Momentum and Kinetic Energy equations are developed from the hypothesis that oppositely directed components of harmonically oscillating pseudo standing waves pass through a quantum particle center and can be represented by Longitudinal Matter Waves that carry the particle’s momentum and energy. The Doppler effect on the component wave lengths allows the net forward momentum and kinetic energy to increase with speed well beyond classical values. De Broglie (1925) issues with stationary wavelength and moving pulse rate are resolved in a different manner. Because a quantum particle is considered to be nothing more than the sum of “in” and “out” matter waves focused through its center, whatever happens to these matter waves determines the future location of that center. This opens the door to physical explanations for gravity, interference, and the slowdown of light in transparent mediums. Gravity, for example, is shown in section 6, to possibly be caused by the local gradient in matter wave speed near a large body like earth.
Momentum and Kinetic Energy equations are developed from the hypothesis that oppositely directed components of harmonically oscillating pseudo standing waves pass through a quantum particle center and can be represented by Longitudinal Matter Waves that carry the particle’s momentum and energy. The Doppler effect on the component wave lengths allows the net forward momentum and kinetic energy to increase with speed well beyond classical values. De Broglie (1925) issues with stationary wavelength and moving pulse rate are resolved in a different manner. Because a quantum particle is considered to be nothing more than the sum of “in” and “out” matter waves focused through its center, whatever happens to these matter waves determines the future location of that center. This opens the door to physical explanations for gravity, interference, and the slowdown of light in transparent mediums. Gravity, for example, is shown in section 6, to possibly be caused by the local gradient in matter wave speed near a large body like earth.
The electromagnetic component waves, comprising together with their generating oscillatory massless charge a material particle, will be Doppler shifted when the charge hence particle is in motion, with a velocity v, as a mere mechanical consequence of the source motion. We illustrate here that two such component waves generated in opposite directions and propagating at speed c between walls in a one-dimensional box, superpose into a traveling beat wave of wavelength ${\mitΛ}_d$$=(\frac{v}{c}){\mitΛ}$ and phase velocity c2/v+v which resembles directly L. de Broglie's hypothetic phase wave. This phase wave in terms of transporting the particle mass at the speed v and angular frequency ${\mitΩ}_d=2πv /{\mitΛ}_d$, with ${\mitΛ}_d$ and ${\mitΩ}_d$ obeying the de Broglie relations, represents a de Broglie wave. The standing-wave function of the de Broglie (phase) wave and its variables for particle dynamics in small geometries are equivalent to the eigen-state solutions to Schrödinger equation of an identical system.
摘要:德布罗意的物质波假说宣告波粒二象性为所有物质的普遍属性,但物质波的物理本质,它的波幅代表什么,它为何是复数形式,测量为何导致坍缩,在正统量子力学中始终缺乏一个直观的本体论解释。本文基于“存在的本质是不均匀”这一核心命题,提出一种替代诠释:物质波不是粒子的附属属性,而是时空不均匀性的局域涟漪。波函数是涟漪的完整数学描述,其振幅对应不均匀性的强度,其相位对应时间不均匀性的周期性展开,其波长由德布罗意关系与粒子动量关联。本文将德布罗意关系重新表述为时间不均匀性向空间延展的转换方程:能量 E = h/∇t(其中 ∇t 为时间不均匀性),物质波频率即时间不均匀性的倒数 ν = 1/∇t。在此基础上,薛定谔方程被重新解读为涟漪的动力学平衡方程,一边是涟漪的时间脉动能量,另一边是涟漪的空间曲率能量与外部不均匀性场的约束能量之和。波粒二象性、不确定性原理与测量坍缩等量子力学的基本困境,在此框架中均获得自然的几何-物理解释,不再需要观测者的特殊地位或多世界假设。这一诠释保留了量子力学的全部数学形式和实验预言,只改变了物理实在的指认,正如哥白尼改变了坐标原点而不改变天文学数据。 Abstract:De Broglie's matter wave hypothesis proclaimed wave-particle duality as a universal property of all matter. Yet the physical essence of matter waves,what their amplitude represents, why they are inherently complex-valued, and why measurement induces collapse has remained without a clear ontological interpretation in orthodox quantum mechanics. Building on the core proposition that "the essence of existence is inhomogeneity," this paper proposes an alternative interpretation: matter waves are not properties attached to particles, but localized ripples of spacetime inhomogeneity. The wave function is the complete mathematical description of such a ripple: its amplitude corresponds to the intensity of inhomogeneity, its phase to the periodic unfolding of temporal inhomogeneity, and its wavelength,via the de Broglie relation—to the particle's momentum. The de Broglie relation is reformulated as a conversion equation from temporal inhomogeneity to spatial extension: E=h/∇t(where ∇t denotes temporal inhomogeneity), and the matter-wave frequency is the reciprocal of temporal inhomogeneity, ν=1/∇t. The Schrödinger equation is reinterpreted as the dynamical equilibrium equation of the ripple: on one side stands the temporal pulsation energy of the ripple, and on the other the sum of the ripple's spatial curvature energy and the constraining energy of the external inhomogeneity field. Wave-particle duality, the uncertainty principle, and measurement collapse,the foundational dilemmas of quantum mechanics,all acquire natural geometric-physical explanations within this framework, requiring neither a privileged role for the observer nor a many-worlds hypothesis. This interpretation preserves all mathematical forms and experimental predictions of quantum mechanics; it merely changes the identification of physical reality, just as Copernicus changed the coordinate origin without altering astronomical data.
Matter waves were discovered in the early 20th century from their wavelength, predicted by DeBroglie, Planck’s constant divided by the particle’s momentum, that is, λmw = h/m.v. But, the failure to obtain a reasonable theory for the matter wave frequency resulted somewhat in loss of further interest. It was expected that the frequency of the matter wave should correspond to the particle kinetic energy, that is, fmw = 1/2 . m . v2/h but the resulting velocity of the matter of the particle, v = fmw . λmw , is that the matter wave moves at one half the speed of the particle, obviously absurd as the particle and its wave must move together. If relativistic mass is used (as it should in any case) the problem remains, the same mass appearing in numerator and denominator and canceling. It is no help to hypothesize that the total energy, not just the kinetic energy, yields the matter wave. That attributes a matter wave to a particle at rest. It also gives the resulting velocity as c2/v the wave racing ahead of its particle. A reinterpretation of Einstein’s derivation of relativistic kinetic energy (which produced his famous E = m.c2 ) leads to a valid matter wave frequency and a new understanding of particle kinetics and of the atom’s stable orbits.
Based on the law of conservation of energy, we have shown that, the steady state electronic motion around a given nucleus in a non-circular orbit depicts a rest mass variation, though the overall relativistic energy remains constant. This is, in no way, conflicting with the usual quantum mechanical approach. On the contrary, it provides us with the possibility of bridging the special theory of relativity and quantum mechanics, to finally achieve a natural symbiosis between these two disciplines, and furthermore, elucidating the “quantum mechanical weirdness”, simply based on the mere law of relativistic conservation of energy. Our theory was developed originally, vis-a-vis gravitational bodies in motion with regard to each other; hence, it is comforting to have both the atomic scale and the celestial scale described on just the same conceptual basis. One way to conceive the rest mass variation of concern is to consider a “jet effect”. Accordingly, a particle on a given orbit through its journey must eject a net mass from its back to accelerate, or must pile up a net mass from its front to decelerate, while its overall relativistic energy stays constant throughout. In other words, a minimal rest mass is transformed into extra kinetic energy through an acceleration process, and kinetic energy condenses into extra rest mass through a deceleration process. The tangential speed of the jet in question, strikingly points to the de Broglie wavelength. This, on the whole, makes the jet speed ‘’superluminal”, yet excluding any transport of energy. This conjecture coincides with the recent measurements (Kholmetskii et al., 2007; Salart et al., 2008), and provides a clue for the wave-particle duality, also insures their concurrent coexistence. An important consequence of the approach presented herein is that, either gravitationally interacting macroscopic bodies, or electrically interacting microscopic objects, sense each other, with a speed much greater than that of light, and this, in exactly the same way. In which case, though, the interaction coming into play, excludes any energy exchange; thus, we would like to call it, “wave-like interaction”. The present approach ends up the existing schizophrenia, between different conceptions painting separately the micro world and the macro world, and unites these two worlds with an unequal, single and simple conception, based on just the law of relativistic energy conservation.
Key words: Special theory of relativity, electric interaction, tachyons, de Broglie relationship, superluminal or wave-like interaction, general theory of relativity, gravitation.
We will here show that there is one more relativistic wave equation rooted in the relativistic energy Compton moment relation, which should not be confused with the standard relativistic energy momentum relation. The standard momentum is, from a quantum perspective, rooted in the de Broglie wave. The de Broglie wave is not mathematically defined for rest-mass particles and has strange properties such as converging to infinity when the particle is almost at rest. As mentioned in the previous paper, the de Broglie wave is likely just a mathematical derivative of the true matter wave, which we have good reasons to think is the Compton wave. A wave equation that satisfies the relativistic energy Compton momentum relation will, in addition automatically satisfy the standard relativistic energy momentum relation, so there is no conflict between these two relations. The new one related to Compton is just the deeper reality and help explain why it gives simpler and more elegant relativistic wave equations, which are likely easier to interpret in terms of the physical reality.
It is argued that the de Broglie wave is not the wave usually supposed, but the relativistically induced modulation of an underlying carrier wave that moves with the velocity of the particle. In the rest frame of the particle this underlying structure has the form of a standing wave. De Broglie also assumed the existence of this antecedent standing wave, but it would appear that he failed to notice its survival as a carrier wave in the Lorentz transformed wave structure. Identified as a modulation, the de Broglie wave acquires a physically reasonable ontology, evidencing a more natural unity between matter and radiation than might otherwise be contemplated, and avoiding the necessity of recovering the particle velocity from a superposition of such waves. Because the Schrödinger and other wave equations for massive particles were conceived as equations for the de Broglie wave, this interpretation of the wave is also relevant to such issues in quantum mechanics as the meaning of the wave function, the nature of wave-particle duality, and the possibility of well-defined particle trajectories.