In this paper we pose two fundamental ideas on the motion of an elementary particle supporting the internal "spin motion" or $\textit{Zitterbewegung}$ and a particle as concentrated energy. First, the particle moves randomly in a limited area (in a quantum sized-volume) like random vibrating system where the particle will diffuse in a quantum-sized volume when it absorbs or emits the quantized amount of energy. The quantum sized-volume can move too and plays role similar to the carrier amplitude, while the vibrational motion of the fundamental particle with frequency and amplitude represents a modulating signal. The current of diffusion process taking place in the quantum sized-volume will represent the emergence of a spin phenomenon shown by the existence of Clifford algebra. Second, the particle is pure energy concentrated on the surface of 3 dimensional sphere-form (2-manifold without boundary). Afterward we show that by defining the particle mass as an invariant quantity based on the two fundamental ideas, we can derive both the diffusion constant of the particle in the quantum sized-volume as $β= \hslash/2m$ and the Schrödinger equation. Furthermore, by posing that the vibrational motion of the particle limited on the quantum sized-volume plays fundamental role as time interval unit (proper time or particle clock), we show that the relativistic effects of the particle must represent atomic processes.
In this paper we pose two fundamental ideas on the motion of an elementary particle supporting the internal "spin motion" or Zitterbewegung and a particle as concentrated energy. First, the particle moves randomly in a limited area (in a quantum sized-volume) like random vibrating system where the particle will diffuse in a quantum-sized volume when it absorbs or emits the quantized amount of energy. The quantum sized-volume can move too and plays role similar to the carrier amplitude, while the vibrational motion of the fundamental particle with frequency and amplitude represents a modulating signal. The current of diffusion process taking place in the quantum sized-volume will represent the emergence of a spin phenomenon shown by the existence of Clifford algebra. Second, the particle is pure energy concentrated on the surface of 3 dimensional sphere-form (2-manifold without boundary). Afterward we show that by defining the particle mass as an invariant quantity based on the two fundamental ideas, we can derive both the diffusion constant of the particle in the quantum sized-volume as β=ℏ/2m and the Schrödinger equation. Furthermore, by posing that the vibrational motion of the particle limited on the quantum sized-volume plays fundamental role as time interval unit (proper time or particle clock), we show that the relativistic effects of the particle must represent atomic processes.
The study of Schrödinger equation based on a hypothesis that every particle must move randomly in a quantum-sized volume has been done. In addition to random motion, every particle can do relative motion through the movement of its quantum-sized volume. On the other way these motions can coincide. In this proposed model, the random motion is one kind of intrinsic properties of the particle. The every change of both speed of randomly intrinsic motion and or the velocity of translational motion of a quantum-sized volume will represent a transition between two states, and the change of speed of randomly intrinsic motion will generate diffusion process or Brownian motion perspectives. Diffusion process can take place in backward and forward processes and will represent a dissipative system. To derive Schrödinger equation from our hypothesis we use time operator introduced by Nelson. From a fundamental analysis, we find out that, naturally, we should view the means of Newton’s Law F⃗ = ma⃗ as no an external force, but it is just to describe both the presence of intrinsic random motion and the change of the particle energy.
This paper proposes mass interaction principle (MIP) as: the particles will be subjected to the random frictionless quantum Brownian motion by the collision of space time particle (STP) prevalent in spacetime. The change in the amount of action of the particles during each collision is an integer multiple of the Planck constant h. The motion of particles under the action of STP is a quantum Markov process. Under this principle, we infer that the statistical inertial mass of a particle is a statistical property that characterizes the difficulty of particle diffusion in spacetime. Starting from this principle, this article has the following six aspects of work: First, we derive the mass-diffusion coefficient uncertainty and the quantized commutation, and derive the most basic coordinate-momentum uncertainty and time-energy uncertainty of quantum mechanics, and then clearly reveal the particle-wave duality, which are properties exhibited by particles collided by STP. Second, we created the three decompositions of particles velocity. The comprehensive property of three velocities deduced the equation of motion of the particle as Schrodinger equation, and made a novel interpretation of Heisenberg’s uncertainty principle and Feynman’s path integral expression. And reexamine the quantum measurement problem, so that the EPR paradox can be explained in a self-consistent manner. Third, we reinterpret the physical origin of quantum spins. Each spacetime random impact not only gives the particle of matter the action of a Planck constant , but also produces the quantum fluctuation properties of the material particles. Futhermore, the quantum spin properties of the material particles are also produced, which reveals the statistical quality of 1/2 spin particles and the coexistence relationship of their spins. The particle spin properties ultimately reflect the spacetime properties of STP and particles, which leads to an important result that any spin 1/2 elementary particles will be massive. Fourth, we derive the physical origin of the special relativity, and prove that the hypothesis of constant speed of light is actually the intrinsic property of spacetime. This naturally leads to the three basic inferences of the special theory of relativity, namely, “mass enhancement”, “time dilation” and “length contraction” effects. Fifth, we can perfectly explain the nature of photons based on the topological and dynamic properties of STP, thus naturally obtain the complete electromagnetic theory and all important properties of charge. Sixth, we naturally derive the gravitation from the interaction of the fundamental particles of microscopic matter, namely the massive fermion and STP. Furthermore, we can judge from the overall perspective of modern physics that the inertia mass of fermions must be equal to the gravitational mass. We have obtained the equivalent principle combined with Newton’s universal gravitation, from which we can derive all the important contents of general relativity. Both inertial mass and gravitational mass are no longer the basic physical quantities. The two are indeed equivalent, which come from the statistical mass of STP collisions. This paper shows that STP can interact with matter particles in space time. The particles of matter are affected by the impact of STP and change their motional state. The mass of a particle is a statistical property exhibited by STP collision. Under the MIP framework of interaction between STP and matter particles, the relativistic quantum electromagnetic and spin properties of particles are all self-consistent. The relativistic behavior and quantum behavior of matter particles with statistical mass are all derived from the collision of STP on matter particles. We have systematically solved all the basic problems of modern physics with MIP, which is the common origin of special theory of relativity, general theory of relativity, electromagnetic theory and quantum mechanics.
Essentially, in this paper we propose a new description of the quantum dynamics by two relativistic propagation wave packets, in the two conjugated spaces, of the coordinates and of the momentum. Compared to the Schrödinger-Dirac equation, which describes a free particle by a wave function continuously expanding in time, considered as the amplitude of a probabilistic distribution of this particle, the new equations describe a free particle as an invariant distribution of matter propagating in the two spaces, as it should be. Matter quantization arises from the equality of the integral of the matter density with the mass describing the dynamics of this density in the phases of the wave packets. In this description, the classical Lagrange and Hamilton equations are obtained as the group velocities of the two wave packets in the coordinate and momentum spaces. When to the relativistic Lagrangian we add terms with a vector potential conjugated to coordinates, as in the Aharonov-Bohm effect, and a scalar potential conjugated to time, we obtain the Lorentz force and the Maxwell equations as characteristics of the quantum dynamics. In this framework, the conventional Schrödinger-Dirac equations of a quantum particle in an electromagnetic field obtain additional terms explicitly depending on velocity, as is expected in the framework of relativistic theory. Such a particle wave function takes the form of a rapidly varying wave, with the frequency corresponding to the rest energy, modulated by the electric potential where this particle is confined, the vector potential of the electromagnetic radiation, and the gravitational potential. In the gravitational field of a black hole, the velocity of a quantum particle is directed to the Schwarzschild boundary from the outside and from the inside, without passing this boundary. When the very strong gravitational field of a large agglomeration of matter has spherical symmetry with a radius smaller than the Schwarzschild radius, the quantum particles in the central region are crushed up to quasi-uniform distributions of matter, exploding with velocities much larger than the light velocity, towards the Schwarzschild boundary, but decelerating in the gravitational field and reaching this boundary only in an infinite time. The matter of a black hole has the tendency to concentrate around the Schwarzschild boundary, with a radius proportional to its mass. In this framework, we believe that our universe is a huge black hole, with the explosion of its central matter as the Big Bang-inflation process, and an increasing radius on account of an absorption of matter from the Total Universe, where our universe has been formed. In a gravitational wave, the time-space interval in the first-order approximation is the product of a gravitational invariant including the amplitude tensor, and a coordinate invariant including the polarization vector. The gravitational invariant describes a rotation of the metric tensor around the direction of the propagation of this wave, with spin 2, as a gravitational quantum called graviton. The coordinate invariant describes a matter rotation with the spins ½ for Fermions, and 1 for Bosons. From the new dynamic equations, for a free particle in the coordinate and momentum spaces, we reobtain the two basic equations of the quantum field theory, but with a change of sign, and an additional term depending on momentum, to the rest mass as the eigenvalue of these equations. However, when these eigenvalues are eliminated, the wave function takes the form of a wave packet of spinors of the same form as in the conventional quantum field theory, with a normalization volume as the integral of the ratio of the energy to the rest energy, over the momentum domain which gives finite dimensions to the quantum particle, as a finite distribution of matter in the coordinate space.
The present contribution is based on the assumption that the probabilistic character of quantum mechanics does not originate from uncertainties caused by the process of measurement or observation, but rather reflects the presence of objectively existing vacuum fluctuations whose action on massive particles is calibrated by Planck's constant and effects an additional irregular motion. We describe a one-particle system by introducing two equally large sub-ensembles for each of which one obtains an equation of motion that has the form of a Navier-Stokes- or ''anti''-Navier-Stokes-type equation, respectively. By averaging over the total ensemble one obtains a new equation of motion which can be converted into the time-dependent Schroedinger equation. The concept allows the inclusion of electromagnetic fields and can be extended to interacting N-particle systems. We analyze the problem of how an experimental setup can consistently be decomposed into the quantum system under study and the residual quantum system ''apparatus''. The irregular extra motion of the particle under study allows a decomposition of the associated ensemble into two sub-ensembles the members of which perform, respectively, a right-handed or left-handed irregular circular motion about a given axis which becomes physically relevant in the presence of a magnetic field. We demonstrate that this orientation-decomposed ''Zitterbewegung'' behaves - in accordance with Schroedinger's original idea - as a spin-type angular momentum which appears in addition to a possible orbital angular moment of the particle. We derive the non-relativistic time-dependent Pauli equation and propose a theory of the Stern-Gerlach experiment. The Dirac equation can be derived similarly.
Development of the contemporary theory of physical phenomena in the microcosm is considered to be a result of development of Einstein's ideas on a possibility of the event space modification and on a possibility of stochastic (Brownian) motion of free particles. One considers the space-time modification, based on a new conception of geometry. In the framework of this conception any geometry is obtained as a result of the proper Euclidean geometry deformation. In the framework of this conception it is possible such a space-time geometry, where the free particle motion appears to be stochastic, although the geometry in itself remains to be deterministic. The stochasticity intensity depends on the particle mass. It is small for particle of a large mass, and it is essential for the particle of a small mass. The space-time geometry may be chosen in such a way, that the statistical description of random world lines of particles be equivalent to the quantum description (the Schrödinger equation). At such a description the quantum principles are not used. They can be obtained as a corollaries of the statistical description of nonrelativistic stochastic particles. The nonrelativistic quantum principles may not be used for description of relativistic phenomena.
From the invariance properties of the Schrodinger equation and the isotropy of space we show that a generic (non-relativistic) quantum system is endowed with an ``external'' motion, which can be interpreted as the motion of the centre of mass, and an ``internal'' one, whose presence disappears in the classical limit. The latter is caused by the spin of the particle, whatever is its actual value (different from zero). The quantum potential in the Schrodinger equation, which is responsible of the quantum effects of the system, is then completely determined from the properties of the internal motion, and its ``unusual'' properties have a simple and physical explanation in the present context. From the impossibility to fix the initial conditions relevant for the internal motion follows, finally, the need of a probabilistic interpretation of quantum mechanics.