In this paper,I introduce the virtual velocity of the particle. It is from the spetial theory of relativity, because of the velocity of the particles or Dirac equation be not able to explaine hydrogen atom phenamina. In the spetial theory of relativity, time dilatation and lenth constraction are related by the equation (1). I get from the above relation, the vitual velocity of a particle and the virtual speed of a particle can be beyond the speed of light. I think the virtual velocity and potential have nonlocality in physics, and wave function may exists there before we observe the particle's position. New quantum machanics is similar to Shrodinger equation.
In this paper,I introduce the virtual velocity of the particle. It is from the spetial theory of relativity, because of the velocity of the particles or Dirac equation be not able to explaine hydrogen atom phenamina. In the spetial theory of relativity, time dilatation and lenth constraction are related by the equation (1). I get from the above relation, the vitual velocity of a particle and the virtual speed of a particle can be beyond the speed of light. I think the virtual velocity and potential have nonlocality in physics, and wave function may exists there before we observe the particle's position. New quantum machanics is similar to Shrodinger equation.
The velocity is a macroscopic concept. The question what is the meaning of velocity in Quantum Mechanics( QM) ,this problem itself is inno answersituation. In the semi-classical theory,for the reconstruction of the velocity definition,we have v→= ▽S / m[m is the particle's mass and ψ = Aexp( j S /h) ]. This method builds the relation of velocity and wave function,but it is not the necessary and useful concept of wave's speed. The velocity of light in vacuum is a common basic constant of physics,however QM also need this parameter obviously,i. e. the new wave mechanics is on need of this physical quantity.The process and result of people's practice show that,scientist has intended to bring forth in the measurement of c with very high accuracy does stand out,if he used the scalar equation c = fλ. Modern physics maintain that the wave velocities( phase velocityvp、group velocity vg) are scalars,not vectors.The wave has its special scientific features; the regular pattern is different from the Classical Mechanics( CM). It needs supports of the QM,but it is not identical with the serious QM. Now,it has not only a theory that can explain the wave problems perfectly,so it is support by the classical physics and quantum physics.The quantization process of EM fields explains the particle-wave duality mathematically. Post quantization,from the EM fields we obtained the photons. But scientist still is puzzled by a difficult question:what is photon. As the common knowledge,the matter waves of photon still a paradox in physics. In addition,the electronic probability waves corresponding the Schrdinger equation,but people says the photonic probability waves have not that wave equation. In other words,the physical meanings of matter wave's phase velocity are not clear,and why the phase velocity of de Broglie waves is faster-than-light,many explanations will be needed.Many instances similar to these examples make the particle-wave duality still the magic ghost in modern physics. Finally,the study on negative wave velocity( NWV) in recent years has a great deal of experience on wave sciences,and bring the new chance on theoretical thinking.
When the solution of the time independent Schrödinger equation is a real function, the velocity of the associated quantum particle is vanishing in Bohmian Mechanics. We can obtain a moving particle if we consider that its velocity can be related not to the phase of the wave function but to its amplitude. By using the rules of standard quantum mechanics, we have constructed a model generalizing the momentum operator and modifying the corresponding Schrödinger equation. We obtain a new nonlinear equation of the form studied by Ermakov and Pinney and we apply the model to the cases of the particle in a box and of a bouncing ball. The new formula of quantum velocity and the corresponding motion of quantum particles have an immediate correspondence with the behavior of the bodies in classical mechanics.
One of the concepts of Relativity theory that challenges conventional intuition the most is time dilation and length contraction. Usual approaches for describing relativistic effects in quantum systems merely postulate the consequences of these effects as physical constraints. Here, we propose to rebuild Special Relativity from quantum mechanical considerations. This is done by dropping one of its fundamental postulates: the universality of the speed of light. Lorentz transformations are obtained by a quantum mechanism. We use the fact that quantum states depend on the Galilean reference frame where they are defined. In other words, quantum states outside an observer's Galilean reference frame are distorted. Then, we show in a theorem the existence of time-dependent observables that are sensible to this distortion in such a way that their expectation value is a Lorentz-covariant function of time. We then postulate this mechanism as the source of the phenomena of Special Relativity. As a corollary of the main theorem, we show the existence of a Lorentz covariant momentum and mass operators which yield the relativistic momentum and mass. In this theory, the fundamental limit of the speed of light imposes a transparency condition for faster-than-light particles: they are allowed but they are not observable. The transparency effect could explain dark matter in a more general theory following this quantum formalism.
The concept of position and its measurement are fundamental to modern navigation technology as well as to theoretical physics. Nevertheless, a consistent notion of position has not been found in modern physics because of apparent inconsistencies between quantum mechanics and relativity. In quantum mechanics the probability distribution for a particle's position is determined by its wave function. A wave function strictly localized in space describes a particle within that locality, and nowhere else. But the quantum equations of motion predict the function will disperse, after any length of time at all, to occupy all space. Therefore the theoretical prediction is that, shortly after detection in a laboratory, a particle may be found anywhere in the universe, including regions requiring faster-than-light travel to reach. This contradicts the theory of relativity, which precludes a body traveling faster than the speed of light. The conflict arises from unexamined assumptions regarding the time of the measurement event and the time of the system under measurement. The prevailing view in physics is that time is only a parameter, having a definite value, describing dynamic changes in physical systems. This view endures even though quantum mechanics recognizes position as a quantum variable with inherent uncertainty, and relativity indicates that time should be placed on the same footing as position. But if time is recognized as a quantum variable with inherent uncertainty, the conceptual problems with position are resolved. The particle has finite probability of being in the past (or future) of the observer, while the quantum mechanical operator describing the position measurement contains a term which extrapolates from the intrinsic time of the particle to the time of the observer. Being potentially well in the past of the measurement event, the particle has time to travel to remote regions without exceeding the speed of light, and the conflict with relativity is resolved. A relativistic quantum theory can therefore be constructed incorporating a well-defined concept of position.
The starting point of this research is a representation of a quantum particle according to the Schrodinger equation of the conventional quantum mechanics. In this representation, a quantum particle is described by a wave packet in the coordinate space and the conjugated wave packet in the momentum space. The problem is that while in the coordinate space the group velocity is in agreement with one of the Hamilton equations, the group velocity in the momentum space is in contradiction with the other Hamilton equation - a minus sign is missing. Group velocities in agreement with the Hamilton equations are obtained only when in the time dependent phase of a quantum particle wave packet, instead of the Hamiltonian coming from the conventional Schrodinger equation, the Lagrangian is considered. This suggests us to consider the relativistic Lagrangian in the time dependent phase. In this way, the conventional relativistic principle of invariance of the time-space interval gets the more physically understandable form of the invariance of the time dependent phase of a quantum particle - the time dependent phase of a quantum particle is the same in any system of coordinates. Based on the relativistic time dependent phase invariance of a quantum particle, from the group velocities of this particle the relativistic kinematics and dynamics are obtained. The interaction with an electromagnetic field is described by a modification of the time dependent phase with a scalar potential conjugated to time and a vector potential conjugated to the space coordinates. In this paper, we find that, according to the formalism of the general relativity, any matter element in a field of forces is accelerated only perpendicularly to its velocity. This means that the matter propagation of a quantum particle can be conceived in planes perpendicular to velocity, while the mater distribution can be considered in a Fourier representation - quantum waves. We study the quantum particle dynamics in gravitational waves and derive the graviton spin. We consider a quantum particle in electromagnetic field and obtain a Schrödinger-Dirac-type equation, with additional terms describing the velocity dependence of the particle dynamics.
The Schrodinger equation has been considered to be a postulate of quantum physics, but it is also perceived and derived heuristically as the quantum equivalent of the classical energy relation. We indicate that the Schrodinger equation cannot be a physical postulate, and we show that the heuristic derivations wrongly consider that the particle kinetic energy is proportional to the square of the momentum operator acting on the wavefunction. The correct term is proportional to the square of the momentum. Analyzing particle interactions, we realize that particles have multiple virtual motions and that each motion is accompanied by a wave that has constant amplitude. Accordingly, we define the wavefunction as the superposition of the virtual waves of the particle. As a result, quantum mechanics becomes a local and global theory, while in the traditional formulation it is a local theory. In several interaction settings we can tell what particle motions arise and explain the outcomes in simple and tangible terms. Most importantly, the mathematical foundation of quantum mechanics becomes clear and justified, and we derive the Schrodinger, Dirac, etc. equations as the conditions the wavefunction must satisfy at each space-time point in order to fulfill the respective total energy equation.