The elusive unity of microscopic and macroscopic physics may reflect a profound misunderstanding of the microscopic world. We start with a real, deterministic de Broglie wave, and show how this leads to the equations of both special and general relativity, providing a unified picture for physics at all scales. In this picture, transformations of ω and k are more fundamental than spacetime transformations of t and r. Local metrics compatible with general relativity may be derived, but are not necessary for calculations. Furthermore, coupling constants and h are invariant, while c, G, e, and particle rest masses are not. Such variations cannot be observed using local measurements, due to the principle of relativity.
The elusive unity of microscopic and macroscopic physics may reflect a profound misunderstanding of the microscopic world. We start with a real, deterministic de Broglie wave, and show how this leads to the equations of both special and general relativity, providing a unified picture for physics at all scales. In this picture, transformations of ω and k are more fundamental than spacetime transformations of t and r. Local metrics compatible with general relativity may be derived, but are not necessary for calculations. Furthermore, coupling constants and h are invariant, while c, G, e, and particle rest masses are not. Such variations cannot be observed using local measurements, due to the principle of relativity.
A wave equation complying with Galilean transformations is proposed for electromagnetic and matter waves. A fundamental feature entirely different from the principle of relativity is that the wave equation is referred specifically to the proposed local-ether frame. For electromagnetic wave, the local-ether wave equation accounts for a wide variety of experiments of propagation or interference. For matter wave, the wave equation leads to modifications of Schrodinger's equation which in turn lead to a unified quantum theory of electromagnetic and gravitational forces in conjunction with the identity of inertial and gravitational mass. Further, it leads to modifications of the Lorentz force law and of Maxwell's equations. Moreover, the wave equation leads to dispersion of matter wave, from which the speed-dependences in the mass of a particle and in the wavelength, angular frequency, and quantum energy of a matter wave are derived. The consequences of the wave equation are in accord with a wide variety of experiments which are commonly ascribed to the special relativity, the general relativity, the Lorentz mass-variation law, or to the de Broglie matter wavelength. Thereby, the local-ether wave equation unifies quantum mechanics, electromagnetics, and gravitation.
A physical picture of macroscopic and microscopic worlds is presented. In the space-time description, both the macroscopic and microscopic worlds are described simultaneously in space-time being a single boundless four dimensional continuum in which the motion of the observer is represented as a world line. In our picture, the space-time description is valid only for the macroscopic world and the microscopic world is local in the sense that it is described in a finite space associated with each point of the macroscopic space-time. In this case, space-time does not exist in the microscopic world in which the observer can not move. For the description of our picture, the language of the non-space-time description is necessary in which space-time is not presupposed. We can utilize the space-time description for the macroscopic world and, at the same time, we have a theory of finite degree of freedom describing creations and annihilations of elementary particles in the microscopic world free from the divergence difficulty, instead of the divergent quantum field theory in the space-time description which is considered in our picture a limit of an approximation like the ideal gas in gas theories. The finite degree of freedom is given by a one-particle state-vector space of a finite dimension from which the second quantization leads to a state-vector space of a countable dimension (a Hilbert space) for the theory of creations and annihilations of elementary particles describing a local microscopic world. The relation between microscopic worlds associated with different macroscopic space-time points is given by a dynamical principle up to a phase factor due to possible fluctuations of phases of local state-vector spaces. The experiment on interference of light performed recently by Franson and Potocki is interpreted in terms of fluctuation of the local phases and is considered to support the theory of finite degree of freedom which leads to the idea of local microscopic worlds.
摘要:狭义相对论与量子力学是当代物理学的两大支柱。狭义相对论描述高速运动粒子的运动学,以光速不变和洛伦兹变换为出发点;量子力学描述微观世界的粒子行为,以波函数和薛定谔方程为核心。两者各自取得了惊人的经验成功,但它们基于不同的概念基础和数学结构,彼此之间的逻辑关系并不清楚。本文尝试从一个不同的方向出发,为这两个理论之间的逻辑关系提供一种新的理解。这个方向的出发点是“存在的本质是不均匀”这一核心命题,以及在此基础上建立的涟漪图像,“物质波是时空不均匀性的局域涟漪”。在涟漪框架中,能量被重新定义为时间不均匀性的度量E=h/∇t。狭义相对论的时间膨胀、长度收缩、质能等价、相对论能量-动量关系、光速极限和洛伦兹协变性,均可以从涟漪的三个基本属性,能量与时间不均匀性的关系、涟漪相位不变性、以及不同参考系中能量比等于频率比自然导出。这一推导表明,狭义相对论效应并非独立于量子力学的基本定律,而是涟漪动力学在不同运动状态下的必然推论。量子力学与狭义相对论,在涟漪框架中被统一为同一本体论(时空不均匀性)在微观和宏观两个层次上的表现。这一框架保留了全部已有物理理论的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: Special relativity and quantum mechanics are the two pillars of contemporary physics. Special relativity describes the kinematics of high-speed particles, taking the constancy of the speed of light and Lorentz transformations as its starting point; quantum mechanics describes the behavior of particles in the microscopic world, with the wave function and the Schrödinger equation at its core. Both have achieved astonishing empirical success, yet they rest on different conceptual foundations and mathematical structures, and the logical relationship between them remains unclear. This paper attempts to provide a new understanding of this relationship from a different direction. The starting point is the core proposition that "the essence of existence is inhomogeneity" and the ripple picture established on this basis—that "matter waves are localized ripples of spacetime inhomogeneity." In the ripple framework, energy is redefined as the measure of temporal inhomogeneity, E=h/∇t. Time dilation, length contraction, mass-energy equivalence, the relativistic energy-momentum relation, the light-speed limit, and Lorentz covariance of special relativity can all be naturally derived from three fundamental properties of ripples: the relation between energy and temporal inhomogeneity, the phase invariance of ripples, and the equivalence between the energy ratio and the frequency ratio in different reference frames. This derivation shows that special relativistic effects are not fundamental laws independent of quantum mechanics, but necessary consequences of ripple dynamics in different states of motion. Quantum mechanics and special relativity are unified within the ripple framework as manifestations of a single ontology—spacetime inhomogeneity—at the microscopic and macroscopic levels. This framework preserves the full mathematical formalism and all empirical predictions of the existing physical theories, altering only the assignment of physical reality—just as Copernicus changed the coordinate origin without changing the astronomical data.
Thus far I have been primarily concerned with how an interpretation of quantum mechanics might, or might not, be local. This question is traditionally not sharply distinguished from the question of whether quantum mechanics is consistent with the theory of relativity. However, the two questions are indeed quite distinct, and should be recognized as such explicitly. The theory of relativity What does relativity require? As a first approximation, we may make the distinction by noting that the requirements of the theory of relativity are themselves unclear. Minimally, relativity seems to require that there be no way to distinguish one reference frame from another – i.e., that there be no experimental procedure that can determine which of two inertial observers is ‘really’ moving, or more generally that there be no way to discover an observer's absolute velocity. Most authors are willing to find in (special) relativity a stronger requirement: namely, Lorentz-invariance. They say that relativity requires that in fact there is no such thing as absolute velocity. This requirement goes beyond the minimum – it might be that there is an absolute rest frame (so that absolute velocities are given by motion relative to this frame) while there is no way to find it. (As I will discuss in chapter 9, exactly this situation occurs in Bohm's theory.)
Despite its successes, quantum mechanics (QM) has remained mysterious to all who have encountered it. Starting with Bohr and progressing into the present, the departure from intuitive, physical reality has widened. The connection between QM and reality is more than just a “philosophical” issue. It reveals that QM is not a correct or complete theory of the physical world and that inescapable internal inconsistencies and incongruities arise when attempts are made to treat it as physical as opposed to a purely mathematical “tool.” Some of these issues are discussed in a review by F. Laloe [Am. J. Phys. 69, 655 (2001)]. In an attempt to provide some physical insight into atomic problems and starting with the same essential physics as Bohr of e moving in the Coulombic field of the proton and the wave equation as modified by Schrodinger, a classical approach is explored that yields a remarkably accurate model and provides insight into physics on the atomic level. The proverbial view, deeply seated in the wave-particle duality notion, that there is no large-scale physical counterpart to the nature of the electron may not be correct. Physical laws and intuition may be restored when dealing with the wave equation and quantummechanical problems. Specifically, a theory of classical quantum mechanics (CQM) is derived from first principles that successfully applies physical laws on all scales. Rather than using the postulated Schrodinger boundary condition “Ψ → 0 as r → ∞,” which leads to a purely mathematical model of the electron, the constraint is based on experimental observation. Using Maxwell’s equations, the classical wave equation is solved with the constraint that the bound (n = 1)state electron cannot radiate energy. By further application of Maxwell’s equations to electromagnetic and gravitational fields at particle production, the Schwarzschild metric is derived from the classical wave equation, which modifies general relativity to include conservation of spacetime in addition to momentum and matter/energy. The result gives a natural relationship among Maxwell’s equations, special relativity, and general relativity. CQM holds over a scale of spacetime of 85 orders of magnitude — it correctly predicts the nature of the universe from the scale of the quarks to that of the cosmos. A review is given by G. Landvogt [Internat. J. Hydrogen Energy 28, 1155 (2003)].
In Hawking’s view physics has been broken up into many partial theories, while the ultimate goal of physicists is to unify them. The two basic theories of 20th-century physics, relativity theory and quantum theory, are based on completely different logical prerequisites and exactly separate: matter is described as particles in relativity theory and as waves in quantum mechanics. Here, based on the identical logical prerequisites, we unify Einstein’s special relativity (SR) and de Broglie’s matter-wave theory (MWT) into the theory of dualistic relativity (DR), taking a significant step toward the unification of relativity and quantum mechanics. From the definition of time, we derive the Lorentz transformation in differential form and establish the theory of DR, which generalizes the wave-particle duality of matter motion, and uniformly derives Einstein’s formula E=mc2, Planck’s equation E=hf, and de Broglie’s relation λ=h/p. From the logical prerequisite completely different from Einstein’s hypothesis of the invariance of light speed and along the logical path completely different from Einstein’s SR, we have deduced the whole theoretical system of Einstein’s SR and de Broglie’s MWT. In the theory of DR, the two great formulae originally separated, Einstein’s formula E=mc2 and Planck’s equation E=hf, become a pair of twin formulae unified in an identical theoretical system.