The theory of 4-dimensional matter waves describes a physical model which explains the effects of relativity and quantum theory in a unified theory. It explains and quantifies the observations in an intuitive manner. Since in the scientifically and mathematically exact explanations of this theory you can easy lose the whole picture, this is an attempt of a comprehensible summary. The mathematically and logically exact derivations can be found in the listed literature. I hope to hereby support the overall view of the model.
The theory of 4-dimensional matter waves describes a physical model which explains the effects of relativity and quantum theory in a unified theory. It explains and quantifies the observations in an intuitive manner. Since in the scientifically and mathematically exact explanations of this theory you can easy lose the whole picture, this is an attempt of a comprehensible summary. The mathematically and logically exact derivations can be found in the listed literature. I hope to hereby support the overall view of the model.
This paper describes a physical model to intuitively explain quantum theoretical effects. The developed model describes a mechanism, which gives a logical sense to the calculation of probability amplitudes. Hence the double-slit experiment and Schrodinger’s cat become understandable. The here described model is an extension of the physical model described in the prior manuscript “Theory of the 4-dimensional matter wave”. That paper describes a model which postulates a particle as a real matter wave in a 4-dimensional and absolute space. With that theory it is possible to describe the relativistic effects in qualitatively and quantitatively accuracy. The quantum theory of the 4-dimensional matter wave shows that this model already presages a way to explain the quantum theoretical effects. From the introduction of the long extent in the 4th dimension it is not far to a model in which a particle uses many paths simultaneously. It is a conclusive derivation of the quantum theoretical effects using the model to describe the relativistic effects.
The theoretical physics of a quantum mechanical model of space, relativistic quantum holography, is described. It specifies three dimensions, such as is validated by the nature of our spatial experience, but where additionally, quantum non-locality, which Feynman described as the only mystery of quantum theory, is made manifest by means of observable phase relationships. For example, synchronicity between events, and other phenomena such as are described by the geometric/Berry phase, etc., which are outside the bounds of classical explanation. It can therefore be hypothesized: a) that we live in a entirely quantum mechanical world/universe and not a classical mechanical one (where quantum phenomena are confined to the microscopic scale) as is the current generally held scientific view, b) that three spatial dimensions are a fundamental consequence of quantum mechanics, c) that quantum holography is a natural candidate to explain quantum gravity, such that mass/inertia concerns not the eigenvalues of some operator, but rather the observable gauge invariant phases of a state vector, postulated to be that of the universe itself, as a whole, and d) that this model provides a natural explanation in terms of relativistic quantum signal processing of any each individual’s perception and cognition will be of a three dimensional world, defined similarly in relation to each individual’s quantum state vector, describing its mind/body and associated gauge invariant phases or mindset, which have observable consequences, such that mental processes and events can cause neural events and processes! These testable hypotheses, if validated, will have profound implications for our understanding, radically changing our scientific perspective on the world, as we enter the new millennium.
Where did we get that [equation] from? Nowhere. It is not possible to derive it from anything you know. It came out of the mind of Schrödinger. Richard Feynman De Broglie's matter waves The early struggles of physicists towards a quantum theory were mostly concerned with attempts to understand the nature of light. The traditional picture of light as a wave motion had been challenged by Planck and Einstein. They had shown that certain experimental results that were impossible to understand in terms of a wave picture could be easily explained if light was thought of as a stream of particles, now called photons. William Bragg, who, with his son, won the 1915 Nobel Prize for studies of crystal structure using X-rays, summarized this dilemma for physics by exclaiming in despair that he was teaching the corpuscular theory of light on Mondays, Wednesdays and Fridays, and the undulatory theory on Tuesdays, Thursdays and Saturdays! Physicists were still wrestling with these apparently contradictory properties of light when, in 1924, Prince Louis de Broglie (pronounced ‘de Broy’) suggested that all matter, even objects that we usually think of as particles – such as electrons – should also display wavelike behaviour! This revolutionary idea was completely unexpected and, what is more, was included by de Broglie in his Ph. D. thesis. Like most people, physicists are generally reluctant to accept any wild new idea, especially if there is not a shred of evidence to support it.
The framework of classical physics includes the well-established Helmholtz wave equation, which accurately describes the propagation, interference, and diffraction behaviors of steady-state time-harmonic waves such as acoustic and electromagnetic waves at the macroscopic level. Verified by centuries of experiments, it is a universally recognized deterministic formula in fundamental physics. However, traditional physics has long operated within fixed boundaries: academia has always matched the Helmholtz equation with one-dimensional real scalar coordinates, applying it only to macroscopic matter wave fields, and never attempting to use it to describe the microscopic quantum world or the underlying ontology of the universe. Meanwhile, Heisenberg’s matrix mechanics, starting from the microscopic mathematical properties, derived the uncertainty principle based on the non-commutation relations of matrices, directly proving that microscopic mechanical quantities cannot be completely represented by real scalars. The microscopic universe is inherently adapted to matrix-dimensional structures, which is the fundamental cause of the proliferation of paradoxes in quantum mechanics under the real-coordinate framework.Addressing these dual shortcomings of the existing physical system, this paper presents original research: it fully retains the differential operators, wave constraints, and steady-state solution rules of the classical Helmholtz equation, introduces no new physical constants or artificial ad-hoc assumptions, and only replaces the real-space coordinates X and Y within the equation with second-order two-dimensional linear matrix coordinates, independently constructing a theoretical system of two-dimensional linear two-dimensional waves adapted to the microscopic ontology of the universe. It must be clearly defined: classical physics only has real-coordinate Helmholtz waves, used to explain macroscopic waves; the Helmholtz wave model based on two-dimensional linear matrix coordinates is an exclusive original theory of this paper, forming a dedicated new classical system to describe the true microscopic ontology of the universe.Drawing on rigorously verified traditional mathematical and physical tools such as the classical Helmholtz wave principle, Heisenberg’s matrix mechanics, the uncertainty principle, the linear projection theorem, and the principle of wave field superposition, this paper systematically elaborates the mathematical structure, dimensional characteristics, and evolutionary laws of two-dimensional linear two-dimensional waves, and reveals the ultimate physical nature of quantum observation collapse: all material entities in the microscopic world are two-dimensional linear two-dimensional Helmholtz waves, while the human macroscopic perceptual world and detection devices can only carry one-dimensional real information. The essence of the observation process is not the random collapse of the wavefunction as defined by quantum mechanics, but rather the observation system actively extracting one degree of freedom from the two-dimensional matrix wave, with the remaining single dimension completing dimensionality-reduction projection and mapping into the one-dimensional real physical space, ultimately forming the observational illusion of localized particles.This original theory can explain the two core experimental puzzles that have plagued quantum physics for a century without contradictions or ad-hoc patches: First, when observing the interference pattern throughout the double-slit experiment, this observation mode collects the steady-state information of the global superposition of two-dimensional waves without performing dimensional extraction, and thus does not trigger collapse; Second, when a single photon enters the human eye’s retina or a single-point detector completes fixed-point detection, the observation system imposes localized boundary conditions to force the extraction of the wave field dimension, realizing the "screen projection" imaging of two-dimensional waves onto one-dimensional reality, which macroscopically manifests as wavefunction collapse. This study breaks down the barriers between macroscopic classical waves and microscopic quantum phenomena, providing a unified explanation for microscopic phenomena such as wave-particle duality and quantum observation collapse with an original classical model, and offering a new underlying perspective for the grand unification research in fundamental physics.
The answer lies right in front of us, but we refuse to see it. Both relativity and quantum theory, the two pillars of fundamental physics, are modified in this paper to make them also explain the physical phenomena they describe. With this explanation, all current inconsistencies between the two vanish. The modifications relate to the presence of a medium, which is in fact potential energy, in three-dimensional space. This medium acts as a reference system, in accordance with Mach’s principle. The speed of light, therefore, is not absolute but relative to the medium and thus to the observer. It is also dependent on medium density. Quantum waves are real scalar waves occurring in the potential energy medium, not probabilities of particles being present. Real scalar quantum waves in three-dimensional space make up the whole of physics representing manifest energy. Particles therefore do not exist; they are local manifestations of real scalar quantum waves. As a result, the Doppler effect and wave interference play a central role in physics. Moreover, the dependence of quantum wave velocity (speed of light) on medium density provides the energy exchange mechanism that is central to physics because all physical phenomena, including observation, concern energy exchange, or interaction. The conceptual simplicity of the model of physics proposed in this paper is shown to clarify a series of paradoxes and ill-understood phenomena at the fundamental level of physics such as wave-particle duality, the twins paradox, and the double slit experiment. As to entanglement, superposition, and nonlocality, the model implies that only weak versions of these properties exist.
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.