With the deep research of measurement for microscopic or nanometer level scale at present the concept of Critical Dimension(CD) is pointed out in many papers[1,4,], they always include some analyses of measuring uncertainty for current technology of measurement, but our new idea or definition for geometrical action scale (GAS) is the limited scale or uncertainty of measurement in microscope that we can approach to for the most advanced method, technology, set-up or instrument, for example: The modern interferometer, SPM[5] and other various scattering experiments using the beam of microscopic particles. It would be found that the research included fundamentals for microscopic particle geometric scale is not easy to explore, some reasons perhaps are affected by which the classical quantum mechanics study of matter usually start from energy or energy level not from geometrical scale and by the Heisenberg relation of measuring uncertainty. Our work just wants to research on these fundamentals in physics for microscopic particles geometric scale. At first, a new physical quantity relative to microscopic particle geometric scale is directly suggested in this paper, it also may be deduced from the completeness of units system or dimension system refer to optics principles or quantum optics principles. We find that the wavelength of Louis de Broglie matter wave is either the length dimension or relative to the geometric scale of microscopic particles, and we define it as the geometrical action scale (GAS) of microscopic particles. The significance of the geometrical scale of microscopic particles or GAS in physics is discussed.
With the deep research of measurement for microscopic or nanometer level scale at present the concept of Critical Dimension(CD) is pointed out in many papers[1,4,], they always include some analyses of measuring uncertainty for current technology of measurement, but our new idea or definition for geometrical action scale (GAS) is the limited scale or uncertainty of measurement in microscope that we can approach to for the most advanced method, technology, set-up or instrument, for example: The modern interferometer, SPM[5] and other various scattering experiments using the beam of microscopic particles. It would be found that the research included fundamentals for microscopic particle geometric scale is not easy to explore, some reasons perhaps are affected by which the classical quantum mechanics study of matter usually start from energy or energy level not from geometrical scale and by the Heisenberg relation of measuring uncertainty. Our work just wants to research on these fundamentals in physics for microscopic particles geometric scale. At first, a new physical quantity relative to microscopic particle geometric scale is directly suggested in this paper, it also may be deduced from the completeness of units system or dimension system refer to optics principles or quantum optics principles. We find that the wavelength of Louis de Broglie matter wave is either the length dimension or relative to the geometric scale of microscopic particles, and we define it as the geometrical action scale (GAS) of microscopic particles. The significance of the geometrical scale of microscopic particles or GAS in physics is discussed.
The principle of uncertainty is one of the essential principles of quantum mechanics as it outlines that there is a reflective limit to the measurement of microscopic particle motion. However it is impossible to measure at once and accurately both the position and momentum data of any microscopic particle no matter what means are used to do so. This paper starts by discussing the notion and mathematical derivation of the uncertainty principle as put forth by Heisenberg explaining the physical relevance of the principle. It introduces the natural uncertainty the principle introduces to the dynamics of particles in the microscopic world, and the significant part it plays in the theory of quantum mechanics. The article overviews the explanations of the principle on phenomena including atomic stability and scanning tunneling microscopes, and the interference of measurement actions on the states of particles and the shortcomings of measurement precision. According to the wave-particle duality of quantum mechanics, this article gives a required theoretical basis of microscopic phenomena. Likewise, the use of the research theory on the uncertainty principle by distinguished scholars in the physics fraternity helps the readers in achieving the knowledge in related subjects more easily.
The proposed geometric model is not a return to 19th-century classical mechanics, but rather builds on the latest trends in Planck-scale deterministic cellular automata ('t Hooft, 2021), the theory of internal quantum clocks (Donadi, 2023), and the nonlinear quantum dynamics of asymmetric rotors (Micheli and Stone, 2022). The model directly resolves the topological crisis of describing light nuclei as saturated manifolds, documented in the current literature (Manton, 2022; Lau, 2020). We derive a direct, non-linear relation between the internal phase time per radian , the macroscopically observable coordinate time , and the relative energy fluctuation . Through rigorous differentiation and integration of these phase relations, we demonstrate that for topologically synchronized systems, the product of energy and observable time constitutes a strict dynamic process invariant: . Moving beyond phenomenological interpretations, we deduce the classical Heisenberg uncertainty relation without invoking independent quantum postulates, showing it to be a special boundary limit governing a single elementary phase cycle () under critical fluctuation. Furthermore, we prove that Louis de Broglie’s matter wave equation () is not an independent axiom but emerges naturally as the spatial displacement executed by a localized particle during a single complete internal chronal rotation. Finally, we bridge the gap between microscopic quantum reversibility and the macroscopic thermodynamic arrow of time by analyzing the dynamics of synchronization breakdown and phase slippage () using the latest advancements in deterministic quantum mechanics.
This chapter describes the dual nature of electron/de Broglie waves. de Broglie suggested that like light, an electron also behaves as both a particle and a wave. Based on this hypothesis, a relationship between wavelength of electrons (a particle) and momentum was developed. It opines that ‘wavelength of the particle is inversely proportional to momentum’. This is called the de Broglie relation. On the basis of the above facts, we have developed a relationship between wavelength and voltage applied and this relation may be stated as ‘the wavelength of a particle is inversely proportional to the square root of the voltage applied to the system’. This chapter also uses the Davisson and Germer experiment to show the wave nature of the particle, i.e., diffraction of electrons by crystal lattice. The experimental results were the same as found in the case of the diffraction of X-ray by crystals. This chapter also provides an idea on quantisation of angular momentum. It also discusses Heisenberg’s uncertainty principle, phase velocity, group velocity, and uncertainty relation between energy and time. The chapter comprises the experimental evidence of Heisenberg’s uncertainty principle, such as by diffraction of electrons through a slit and gamma ray microscope thought experiment, which is shows the physical significance of the uncertainty principle. Sufficient references, solved problems, and questions on concepts have been provided at the end of chapter.
Quantum mechanics describes physical systems through probabilistic wave functions, accounting for phenomena such as wave–particle duality and the uncertainty principle. Although the mathematical formalism of quantum mechanics is well established, conceptual understanding of how quantum entities transition between wave-like and particle-like behavior remains an active area of research. In this work, quantum mechanical principles are re-examined from an interaction-based perspective, emphasizing the roles of environmental coupling, measurement geometry, and energy exchange. Using the photoelectric effect, de Broglie relations, and Heisenberg’s uncertainty principle as foundational elements, a conceptual framework is proposed in which particle identity emerges dynamically from wave interaction with matter and measurement constraints. This interpretation provides an intuitive bridge between classical reasoning and quantum behavior while fully preserving the standard mathematical structure of quantum mechanics...........Please check the attachment for details
The Wave-Particle Duality is a basic property of microscopic particles. As a basic concept of quantum mechanics, the wave-particle duality theory from elementary particles to big molecules had been verified by lots of experiments. Different from electromagnetic wave, the matter wave’s propagation is not only fast but also adjustable. The group velocity with which the overall envelope shape of the wave , namely the related particle’s propagation and information convey speed is changeable with its wavelength. When the particle’s energy and wavelength, in its non-dispersive propagation, reach to definite values, the group velocity can turn to very high and perhaps is possible to exceed over the light speed in vacuum. Take electron as an example, if the free electron beam gains energy higher than around 4.094×10ˉᴵ⁴J and wavelength shorter than around 2.426×10ˉᴲnm, the group velocity could surpass the light speed in vacuum. According to the special relativity theory, the light speed in vacuum is the upper limit in the Universe and no matter can exceed over that. As the de Broglie hypothesis and the deduction in this paper do not take relativity theory as premise, the conclusion in this paper should be universality. Wish this paper could provide a different viewpoint for exploration of some scientific problems, such as Faster-Than-Light movement, quantum entanglement mechanism and so on
The Wave-Particle Duality is a basic property of microscopic particles. As a basic concept of quantum mechanics, the wave-particle duality theory from elementary particles to big molecules had been verified by lots of experiments. Different from electromagnetic wave, the matter wave’s propagation is not only fast but also adjustable. The group velocity with which the overall envelope shape of the wave , namely the related particle’s propagation and information convey speed is changeable with its wavelength. When the particle’s energy and wavelength, in its non-dispersive propagation, reach to definite values, the group velocity can turn to very high and perhaps is possible to exceed over the light speed in vacuum. Take electron as an example, if the free electron beam gains energy higher than around 4.094×10ˉᴵ⁴J and wavelength shorter than around 2.426×10ˉᴲnm, the group velocity could surpass the light speed in vacuum. According to the special relativity theory, the light speed in vacuum is the upper limit in the Universe and no matter can exceed over that. As the de Broglie hypothesis and the deduction in this paper do not take relativity theory as premise, the conclusion in this paper should be universality. Wish this paper could provide a different viewpoint for exploration of some scientific problems, such as Faster-Than-Light movement, quantum entanglement mechanism and so on