The aim of the paper is to show the fundamental advantage of the Euclidean Model of Space and Time (EMST) over Special Relativity (SR) in the field of wave description of matter. The EMST offers a unified description of all particles of matter as waves moving through four-dimensional Euclidean space at the speed of light. Unlike the usual description in three dimensions, where the group and phase velocities of a particle differ, in four-dimensional space the wave and the associated particle can be treated as a single object. The paper deepens understanding of the EMST as a viable alternative to SR. The EMST clarifies the origin of relativistic phenomena and at the same time explains the apparent mysteries associated with the wave nature of matter. From the broader perspective, the EMST has all the prerequisites to become the starting point for the mutual combination of “relativistic” and “quantum” physics into a single physical theory.
The aim of the paper is to show the fundamental advantage of the Euclidean Model of Space and Time (EMST) over Special Relativity (SR) in the field of wave description of matter. The EMST offers a unified description of all particles of matter as waves moving through four-dimensional Euclidean space at the speed of light. Unlike the usual description in three dimensions, where the group and phase velocities of a particle differ, in four-dimensional space the wave and the associated particle can be treated as a single object. The paper deepens understanding of the EMST as a viable alternative to SR. The EMST clarifies the origin of relativistic phenomena and at the same time explains the apparent mysteries associated with the wave nature of matter. From the broader perspective, the EMST has all the prerequisites to become the starting point for the mutual combination of “relativistic” and “quantum” physics into a single physical theory.
In this study, a radical hypothesis concerning the wave-particle duality exhibited by extremely small objects in nature is explored by developing a Planck lattice model of space–time that grapples with the uncertain dynamic quantum structure of space–time at the Planck scale. Upon applying the Planck lattice model to two notable experiments that most clearly demonstrate the essence of wave-particle duality, one immediately finds that it successfully shows in a relatively straightforward and physically consistent manner how parcels of matter and energy, i.e., electrons and photons, respectively, can behave like waves. The heuristic concepts regarding the underlying structure of space–time contained herein are intended to show the classical particle description of matter and energy as fundamental, while at the same time doing away with the widely held notion of a continuous space–time.
A new, very different physical model of the universe is proposed. Its virtues include unifying relativity and quantum mechanics, and particles with de Broglie waves. It also appears to provide a truly unified physical basis for electromagnetic, gravitational and nuclear forces. The basic system is a four-dimensional Euclidean space, containing an array of nonlinear "flow" waves. These repeat in one dimension, called [phi]. As in Newtonian mechanics, time is treated as an additional, unidirectional parameter describing the evolution of the system. Nevertheless, this wave system is shown be inherently relativistic. Further self-organizing patterns arise within the overall wave structure. Called "wavicles," these have intrinsic quantized fields, "spin," and rest energy, and represent elementary particles. Relativistic expressions are derived for particle behavior in scalar, vector and gravitational potentials. Proper representations of these potentials, based on the wave fields and associated [phi] flows of wavicles, are also obtained. As in the causal quantum mechanics of de Broglie and Bohm, wavicles exist continuously and follow definite, stochastic trajectories. Although experimentally equivalent to Einstein's special relativity, this theory differs fundamentally from his general relativity and the associated Big Bang model. According to Linde, the latter predict a large-scale space-time curvature roughly 60 orders of magnitude greater than observed values. Here a flat large-scale geometry is predicted, in agreement with the observed distribution of galaxies. This theory is also consistent with recent observations pertaining to the age of the universe.
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.
According to the thesis presented here, the correct model of reality should be based on two major discoveries of the 20th century: Einstein's discovery that reality is four-dimensional (1905) and de Broglie's wave structure of matter (1924). In 1905, Einstein did not have all the information necessary to construct the proper model of relativity; therefore, by publishing the Theory of Relativity without knowledge of the wave structure of matter, he made a kind of a false start, which resulted in the excessive complexity and unintuitive nature of the Theory of Relativity. Including the wave nature of matter in the basic assumptions of the model of reality allows to greatly simplify the model, expand its capabilities compared to the model currently in force, and remove many problems specific to the Theory of Relativity. In this work, using the trivial example of waves on the surface of water, I derive relativistic relationships and give an unambiguous and precise interpretation of basic concepts like time, space, relativity of motion, and simultaneity of events. The new definition of time- and space dimensions also allows to define the proper time of particles directly as the number of de Broglie’s wave periods for both relativistic physics and Quantum Mechanics.
The nature of physical objects cannot be clarified independent of our concepts of space and time. We present arguments to show that neither the classical 3D space - 1D time nor 4D space-time of special relativity provide a satisfactory theoretical framework to this end, as we encounter non-classical objects. The general relativity is perhaps able to accomplish this task. But, it does so only at the expense of rendering the empty physical space neither isotropic nor homogeneous. Waves are not candidates to represent fundamental objects. We use the celebrated example of Compton scattering to argue that the full description of the experiment makes use of both wave-like and particle-like behavior in the early quantum-mechanical formulations. The later quantum field theoretical descriptions of the same phenomenon abandon causality. We present model arguments from modern particle physics experiments that the photon may be a hadron, at least part of the time.
An operational approach to quantum mechanics has been developed in the past decades in our group in Brussels. A similar approach is taken in this work, making use of the extra operational depth offered by this approach, to show that the construction of spacetime is specific to each observer. What is usually referred to as the block universe then emerges by noting that parts of the past and future are also contained in the present, but without the limitations that a four-dimensional block universe usually implies, of a reality in which change would be impossible. In our operational approach, reality remains dynamic, with free choice playing a central role in its conceptualization. We also show that, when operationally analyzed, the theory implies that objects move not only in space, but also and especially in time, and more generally in spacetime, with their rest mass being a measure of their kinetic time energy. We therefore claim that Einstein’s relativity revolution has not been fully realized, since most physicists are not ready to accept these consequences of the theory although the formula’s showing them, when operationally analyzed, are in every relativity textbook. In particular, when relativistic motion is revisited as a genuine four-dimensional motion, it becomes possible to reinterpret the parameter c associated with the coordinate speed of light, which becomes the magnitude of the four-velocity of all material entities. We observe that this four-dimensional motion in Minkowski space can also be better understood if placed in the broader perspective of quantum mechanics, provided that non-locality is interpreted as non-spatiality, thus indicating the existence of an underlying non-spatial reality, the nature of which could be conceptual, consistent with the conceptuality interpretation of quantum mechanics. This hypothesis is reinforced by noting that when observers, or experiencers, as they will be referred to in this article, are described by acknowledging their cognitive nature of entities moving in a semantic space, Minkowski metric emerges in a natural way.