The bicomplex extension of quantum mechanics introduces an ideal sector J1 whose phases are algebraically coupled to the complex sector C1 via the algebraic identity e^(iα)*k*e^(jβ) = k*e^j(α+β). In an earlier work, a double-slit test proposal for a possible physical realization of this phase coupling was formulated, which contained a calculation error. The present work refines this proposal and presents the corrected theoretical interpretation. The starting point is a bicomplex state Y = S + R, where S represents the complex component and R the ideal component, which is phenomenologically associated with a monochromatic laser source. In a nonlinear, frequency-doubling crystal, the state is phenomenologically mapped to Y^2 = S^2 + 2SR + R^2. The component S^2 lies in the complex sector, while the mixing term SR according to the above equation lies in the ideal sector and carries phase information transferred by the algebraic phase coupling. For a measurement at a detector or screen, this ideal mixing term must be transferred into a complex measurable channel with an effective coupling strength ηeff . This detector coupling is a phenomenological assumption and does not follow from the algebra alone. The mathematical evaluation of the double-slit interference, taking into account the given field structure (superposition of two slit contributions, cosine profile), shows that within the used Fraunhofer effective model the principal maxima follow the classical geometric shift to first approximation. An effectively coupled SR term at the detector primarily generates contrast and brightness modulations of the interference pattern. The double slit is interesting as a spatial structure test because a brightness modulation of the interference fringes depending on the position of the source is at least surprising.
The bicomplex extension of quantum mechanics introduces an ideal sector J1 whose phases are algebraically coupled to the complex sector C1 via the algebraic identity e^(iα)ke^(jβ) = k*e^j(α+β). In an earlier work, a double-slit test proposal for a possible physical realization of this phase coupling was formulated, which contained a calculation error. The present work refines this proposal and presents the corrected theoretical interpretation. The starting point is a bicomplex state Y = S + R, where S represents the complex component and R the ideal component, which is phenomenologically associated with a monochromatic laser source. In a nonlinear, frequency-doubling crystal, the state is phenomenologically mapped to Y^2 = S^2 + 2SR + R^2. The component S^2 lies in the complex sector, while the mixing term SR according to the above equation lies in the ideal sector and carries phase information transferred by the algebraic phase coupling. For a measurement at a detector or screen, this ideal mixing term must be transferred into a complex measurable channel with an effective coupling strength ηeff . This detector coupling is a phenomenological assumption and does not follow from the algebra alone. The mathematical evaluation of the double-slit interference, taking into account the given field structure (superposition of two slit contributions, cosine profile), shows that within the used Fraunhofer effective model the principal maxima follow the classical geometric shift to first approximation. An effectively coupled SR term at the detector primarily generates contrast and brightness modulations of the interference pattern. The double slit is interesting as a spatial structure test because a brightness modulation of the interference fringes depending on the position of the source is at least surprising.
The bicomplex algebra B = C ⊗R C has recently been identified as a minimal commutative and associative extension of the complex scalar algebra underlying quantum mechanics. This structure contains a proper ideal J ∼= C that admits a complex-like exponential representation and leads to an additive phase relation between the complex and ideal sectors. The present work explores the consequences of this algebraic phase coupling under the hypothesis that it may become physically effective in suitable experimental conditions. In particular, we consider an optical setup involving a nonlinear medium, where mixed terms between complex and ideal components may arise. Within this framework, a specific, testable prediction is derived: a lateral displacement of the source in a double-slit experiment could lead to an amplified fringe shift, whose magnitude depends on the geometric parameters of the setup. The predicted scaling differs significantly from the standard geometric expectation of conventional wave optics. The analysis is explicitly conditional on the assumed physical realization of the bicomplex phase coupling. The proposed experiment therefore provides a direct way to test whether the additional algebraic structure has observable consequences or remains purely formal.
This manuscript presents a deterministic boundary-phase model of the double-slit experiment. In this framework, particles follow continuous, definite trajectories while interference arises from structured curvature induced by slit boundary microstructure. The wavefunction is treated as a mathematical representation of a real boundary-generated field rather than a physical matter wave.The model preserves established interference results while introducing a falsifiable experimental prediction: coherent fringe displacement scaling with engineered slit roughness. For a baseline electron configuration (100 eV beam energy, 1 m screen distance, 1 µm slit separation), a measurable 2 µm fringe shift requires a relative phase offset of approximately 0.10 radians, corresponding to the coupling condition β_eff(δ/r) ≈ 0.10.A quantitative δ-sweep prediction is provided along with explicit experimental control requirements necessary to distinguish coherent boundary-phase displacement from conventional scattering or electrostatic effects. If the predicted scaling is observed under controlled conditions, the double-slit paradox can be resolved deterministically without invoking intrinsic randomness or wavefunction collapse.This work is presented as a falsifiable experimental proposal in quantum foundations and electron interferometry.
Abstract The double slit test, as it is known, results in a series of alternating streaks of light and dark, presumed to be caused by interfering light waves. Careful comparison of experimental results and mathematical models reveals that the plausible theory of light-wave interference contains many fatal flaws. For example, the mathematical model does not have a mechanism for regularly producing multiple dark streaks. In practice, the spot where the dark streaks should appear is the brightest spot. Since only the electron radiates photons outward as it lowers its energy and returns to its ground state, the photon waves generated in the slit (possibly a vacuum) are of unknown origin. When light waves interfere with each other, photons can be infinitely subdivided and multiplied; After the head of the photon reaches the screen, the rest of the photon can still participate in interference; The effects of reflected light waves that most satisfy the interference conditions are not shown in the fringe. The important influence of polarization direction is not considered in the interference condition. In the causality test, the photon that has collapsed into a particle should be retested with a double slit test. In the causality test, the photon that has collapsed into a particle should be retested with a double slit test. The phenomenon of "observation determines outcome" has also been observed. When the phase is shifted π or the signal is reversed, it becomes a negative wave that cancels itself out. The transmittance of light waves through a double-slit device should not be so weak. As a fundamental physical property, waves must have bandwidth, but light and quantum only have a single frequency, which does not conform to the Fourier transform principle that waves must follow. Light waves in optical fiber communication must produce modulation effect, which has not been shown in reality. If the light waves from different slits interfere with each other, a mask similar to a two-slit device will not allow the lithographer to work properly. A photon whose size is much smaller than the wave length does not represent the whole wave but only represents a sample of the wave, but the corresponding physical properties are not shown. A pair of stars orbiting each other without changing color only proves that redshift is impossible but not that the speed of light is constant. Due to the late birth of radio technology, many physical properties of electromagnetic waves were not included in the light and matter waves proposed earlier. The results of the double slit test only prove that the simple quantum particle model is incorrect but do not provide evidence that the wave model is correct.
Abstract The double slit test, as it is known, results in a series of alternating streaks of light and dark, presumed to be caused by interfering light waves. Careful comparison of experimental results and mathematical models reveals that the plausible theory of light-wave interference contains many fatal flaws. For example, the mathematical model does not have a mechanism for regularly producing multiple dark streaks. In practice, the spot where the dark streaks should appear is the brightest spot. Since only the electron radiates photons outward as it lowers its energy and returns to its ground state, the photon waves generated in the slit (possibly a vacuum) are of unknown origin. When light waves interfere with each other, photons can be infinitely subdivided and multiplied; After the head of the photon reaches the screen, the rest of the photon can still participate in interference; The effects of reflected light waves that most satisfy the interference conditions are not shown in the fringe. The important influence of polarization direction is not considered in the interference condition. In the causality test, the photon that has collapsed into a particle should be retested with a double slit test. In the causality test, the photon that has collapsed into a particle should be retested with a double slit test. The phenomenon of "observation determines outcome" has also been observed. When the phase is shifted π or the signal is reversed, it becomes a negative wave that cancels itself out. The transmittance of light waves through a double-slit device should not be so weak. As a fundamental physical property, waves must have bandwidth, but light and quantum only have a single frequency, which does not conform to the Fourier transform principle that waves must follow. Light waves in optical fiber communication must produce modulation effect, which has not been shown in reality. If the light waves from different slits interfere with each other, a mask similar to a two-slit device will not allow the lithographer to work properly. A photon whose size is much smaller than the wave length does not represent the whole wave but only represents a sample of the wave, but the corresponding physical properties are not shown. A pair of stars orbiting each other without changing color only proves that redshift is impossible but not that the speed of light is constant. Due to the late birth of radio technology, many physical properties of electromagnetic waves were not included in the light and matter waves proposed earlier. The results of the double slit test only prove that the simple quantum particle model is incorrect but do not provide evidence that the wave model is correct.
The double-slit experiment is commonly interpreted as evidence that a single electron must be described by a spatially extended wavefunction whose path amplitudes interfere. Here, we present an alternative geometric formulation within the Bivector Standard Model, in which the observed far-field interference pattern is reproduced while the phase is attributed to an internal bivector clock carried by the electron. In this approach, each electron remains localized and produces a single detection event, while the familiar fringe pattern emerges statistically from the accumulation of many impacts. Interference arises from the comparison of clock phases associated with geometrically distinct paths, rather than from the superposition of spatial waves. The resulting probability distribution recovers the standard two-slit interference factor, the single-slit diffraction envelope, and the usual fringe-spacing relation in the Fraunhofer regime. The de Broglie wavelength emerges as the spatial manifestation of this transported phase. This formulation provides a geometric account of the origin of phase in single-electron interference, consistent with standard results while offering a distinct physical interpretation.
We propose a mathematical model for the double-slit experiment based on the block-alternating infinite products A(K,d) and B(K,d). The two products play strictly separated roles: B(K,d) encodes the background Minkowski spacetime (the stage), invariant under observation, while A(K,d) encodes the propagating matter wave (the actor), whose coherence parameter d acts as a phase switch. The coherence parameter d=1 corresponds to alternating phase (AC structure, full interference), while d=1/2 and d=infinity are algebraically identical and correspond to constant phase (DC structure, no interference). Observation---defined as physical interaction with a detector that makes path information available---transitions the observed path from d=1 to d=1/2. Unobserved paths remain at d=1 and continue to interfere. At the screen (K=1/2, the null boundary), A(1/2,d)=1 for all d, equalising the amplitudes. The interference pattern is then determined by d alone, yielding |psi|^2 = 4cos^2(pi*Delta/2) (unobserved) or |psi|^2 = 2 (observed). Combined with the envelope W[B] proportional to sinc^2(beta) arising from the Minkowski structure of B, the standard formula I proportional to sinc^2(beta)*cos^2(pi*Delta/2) is recovered as a mathematical consequence. The measurement problem is resolved algebraically: decoherence is not a collapse of the wave envelope but a transition of the phase parameter d within the A structure. The spacetime stage B is unaffected by the act of measurement.