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arXiv:1001.4647

A Novel Concept for Mass as Complex-Mass towards Wave-particle Duality

R. C. Gupta, Anirudh Pradhan, Sushant Gupta

Published Jan 26, 2010• 1 citation
arXivHTMLPDF

Abstract

In the present paper a new concept is introduced that: `mass is a complex quantity'. The concept of complex-mass suggests that the total mass M of a moving body is complex sum of: (i) the real-part (grain or rest) mass $m_{g}$ establishing its particle behaviour and (ii) the imaginary-part mass $m_{p}$ governing its wave properties. Mathematically, the complex mass $M = m_{g} + im_{p}$; the magnitude $\mid M \mid = (m_{g}^{2} + m_{p}^{2})^{1/2}. The theory proposed here explains successfully several effects such as `Compton effect' and `refraction of light' which could not be explained otherwise by a single theory of wave or particle. Also explained are `Doppler effect for light', `photo-electric effect', `Uncertainty principle', `Relativity' and `supersymmetry'

DOI
10.48550/arxiv.1001.4647

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In the present paper a new concept is introduced that: mass is a complex quantity'. The concept of complex-mass suggests that the total mass M of a moving body is complex sum of: (i) the real-part (grain or rest) mass $m_{g}$ establishing its particle behaviour and (ii) the imaginary-part mass $m_{p}$ governing its wave properties. Mathematically, the complex mass $M = m_{g} + im_{p}$; the magnitude $\mid M \mid = (m_{g}^{2} + m_{p}^{2})^{1/2}. The theory proposed here explains successfully several effects such as Compton effect' and refraction of light' which could not be explained otherwise by a single theory of wave or particle. Also explained are Doppler effect for light', photo-electric effect', Uncertainty principle', Relativity' and supersymmetry'
Within the framework of quantum mechanics, the wave function squared describes the probability density of particles. In this article, another description of the wave function is given which embeds quantum mechanics into the traditional fields of physics, thus making new interpretations dispensable. The new concept is based on the idea that each microscopic particle with non-vanishing rest mass is accompanied by a matter wave, which is formed by adjusting the phases of the vacuum fluctuations in the vicinity of the vibrating particle. The vibrations of the particle and wave are phase-coupled. Particles move on continuous approximately classical trajectories. By the phase coupling mechanism, the particle transfers the information on its kinematics and thus also on the external potential to the wave. The space dependence of the escorting wave turns out to be equal to the wave function. The new concept fundamentally differs from the pilot wave concept of Bohmian mechanics.
In the wave-particle duality, a free particle can be considered as a wave packet. Is there a wave property that corresponds to the rest mass of the particle? This is an interesting question that has not been extensively explored before. We suggest that this problem may be approached by treating the rest mass on the same footing as energy and momentum. Here we demonstrate that, by assuming that the matter wave of a particle behaves like a photon, one could derive the mass-energy relation from the solution of a simplified wave equation. This solution suggests that the rest mass of a particle is associated with a "transverse wave number", which characterizes the radial variation of the wave function in the transverse plane. This finding has several appealing features. For example, it shows a consistent geometrical relationship between mass, energy and momentum in both the wave and particle perspectives. Also, it predicts that a massless particle must travel at the constant speed of light. Furthermore, from a philosophical point of view, this model suggests that the mass-energy relation attributed to the special theory of relativity may have a root in the wave-particle duality. Indeed, it is shown that the Klein-Gordon equation can be derived naturally based on this model.
The equation of motion for a particle moving in complex space is obtained and then solved. The interaction between the real and imaginary components of motion can produce what can be regarded as a wave motion in real space. The formation of interference patterns and polarization of a matter wave can be accounted for by the particle’s motion in complex space. The deterministic particle view of a free particle can then be reconciled with its dual probabilistic wave picture but the formulation is entirely in complex space.
A satisfactory explanation of the confounding wave-particle duality of matter is presented in terms of the reality of the wave nature of a particle. In this view, a quantum particle is an objectively real wave packet consisting of irregular disturbances of underlying quantum fields. It travels holistically as a unit and thereby acts as a particle. Only the totality of the entire wave packet at any instance embodies all the conserved quantities, for example the energy-momentum, rest mass, and charge of the particle, and as such must be acquired all at once during detection. On this basis, many of the bizarre behaviors observed in the quantum domain, such as wave function collapse, the limitation of prediction to only a probability rather than an actuality, the apparent simultaneous existence of a particle in more than one place, and the inherent uncertainty can be reasonably comprehended. The necessity of acquiring the wave function in its entirety for detection, as evinced by the appearance of collapse of the wave function, supports the paradigm of reality of the wave function described here. Quanta 2016; 5: 93–100.
A study was carried out to explain a wave propagation of the relativistic energy that comes in the squared form. What looks physically incompatible concept of wave and particle was combined into a general wave of the complex energy. From the fact that the energy of matter is expressed by the squared form, a wave of the massless and massive energies was presented, which plays a role in the formation of matter wave. This study revealed that the energy is separated into the complex value with a imaginary mass that makes the wave different from the plane wave. The wave propagation is described by plugging the complex energy into the wavefunction, in which a modified mass-energy equivalence from the special relativity was used. From the fact that the energy of matter is consist of a complex value, it is also explained that the space around a rest-mass is a space with a imaginary mass. As a result, a general expression of matter and wave is described by the complex wave including an imaginary mass and a real momentum, by which a reasonable explanation is given for the radiation of mass energy, and explains the role of imaginary mass in the propagation of energy.
The real and imaginary parts of the complex can well reflect the contradictions of unity of opposites and transformed into each other. The real part of the complex physical quantity reflects the nonlinear and non-superposition characteristics of the particle, the imaginary part reflects the fluctuation characteristics of material linear and superposition. The real part of the complex energy form the macroscopic Einstein mass energy equation, the imaginary part of the complex energy form Planck energy equation. Bosons and fermions are the same substance in different motion state in time and space. The peak of the matter wave form boson state typical; intersection of matter wave and the space formed fermions typical U (20) superunified group covers four kinds of forces.