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International Journal of Physics and Applications

Dualism of newton's elementary particle

Stanislav Ordin

Published Jan 1, 2022• 0 citations
Publisher

Abstract

To describe Light, Newton used a Particle, which, on the one hand, is an element, invariant in space and time, but, on the other hand, whose properties depend on the Color of Light. This dependence of the property of this element is similar to the dependence of the kinetic energy of a material point on speed. But this abstract point does not have the Rest Mass invariant for all speeds. This initial contradiction was simply taken for the specificity of a given particle called a photon, which Einstein linked with the Planck's quantum of energy. Newton's corpuscular theory of light initially encountered difficulties in describing the interference and diffraction of light. But the description of coherent light will raise the question of the size-geometry of this elementary particle. Taking into account the geometry of a photon allows us to really, and not abstractly, show its invariant specificity, which ensures the stitching not only of individual photons into a coherent wave, but also stitching of the corpuscular and wave theory. In this case, the postulated Heisenberg Uncertainty Principle is translated into the mathematical property of the Fourier transform, which determines measurability. Moreover, Newton's Elementary Particle shows how to determine the real specificity of a material particle that has lost its Mass invariance due to its Einstein dependence on velocity and, taking into account the principle of Logarithmic Relativity, allows us to correctly systematize Elementary (Fundamental) Particles.

DOI
10.33545/26647575.2022.v4.i1a.49

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To describe Light, Newton used a Particle, which, on the one hand, is an element, invariant in space and time, but, on the other hand, whose properties depend on the Color of Light. This dependence of the property of this element is similar to the dependence of the kinetic energy of a material point on speed. But this abstract point does not have the Rest Mass invariant for all speeds. This initial contradiction was simply taken for the specificity of a given particle called a photon, which Einstein linked with the Planck's quantum of energy. Newton's corpuscular theory of light initially encountered difficulties in describing the interference and diffraction of light. But the description of coherent light will raise the question of the size-geometry of this elementary particle. Taking into account the geometry of a photon allows us to really, and not abstractly, show its invariant specificity, which ensures the stitching not only of individual photons into a coherent wave, but also stitching of the corpuscular and wave theory. In this case, the postulated Heisenberg Uncertainty Principle is translated into the mathematical property of the Fourier transform, which determines measurability. Moreover, Newton's Elementary Particle shows how to determine the real specificity of a material particle that has lost its Mass invariance due to its Einstein dependence on velocity and, taking into account the principle of Logarithmic Relativity, allows us to correctly systematize Elementary (Fundamental) Particles.
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Modern attempts to understand light go back to Newton who considered light to be particles, the so called corpuscular theory, and the other school of Huygens, Young and others. Huygens and Young viewpoint emphasised the wave property. This difference of opinions persisted for close to two centuries till Maxwell theory solidly established light as a wave phenomenon associated with Electromagnetism. A serious schism so to speak was introduced into the theory of light with the understanding of "Light gas", the so called Black Body radiation. Einstein's photon hypothesis and Bose's successful derivation of the Planck spectrum put the corpuscular theory back in place, while classical description continues to be used as well. One may then wonder if this being a classical limit may have to be corrected when dealing with quantum phenomena. To most people's surprise, the classical description was in fact a subset of the full quantum description, and the classical states of light could be shown to be subsumed within the fully quantum description without having to take the limit of Planck's constant h going to zero. This was the resolution provided by E. C. G. Sudarshan's Diagonal representation as the most general formalism for dealing with light.
It is well known that the mass of a particle has properties different from Newtonian mechanics. First, it is speed-dependent. Second, it is convertible to energy. These properties were generally thought to be derived from the principle of relativity (PR). We have conducted a careful examination of the historical records and found that the non-Newtonian properties of mass were derived not so much based on PR, but more based on Einstein’s intuitive thinking that radiation and matters behave similarly. This gives us a hint: Since both photon and electron can behave as a particle as well as a wave, can such a wave nature account for the deviations from Newtonian mechanics? Thus, we have developed a wave model to describe the motion of a free particle with or without rest mass. We found that both the speed-dependence of mass and the mass-energy equivalence can indeed be derived based on the wave properties of a particle. This wave hypothesis has several advantages; it can naturally explain why particles can be created in the vacuum and why a particle cannot travel faster than the speed of light.
The erroneous prediction of the speed of light in dispersive media has been looked upon historically as unequivocal proof that Newton's corpuscular theory is incorrect. Examination of his arguments shows that they were only directly applicable to the momentum of photons, however, leaving open the possibility that the cause of his mistake was the unavailability of a suitable mechanical theory to enable a correct light speed prediction, rather than his use of a particle model. It is shown that Hamilton's canonical equations of motion remove Newton's error quantitatively, and also lead to the most basic formulas of quantum mechanics without reference to any of the pioneering experiments of the late nineteenth century. An alternative formulation of the wave-particle duality principle is then suggested which allows the phenomena of interference and diffraction to be understood in terms of statistical distributions of large populations of photons or other particles.
Newtonian mechanics (from the 1600s) defines a quantity called momentum p in terms of mv where m is mass and v=dx/dt with dx and dt tending to zero. Newton’s first law is equivalent to conservation of momentum in the absence of a force. The second demonstrates how p changes under a force. If one has equal action/reaction then overall momentum is conserved. As a consequence the idea of a “wave” associated with p does not arise. The main focus is on the idea of force. Fermat’s Least Time Principle for light (1600s), however, is based on minimizing the overall time traveled by light which reflects or refracts. Young’s interference experiments did not occur until the very early 1800s and Newton considered light to be a particle at this time. In fact light bounces off a foil creating an impact like a particle. Fermat’s principle does not directly make use of momentum or its conservation. It is focused on minimizing time. To do so, however, one must take a derivative with respect to a certain variable and set it equal to 0. This variable is the spatially invariant one in a problem. For example consider reflection (stationary or moving mirror) or refraction in two dimensions x,y. Let the mirror or medium face lie along the x axis at y=0. There exists a constraint on y and given a fixed starting point one cannot change y. This leaves x to be varied because it is invariant. Thus the extremization of time is really a statement of invariance of a spatial variable. In other words, Fermat’s principle is linked to the physical variables t and x while Newton’s focuses on p (momentum). This invariance in turn gives rise to conservation of momentum in the direction of the invariant variable i.e. (px). There is still the idea of Newton’s change in momentum as (py) abruptly changes in refraction as it hits the interface of media. The point we wish to make is that from Fermat’s least time principle one sees that conservation of momentum in the absence of a force is completely intertwined with invariance in space. The two cannot be separated in this approach and there is nothing unphysical about t or x. In fact, one may create a function A= -Et + (px)x + (py)y such that dA/dx partial = px = conserved quantity. In this function (px) and x are on the same footing. One does not have one without the other. This idea is carried over into special relativity as -Et+p dot r is a Lorentz invariant. Given that p momentum is physical (it manifests itself in impulse hits) and p and x are inseparable in (px)x we suggest there should exist a physical manifestation in x i.e. in space linked to the maintenance of conservation of momentum in this direction even in the absence of a force. This we argue leads to the physical idea of a wavelength which follows from A=-Et+px with A=0 in all constant velocity frames leading to a frequency proportional to 1/E and wavelength to 1/p. We have discussed these ideas in previous notes, but the main point we wish to make here is that equivalence of spatial invariance in the x direction in Fermat’s principle with conservation of momentum in the same direction suggests that if p is physical, the spatial invariance must also be manifested physically. It is not simply a mathematical convenience to link t to x to px, we argue. Furthermore this wavelength should be linked to establishing conservation of momentum as it does in quantum mechanics where the orthogonality of exp(ipx) i.e. Integral exp(-i p1 x) exp(ip x) dx automatically ensures p1=p without imposing momentum conservation a priori as in Newton’s first law. Both Newtonian mechanics and Fermat’s principle suggest that p may change abruptly due to a force or an immediate change in medium. The idea of a physical wavelength, however, suggests there may be interactions completely different from an abrupt change in p due to an impulse. In particular there may be interference or Bohm-Aharonov interactions. Newtonian Mechanics
The erroneous prediction of the speed of light in dispersive media has been looked upon historically as unequivocal proof that Newton's corpuscular theory is incorrect. Examination of his arguments shows that they were only directly applicable to the momentum of photons, however, leaving open the possibility that the cause of his mistake was the unavailability of a suitable mechanical theory to enable a correct light speed prediction, rather than his use of a particle model. It is shown that Hamilton's canonical equations of motion remove Newton's error quantitatively, and also lead to the most basic formulas of quantum mechanics without reference to any of the pioneering experiments of the late nineteenth century. An alternative formulation of the wave-particle duality principle is then suggested which allows the phenomena of interference and diffraction to be understood in terms of statistical distributions of large populations of photons or other particles.