Paul S. Wesson
In 5D, I take the metric in canonical form and define causality by null-paths. Then spacetime is modulated by a factor equivalent to the wave function, and the 5D geodesic equation gives the 4D Klein-Gordon equation. These results effectively show how general relativity and quantum mechanics may be unified in 5D.
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When the cosmological "constant" is derived from modern five-dimensional relativity, exact solutions imply that for small systems it scales in proportion to the square of the mass. However, a duality transformation implies that for large systems it scales as the inverse square of the mass.
In this note I present the main ideas of my proposal about the theoretical framework that could underlie, and therefore "unify", Quantum Mechanics and Relativity, and I briefly summarize the implications and predictions.
Extending black-hole entropy to ordinary objects, we propose kinetic entropy tensor, based on which a quantum gravity tensor equation is established. Our investigation results indicate that if N=1, the quantum gravity tensor equation returns to Schrodinger integral equation. When N becomes sufficiently large, it is equivalent to Einstein field equation. This illustrates formal unification and intrinsic compatibility of general relativity with quantum mechanics. The quantum gravity equation may be utilized to deduce general relativity, special relativity, Newtonian mechanics and quantum mechani…
I outline a model where a massive particle in 4D spacetime follows a null (photon-like) path in 5D canonical (super-spherically-symmetric) space. This leads to wave-particle duality and quantization, along with other effects which show that it is possible to unify general relativity and wave mechanics in a simple fashion, given an extra dimension.
We take Co-Operative Phenomena as a common physical conceptual base to speculate on the existence of a medium and the properties that it must have to physically understand some of the problems in Special Relativity, Gravitation and Quantum Mechanics.
Assuming that the relativistic universe is homogeneous and isotropic, we can unambiguously determine its model and physical properties, which correspond with the Einstein general theory of relativity (and with its two special partial solutions: Einstein special theory of relativity and Newton gravitation theory), quantum mechanics, and observations, too.
We first define the functions which ensure the transformation of momentum and energy of a tardyon, the transformation of the wave vector and the frequency of the associated wave. Having done this, we show that they ensure the relativistic invariance of the quotient between momentum and wave vector and between energy and frequency if the product between particle velocity u and phase velocity w is a relativistic invariant (uw=c^2), a condition which is a natural combination of special relativity theory and quantum mechanics.
By using the general concepts of special relativity and the requirements of quantum mechanics, Dirac equation is derived and studied. Only elementary knowledge of spin and rotations in quantum mechanics and standard handlings of linear algebra are employed for the development of the present work.
The Hamilton-Jacobi theory of Classical Mechanics can be extended in a novel manner to systems which are fuzzy in the sense that they can be represented by wave functions. A constructive interference of the phases of the wave functions then gives us back Classical systems. In a suitable description this includes both Quantum Theory and General Relativity in the well known superspace formulation. However, there are several nuances which provide insight into these latter systems. All this is considered in this paper together with suitable generalization, to cascades of super universes.
Preons are hypothetic constituents of the standard particles. They were initially assumed to have basically similar properties to those of conventional matter. But this is not necessarily the case: the ultimate constituents of matter may feel a different space-time from that of special relativity and exhibit mechanical properties different from those predicted by standard quantum mechanics. They can also play an important cosmological role (inflation, dark matter, dark energy...). It is even not obvious that energy and momentum would have to be conserved in such a scenario. In this series of p…
This note is to bring to the reader's attention the fact that general relativity and quantum mechanics differ from each other in one main aspect. General relativity is based on the diffeomorphism covariant formulation of the laws of physics while quantum mechanics is constructed such that its fundamental laws remain invariant to a change of topology. It is the goal of this paper to show that in order to obtain a complete description of quantum gravity one has to extend the principle of diffeomorphism invariance from general relativity in the sense of quantum mechanics i.e. the laws of physics …
The aim of this paper is to reveal the deep relationship between matter and vacuum, and to seek for the same physical basis of the relativity and the quantum mechanics. In doing this, three postulates of vacuum fluctuation are proposed first, the basic premises of the relativity and the quantum mechanics including the velocity limit, the energy-frequency relation and the de Broglie wavelength expression of any matter particles are deduced then. As applications, the idea is used to analyze the Compton effect and the electron-positron annihilation. It is found that the calculation becomes simple…
The conceptual evolution of principle of relativity in the theory of special relativity is discussed in detail. It is intimately related to a series of difficulties in quantum mechanics,relativistic quantum mechanics and quantum field theory as well as to new predictions about antigravity and tachyonic neutrinos etc.
In this article, we argue that the theory of special relativity, as formulated by Einstein, is a philosophical rather than a scientific theory. What is scientific and experimentally supported is the formalism of the relativistic mechanics embedded in the Lorentz transformations and their direct mathematical, experimental and observational consequences. This is in parallel with the quantum mechanics where the scientific content and experimental support of this branch of physics is embedded in the formalism of quantum mechanics and not in its philosophical interpretations such as the Copenhagen …
A number of well-known difficulties in physics resulted from merging the theory of relativity with the Compton-de Broglie wave mechanics. Two such problems were the failure of Dirac's relativistic wave equation to predict the correct velocity of the electron, and the fact that the measured yield from nuclear fission was found to be substantially less than the theoretical yield. It is shown that the origin of these and other problems stem from the inconsistency of the relativistic mass-energy equivalence principle with the fundamental assumptions of wave mechanics. An alternative view of the co…
In this paper, we define a new velocity having a dimension of $(Length)^α/(Time)$ and a new acceleration having a dimension of $(Length)^α/(Time)^2$, based on the fractional addition rule. We then discuss the fractional mechanics in one dimension. We show the conservation of fractional energy, and formulate the Hamiltonian formalism for the fractional mechanics. As a matter of illustration, we exhibit some examples for the fractional mechanics.
Curvature of Physical Space and Geometric Projection: A Possible Geometric Understanding of Quantum Mechanics and Relativity
本文对比薛定谔方程与雅可比场方程，提出微观物理空间截面曲率表达式，尝试为量子力学与相对论提供统一几何理解，并拓展至统计力学。
In this paper, the deformed Special Relativity, which leads to an essentially new theoretical context of quantum mechanics, is presented. The formulation of the theory arises from a straightforward analogy with the Special Relativity, but its foundations are laid through the hypothesis on breakdown of the velocity-momentum parallelism which affects onto the Einstein equivalence principle between mass and energy of a relativistic particle. Furthermore, the derivation is based on the technique of an eikonal equation whose well-confirmed physical role lays the foundations of both optics and quant…
We have performed an experimental test under the conditions of which quantum mechanics predicts a spatially-discontinuous single-particle transport. The transport is beyond the relativistic paradigm of movement in Cartesian space and therefore may well be nonlocal. Our test has demonstrated that such transport does exist. This fact opens the door for realistic interpretation of quantum mechanics insofar as the requirement of Lorentz invariance appears inapplicable to any version of quantum theory. Moreover, as quantum mechanics proposes a particle dynamics beyond the relativity, it automatical…
A thought experiment is considered on observation of instantaneous collapse of an extended wave packet. According to relativity of simultaneity, such a collapse being instantaneous in some reference frame must be a lasting process in other frames. But according to quantum mechanics, collapse is instantaneous in any frame. Mathematical structure of quantum mechanics eliminates any contradictions between these two apparently conflicting statements. Here the invariance of quantum-mechanical collapse is shown to follow directly from the Born postulate, without any use of mathematical properties of…
The present work shows that through a suitable change of variables relativistic dynamics can be mapped to light propagation in a non-homogeneous medium. A particle's trajectory through the modified space-time is thus formally equivalent to a light ray and can be derived from a mechanical equivalent of Fermat's principle. The similarities between light propagation and mechanics are then extended to quantum mechanics, showing that relativistic quantum mechanics can be derived from a wave equation in modified space-time. Non-relativistic results, such as de Broglie's wavelength, Schroedinger equa…
By adding generalizations involving translations, the machinery of the quantum theory of free fields leads to the semiclassical equations of motion for a charged massive particle in electromagnetic and gravitational fields. With the particle field translated along one displacement, particle states are translated along a possibly different displacement. Arbitrary phase results. And particle momentum, a spin (1/2,1/2) quantity, is allowed to change when field and states are translated. It is shown that a path of extreme phase obeys a semiclassical equation for force with derived terms that can d…
A proof is given for the Fourier transform for functions in a quantum mechanical Hilbert space on a non-compact manifold in general relativity. In the (configuration space) Newton-Wigner representation we discuss the spectral decomposition of the canonical operators and give a proof of the Parseval-Plancherel relation and the Born rule for linear superposition. We then discuss the representations of pure quantum states and their dual vectors, and construct the Fock space and the associated quantum field theory for Bose-Einstein and Fermi-Dirac statistics.
Theories based on General Relativity or Quantum Mechanics have taken a leading position in macroscopic and microscopic Physics, but fail when used in the other extremity. Thus, we try to establish a new structure of united theory based on General Relativity by forming certain spacetime property and a new model of particle. This theory transforms the Riemann curvature tensor into spacetime density scalar so that gravitational field can be added to the Quantum Mechanics, and supposes the electromagnetic field in General Relativity to be a kind of spacetime fluid. Also the theory carries on Einst…
Towards the end of the 19th century, Kelvin pronounced as the "clouds of physics" 1) the failure of the Michelson-Morely experiment to detect an ether wind, 2) the violation of the classical mechanical equipartition theorem in statistical thermodynamics. And he believed that the removal of these clouds would bring physics to an end. But as we know, the removal of these clouds led to the two great breakthoughts of modern physics: 1) The theory of relativity, and 2) to quantum mechanics. Towards the end of the 20th century more clouds of physics became apparent. They are 1) the riddle of quantum…
The positive mass theorem in general relativity states that in an asymptotically flat spacetime, if the momentum--energy tensor is divergence-free and satisfies a dominant energy condition, then a total momentum--energy four-vector can be formed, of which the energy component is nonnegative. In this paper, we take the wave four-tensor of a plane light wave in free space as a counterexample to show that there is no guarantee that a total four-vector can be formed. Thus the theoretical framework for the positive mass theorem is flawed. In addition, it is also shown as well that the Lorentz covar…
In special relativity theory the physical quantities are generally expressed as function of the velocity. In the particular case of an extended object, the factor 1/gamma of Lorentz contraction of its length in the direction of motion is written as a function of the velocity of the extended object. The same happens with the Lorentz factor gamma of time interval dilation of a moving clock. In this paper we show that when gamma is written as a function of the relativistic energy of the considered object the resulting expressions for the length and for the time interval suggest that the contracti…
General relativity allows solutions exhibiting closed timelike curves. Time travel generates paradoxes and quantum mechanics generalizations were proposed to solve those paradoxes. The implications of self-consistent interactions on acausal region of space-time are investigated. If the correspondence principle is true, then all generalizations of quantum mechanics on acausal manifolds are not renormalizable. Therefore quantum mechanics can only be defined on global hyperbolic manifolds and all general relativity solutions exhibiting time travel are unphysical.
The virial theorem is established in the framework of resolution-scale relativity for stochastic dynamics characterized by a diffusion constant D. It only relies on a simple time average just like the classical virial theorem, while the quantum mechanical virial theorem involves the expectation values of the observables. Nevertheless, by the emergence of a quantum-like potential term, the resolution-scale relativity virial theorem also encompasses quantum mechanical dynamics under the identification hbar <--> 2mD. This provides an illustration of the scale relativistic approach to the foundati…
Observed physical phenomena can be described well by quantum mechanics or general relativity. People may try to find an unified fundamental theory which mainly aims to merge gravity with quantum theory. However, difficulty in merging those theories self-consistently still exists, and no such theory is generally accepted. Here we try to propose a quantum theory with space and time in symmetrical positions in the framework of general relativity. In this theory, Dirac matter fields, gauge fields and gravity field are formulated in an unified way which satisf Dirac equation, Yang-Mills equation an…
The axiomatic definition of mass in classical mechanics, outlined by Mach in the second half of 19th century and improved by several authors, is simplified and extended to the theory of special relativity. According to the extended definition presented here, the mass of a relativistic particle is independent of its velocity and coincides with the rest mass, i.e., with the mass defined in classical mechanics. Then, force is defined as the product of mass and acceleration, both in the classical and in the relativistic framework.
Starting with a consideration of the implication of Bell inequalities in quantum mechanics, a new quantum postulate is suggested in order to restore classical locality and causality to quantum physics: only the relative coordinates between detected quantum events are valid observables. This postulate supports the EPR view that quantum mechanics is incomplete, while also staying compatible to the Bohr view that nothing exists beyond the quantum. The new postulate follows from a more general principle of quantum relativity, which states that only correlations between experimental detections of q…
Gravitation is the common underlying texture between General Relativity and Quantum Mechanics. We take gravitation as the link that can make possible the marriage between these two sciences. We use here the duality of Nature for gravitation: A continuous warped space, wave-like, and a discrete quantum gas, particle-like, both coexistent and producing an equilibrium state in the Universe. The result is a static, non expanding, spherical, unlimited and finite Universe, with no cosmological constant and no dark energy. The Principle of Mach is reproduced here by the convergence of the two cosmolo…
Chaotic motion in time of a number of macroscopic systems has been analyzed, in the framework of scale relativity, as motion in a fractal space with topological dimension 3 and geodesics with fractal dimension 2. The motion equation is then Schrödinger-like and its interpretation in fluid mechanics gives the well-known Euler and Navier-Stokes equations. We generalize here this formalism to the study of a system exhibiting a chaotic behavior both in space and time. We are thus lead to consider macroscopic fluid properties as issuing from the geodesic features of a fractal `space-time' with topo…
I describe a constructive foundation for Quantum Mechanics, based on the discreteness of the degrees of freedom of quantum objects and on the Principle of Relativity. Taking Einstein's historical construction of Special Relativity as a model, the construction is carried out in close contact with a simple quantum mechanical Gedanken experiment. This leads to the standard axioms of Quantum Mechanics. The quantum mechanical description is identified as a tool that allows describing objects with discrete degrees of freedom in space-time covariant with respect to coordinate transformations. An inhe…
Most of the logical objections against the classical laws of motion, as they are usually presented in textbooks, centre on the fact that defining force in terms of mass and acceleration, the first two laws are mere assertions of concepts to be introduced in the theory; conversely, the third law expresses the experimental fact that the ratio of masses is inversely proportional to the ratio of accelerations, but it is known to fail when the interacting bodies are rapidly accelerated or far apart, leading to objections at the research level, particularly when electromagnetic phenomena is present.…
Recently, [10,11], the Heisenberg Uncertainty relation and the No-Cloning property in Quantum Mechanics and Quantum Computation, respectively, have been extended to versions of Quantum Mechanics and Quantum Computation which are re-formulated using scalars in {\it reduced power algebras}, [2-9], instead of the usual real or complex scalars. Here, the Lorentz coordinate transformations, fundamental in Special Relativity, are extended to versions of Special Relativity that are similarly re-formulated in terms of scalars in reduced power algebras, instead of the usual real or complex scalars. The…
A body of theory is completely different between relativity theory and quantum mechanics. Most targeting physical phenomena are different between them as well. Despite that both theories describe our time-space world, no one has succeeded in arriving at one of these theories by using the other one, deductively. Fusion of these two theories produced quantum field theory. However this theory impresses us as a theory that was made by merging the two theories by force. So this theory cannot indicate the reason why both relativity theory and quantum mechanics exist in this world at the same time. H…
The non perturbative guiding center transformation is extended to the relativistic regime and takes into account electromagnetic fluctuations. The main solutions are obtained in covariant form: the gyrating particle and the guiding particle solutions, both in gyro-kinetic as in MHD orderings. Moreover, the presence of a gravitational field is also considered. The way to introduce the gravitational field is original and based on the Einstein conjecture on the feasibility to extend the general relativity theory to include electromagnetism by geometry, if applied to the extended phase space. In g…
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