wave--particle model. Both frameworks yield the same total moment of one Bohr magneton and are indistinguishable in uniform external fields, yet their ontological differences predict distinct couplings to structured fields and spin--spin interactions. These contrasts motivate further exploration of dynamical consequences within the wave--entity framework, including Aharonov--Bohm--like responses that provide testable alternatives to conventional wave--particle duality.
This work proposes a wave-entity perspective of the electron spin qubit, treating the electron as a continuous physical wave rather than a point-like particle. In this theoretical framework, each spin qubit corresponds to a distinct current density configuration, offering a resolution to the paradox of a particle appearing to spin both up and down simultaneously. We further predict the existence of a persistent, azimuthally asymmetric magnetic field associated with the wave-spin qubit, an effect not anticipated by the conventional particle-spin model. Notably, the qubit’s relative phase governs the orientation of both the current and the magnetic field, suggesting a mechanism for direct, local interactions between qubits. This phase-dependent coupling could form the basis for inherently parallel quantum computing architectures, in contrast to the sequential operations of gate-based logic. While this framework is grounded in theoretical analysis, it yields testable predictions—particularly regarding the magnetic field structure—that invite experimental verification. By treating the electron wave as the fundamental physical entity, rather than a probabilistic abstraction, we explore the possibility of a quantum model that is deterministic, local, causal, and fully consistent with special relativity.
The spherical model of electron cannot explain Bohr magneton, de Broglie wave, etc. To explain these properties physically, we propose that spin, one core concept of quantum theory, is a reality, and introduce this alternative solely based on experimental findings, Planck’s, Einstein’s, and Dirac’s insights, and follows classical laws, that an electron is an electrical wave with a literal 21 spin (Dirac), i.e., spins two circles in one cycle, both angular momentum are ℏ. Its wavelength is determined by E=hνm0=λm0hc=m0c2 (Plank and Einstein), λ m 0 is the Compton wavelength. As E⃗ ⊥ c⃗ for a transverse wave, it has a net electricity due to the first spin, f(Eq)=21E0(1−cos(2ω0t)), half of its cycle, i.e., the minimal meaningful unit as F = E q , is related with its charge, q = E q ϵ 0 . Moreover, an electron has a ring shape due to the second spin, 2 π R 0 = λ m 0 , λ m 0 is the electron-impact cross section. As ℏ=λm0h2πλm0=m0cR0, it has a quantized classical angular momentum, with a speed of c . The Bohr magneton, μB=2m0qℏ, g -factor is 2. Critically, the full Dirac’s equation of an electron with a constant velocity is mc=ℏ⊥+p⊥+ℏ//+p//, and its electromagnetic properties due to charge are f(Eq)=f(Eq)cc2−v′2+f(Eq)cv′=Enet//+Eq⊥, v′//ℏ⊥ or v′//ℏ//, and v′//Enet. Assuming heavy charged particles have equivalent though shall not identical mechanisms, mathematically this model is equivalent to Special Relativity, and supports ALL its formulas, i.e., v < c , E = m c 2 , direction-insensitive m = γ m 0 and t=γt0; Moreover, the net electricity Enet// and Bohr magneton is orientation-quantized, direction-sensitive and follows Lorentz transformation, leading to Lorentz transformation of length contraction; while following Relativity, magnetism can be defined by f(B)=f(Eq)c2v′, which is not circularly symmetric and self-evidently does not follow Lorentz transformation. The temporospatial averaged magnetic intensity of a current is relativistic, Bˉ=∑f(Eq)c2Δv=2πϵ0c2I=2πμ0I, and μ 0 ϵ 0 c 2 = 1, supporting Maxwell’s equations. Further implications include chirality therefore magnetic spatial quantization, de Broglie wave, etc. The spherical model should be just an observation due to orientation quantization of Enet. We conclude this model of electron may provide one step further to the ultimate Quantum Theory in a nonrelativistic spacetime.
Our study reveals electron spin in a cavity as a stable circulating current density, characterized by a torus topology. This current density circulates concentrically beyond the cavity boundary, illustrating the concept of evanescent wave spin. While the interaction with a uniform magnetic field aligns with established spin-field observations, our analysis of regional contributions deviates from particle-based spin predictions. The integration of charge and spin properties into a single Lorentz covariant entity suggests that the electron wave constitutes the fundamental and deterministic reality of the electron.
This paper systematically reviews the theoretical progression from blackbody radiation to the foundations of quantum computing. Beginning with Planck’s energy quantization and the representation of electromagnetic wave electric field components, the wave-particle duality of photons is analogized to introduce the de Broglie relation between momentum and wave vector for matter waves, leading to the establishment of the matter wave function and the Schrödinger equation as its governing partial differential equation. The consistency between the rigorous solution for a one-dimensional infinitely deep rectangular potential well and the conclusions for a one-dimensional hydrogen atom is demonstrated. Subsequently, within the Dirac notation formalism, the wave function is expressed, and the correspondence between spatial differentiation and momentum is derived, formalizing the momentum operator (often referred to as first quantization). To lay the physical groundwork for manipulating two-qubit states in quantum computing, the potential energy function of an electron’s orbital magnetic moment in an external magnetic field is introduced, starting from the torque and work on a current-carrying rectangular coil. This is extended to the magnetic moment and potential energy of a spinning electron, where the orientation of the magnetic field determines the form of the potential and accordingly selects the three components of the Pauli operators. The properties of quantum gates corresponding to the Pauli operators are then examined for single-qubit states. A two-qubit state, constructed via the coupling of two arbitrary single-qubit states represented in a two-level system or electron spin, is shown to be uniquely expressible as a superposition of four eigen two-qubit states. The paper further investigates joint manipulations of two-qubit states, including evolution under X and Z gates conditioned on high- and low-level states, the representation of control-flow circuits (with the low-level as control), and the formulation of measurement and CNOT gates. Throughout this work, essential mathematical tools—including integration, matrix operations, complex Euler’s formula, and solutions to simple second-order ordinary differential equations—are incorporated to provide a coherent theoretical framework for state representation and gate operations in quantum computing.