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ACTA PHOTONICA SINICA

Conditional Probability Statistical Distributions in Variant Measurement Simulations

Jeffrey Zheng

Published Jan 1, 2011• 5 citations
Publisher

Abstract

Two quantum interactive experiments are shown in strong wave-like interference properties,ie Young double slit experiment and very lower intensive and very long time explosin experiment for quanta.This paper is based on a classical statistic scheme: Bayes statistics on Conditional Probability to propose conditional probability measurements and relevant statistcal models to visualized complex properties of their interactions.Variant measurement simulation model is established and corresponding measring equations and perameters are formulated.Two typical cases are selected and each time has corresponding to four groups of results in 16 histograms.Under this construction,it is feasible to understand the intrinsic wave-like properties of quantum interactions.Under the conditional probability model,intrinsic wave-like statistical distributions are observed on both normal conditions and interferenced conditions in their spatial statistical distributions respectively.

DOI
10.3788/gzxb20114011.1662

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Two quantum interactive experiments are shown in strong wave-like interference properties,ie Young double slit experiment and very lower intensive and very long time explosin experiment for quanta.This paper is based on a classical statistic scheme: Bayes statistics on Conditional Probability to propose conditional probability measurements and relevant statistcal models to visualized complex properties of their interactions.Variant measurement simulation model is established and corresponding measring equations and perameters are formulated.Two typical cases are selected and each time has corresponding to four groups of results in 16 histograms.Under this construction,it is feasible to understand the intrinsic wave-like properties of quantum interactions.Under the conditional probability model,intrinsic wave-like statistical distributions are observed on both normal conditions and interferenced conditions in their spatial statistical distributions respectively.
Using measure model and statistical approches to simulate quantum interaction on binary level systems,multiple interactive conditions are simulated via double path interference measures.From quantum interaction,Einstein,Mach-Zehnder,Stern-Gerlach and CHSH measuring parameters are investigated.Using multiple variable logic functions and variant principle,N bit vectors of 0-1 input/output pairs form variant quaternion to establish variant double path simulation model.Using probability,symmetry/anti-symmetry,sychronous/asychronous conditions,simulation system generates two groups of eight histograms to express their statistical distributions in relevant conditions.
We demonstrate how the interference effects for a quantum particle in the double-slit experiment can be described by classical probabilities. We investigate a classical field theory for a complex scalar field with probabilistic initial conditions. A central element are conserved charges leading to the concept of particles. These are statistical observables which describe properties of the probability distribution for field configurations. The conserved charges define subsystems for particle excitations of a vacuum state. The classical probability distribution for the one-particle subsystem can be expressed in terms of a complex wave function. The Liouville equation for the classical probability distribution implies that the time evolution of this wave function obeys the Schrödinger equation for a quantum particle in a potential. The potential arises from space-dependent external fields in the otherwise relativistic classical field theory. It can be chosen arbitrarily, realizing the typical quantum effects of interference, tunneling or discrete energy spectra.
Double slit experiments play a key role in Quantum Theory in distinct particle and wave interactions according to Feynman. In this paper, double path models together with variant logic principles are applied to establish a simulation system enabling the exhaustive testing of given targets. Using Einstein quanta interaction, different quaternion measures are investigated. Under conditions of Symmetry / Anti-symmetry and Synchronous / Asynchronous interaction, eight groups of statistical results are generated and presented as eight histograms showing the distributions. From this set of simulation results, it can be seen that not only is the synchronous condition the key factor in generating quantum wave interference patterns but also that the asynchronous condition is the key factor in classical particle distributions. Sample results are illustrated and explanations are discussed.
Quantum measures play a key role in quantum interactions. In this paper, a variant simulation system – a variant double path model – is proposed that uses multiple variable logic functions and variant principle schemes applied to input/output relationships as a variant quaternion. Under this mechanism, a two-state system of quantum interactions can be simulated by the variant double path model. Visual distributions can be expressed by their probability, synchronous/asynchronous, and symmetry/anti-symmetry statistical properties. The simulation system can output eight histograms with different symmetric properties. Sample results are illustrated by two groups of 16 histograms for their intrinsic distributions. Critical evidence from Afshar's experiments is discussed. This particle model is fully capable of simulating double path experiments in systematic methodologies.
Quantum interference is traditionally interpreted as evidence of intrinsic wave–particle duality, invoking self-interference and wavefunction superposition. Here, we propose an alternative causal framework in which interference arises from interactions between a classical electron and a quantized electromagnetic field. In this picture, electrons follow definite, localized trajectories and produce discrete detection events, while the observed interference pattern emerges statistically from stochastic, nonlocal momentum transfers mediated by quantized field modes. Numerical simulations of the double-slit experiment show that dot-like interference fringes arise without invoking wavefunction collapse or intrinsic matter waves. Doubling the electron mass narrows the fringe spacing in agreement with de Broglie scaling, indicating that the effective wavelength emerges dynamically from particle–field coupling rather than representing an inherent property of the particle. The formulation is based on a rigorously defined Hamiltonian and derived equations describing electromagnetic coupling between particles and the slit environment. Although neutral particles such as neutrons or atoms carry no net charge monopoles, they possess electric or magnetic dipole and higher multipole moments that enable electromagnetic interactions with the slit apparatus, allowing discrete momentum transfer through the quantized field. Our simulations show that interference fringes arise from intermittent singleparticle detection events caused by stochastic momentum impulses from quantized electromagnetic modes. These results suggest a reinterpretation of wave–particle duality: the apparent wave-like behavior of matter may arise from interaction with the inherently wave-like quantized electromagnetic field—whose quanta are photons, the massless U(1)-gauge bosons—rather than from an intrinsic wave nature of the particles themselves. Our analysis is rigorous and is not speculative, because the proposed Hamiltonian for this system is physical. Within this nonlocal hidden-variable framework, the dot-like interference pattern observed in the double-slit experiment emerges from individual electrons traversing one slit at a time while receiving discrete momentum impulses from stochastic, spatially extended quantized electromagnetic fields.
In the experiments considered here, we measure the y-component of momentum for a particle passing through a system of slits. The source-slit system is the preparation apparatus that determines the state vector. Recognizing that a system of slits is a position-measuring device allows us to ascertain that the state vector is a position state. Then, writing the state vector in momentum space provides a straightforward calculation for the probability amplitude and its corresponding probability function. Interference effects, if any, are inherent in the probability function We determine the statistical distribution of scattered particles for four different slit systems. The results are in agreement with the well-known interference patterns obtained in classical wave optics.