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Transmission of a Single-Photon Through a Polarizing Filter: an Analysis Using Wave-Particle Non-Duality

Nakka Gurappa

Published Jul 1, 2021• 0 citations
OpenAlex

Abstract

The inner-product, $ $, between a state vector, $|\\psi>$ and its dual, $ $ is a solution of the Schrodinger wave equation. Using this analysis, ``questions about what decides whether a photon is to go through or not and how it changes its direction of polarization when it does go through a polarizing filter - a statement by Prof. Dirac - is unambiguously explained.

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The inner-product, , between a state vector, ∣psi>|\\psi>∣psi> and its dual, is a solution of the Schrodinger wave equation. Using this analysis, ``questions about what decides whether a photon is to go through or not and how it changes its direction of polarization when it does go through a polarizing filter - a statement by Prof. Dirac - is unambiguously explained.
A thorough mathematic analysis was conducted to the negative energy solutions to the Dirac equation in a complex plane due to the fact that the solutions are vectors of complex number. An opposite vector with negative energy state was identified when a vector with positive energy state was defined in a complex plane. We concluded that any opposite vectors in a complex plane must have opposite energy state because their vector heads move always in opposite direction. We configured an electron as a small ball with dimetric vectors instead of a structureless mass point. Based on the new electron configuration, we explained the particle wave duality as the feature of electron’s spinvector in motion, explained the reason for the electrons with half spin quantum number. And we concluded that de Broglie’s standing waves theory would be more rational than the interpretation by current quantum theory.
A new 'wave-particle non-dualistic interpretation of quantum mechanics at a single-quantum level' is presented by interpreting the Schrodinger wave function as an 'instantaneous resonant spatial mode' (IRSM) to which a quantum is confined and moves akin to the case of a test particle in the curved space-time of the general theory of relativity. This union of the wave and particle natures into a single entity is termed as non-duality. Using quantum formalism, the IRSM is shown to induce dual-vectors at the boundaries and interacts according to the inner-product. The overall phase associated with the state vector, which never contributes to the inner-product, is related to a particular eigenstate of an observable where the particle resides. This eigenstate becomes the natural outcome during observation of a single-quantum's single event. Observation over a large number of identical quanta, differing only by overall phases, results in the relative frequency of detection which yields Born's rule as a limiting case proving the absence of measurement problem in quantum mechanics. The non-duality not only provides the actual mechanism for the 'wave function collapse' but also statistically becomes equivalent to the Copenhagen interpretation. An explicit derivation for the Born rule using individual quantum events is provided by considering an example of spin-1/2 particles in the Stern-Gerlach experiment. In this regard, a generalized representation for the SU (2) algebra, facilitating the description of single-quantum events, is constructed without any deviations from the quantum formalism.
Based on the Maxwell theory and the principle of charges quantization, we prove that for any definite V , a symmetrical electromagnetic wave beam of minimum energy possesses the basic characters: ∈ = hv , p = h/λ , spin= and duality. They are the good reasons for us to treat the wave beam as a photon. A photon is consisted of ∈ -(energy) packet and ψ -(electromagnetic)wave. ∈ -packet is a circular polarized electromagnetic field wrapped by a cylindrical lateral membrane with ± charge e. They form an extremely stable structure like a “solid particle”. Under the protect of the membrane, no external electromagnetic field can break it or change its inner structure so as the photons can bring the information unchanged from the deep universe for over ten billion years. Photon ( ∈ -packet) of different frequencies V have different radius but same shape with same ratio L/R ≈ 0.04 like a circular coin. The ∈ -packet is floated on and carried by the ψ -(EM) wave to move together. ψ -wave decides and describes the probability behavior of the ∈ -packet (s). Such structure unifies the duality of photons. Analysis of the pair production shows that symmetry will make the particles produced possess spiral structure of mass. The mass density on particles’ cross section satisfy σ = σR (R/r)k.