Nonlinear Generalisation of Quantum Mechanics

It is known since Madelung that the Schrödinger equation can be thought of as governing the evolution of an incompressible fluid, but the current theory fails to mathematically express this incompressibility in terms of the wavefunction without facing problem. In this paper after showing that the current definition of quantum-mechanical momentum as a linear operator is neither the most general nor a necessary result of the de Broglie hypothesis, a new definition is proposed that can yield both a meaningful mathematical condition for the incompressibility of the Madelung fluid, and nonlinear generalisations of Schrödinger and Klein-Gordon equations. The derived equations satisfy all conditions that are expected from a proper generalisation: simplification to their linear counterparts by a well-defined dynamical condition; Galilean and Lorentz invariance (respectively); and signifying only rays in the Hilbert space.

Nonlinear Generalisation of Quantum Mechanics

A new definition for quantum-mechanical momentum is proposed which yields novel nonlinear generalisations of Schrödinger and Klein-Gordon equations. It is thence argued that the superposition and uncertainty principles as they stand cannot have general validity.

Nonlinear Generalisation of Quantum Mechanics

A new definition for quantum-mechanical momentum is proposed which yields novel nonlinear generalisations of Schrödinger and Klein-Gordon equations. It is thence argued that the superposition and uncertainty principles as they stand cannot have general validity.

Newton’s Third Law in the Framework of Special Relativity for Charged Bodies

Newton’s third law states that any action is countered by a reaction of equal magnitude but opposite direction. The total force in a system not affected by external forces is, therefore, zero. However, according to the principles of relativity, a signal cannot propagate at speeds exceeding the speed of light. Hence, the action and reaction cannot be generated at the same time due to the relativity of simultaneity. Thus, the total force cannot be null at a given time. In a previous paper, we showed that Newton’s third law cannot strictly hold in a distributed system where the different parts are at a finite distance from each other. This analysis led to the suggestion of a relativistic engine. As the system is affected by a total force for a finite period, the system acquires mechanical momentum and energy. The subject of momentum conversation was discussed in another previous paper, while energy conservation was discussed in additional previous papers. In those works, we relied on the fact that the bodies were macroscopically natural. Here, we relax this assumption and study charged bodies, thus analyzing the consequences on a possible electric relativistic engine.

Lorentz Symmetry Group, Retardation and Energy Transformations in a Relativistic Engine

In a previous paper, we have shown that Newton’s third law cannot strictly hold in a distributed system of which the different parts are at a finite distance from each other. This is due to the finite speed of signal propagation which cannot exceed the speed of light in vacuum, which in turn means that when summing the total force in the system the force does not add up to zero. This was demonstrated in a specific example of two current loops with time dependent currents, the above analysis led to suggestion of a relativistic engine. Since the system is effected by a total force for a finite period of time this means that the system acquires mechanical momentum and energy, the question then arises how can we accommodate the law of momentum and energy conservation. The subject of momentum conservation was discussed in a pervious paper, while preliminary results regarding energy conservation where discussed in some additional papers. Here we give a complete analysis of the exchange of energy between the mechanical part of the relativistic engine and the field part, the energy radiated from the relativistic engine is also discussed. We show that the relativistic engine effect on the energy is 4th-order in 1c and no lower order relativistic engine effect on the energy exists.

Analysis of the Phenomena Causing Weave and Wobble in Two-Wheelers

The present work follows in the tracks of previous studies investigating the stability of motorcycles. Two principal oscillation modes of motorcycles are the well-known wobble and weave modes. The research in this field started about fifty years ago and showed how different motorcycle parameters influence the stability of the mentioned modes. However, there is sometimes a minor lack in the physical analysis of why a certain parameter influences the stability. The derived knowledge can be complemented by some mechanical momentum correlations. This work aims to ascertain, in depth, the physical phenomena that stand behind the influence of fork bending compliance on the wobble mode and behind the velocity dependence of the weave damping behaviour. After a summary of the relevant work in this field, this paper presents different rigid body simulation models with increasing complexity and discusses the related eigenvalue analysis and time behaviour. With these models, the mentioned modes are explained and the physical phenomena only partly covered by the literature are shown. Finally, the influence of the rider model on weave and wobble is presented.

Об ускорении релятивистской частицы импульсом излучения

Concerning direct acceleration of charges by pulses of electromagnetic (laser) radiation with arbitrary shapes, we have found a relationship between the components of the mechanical momentum of a relativistic (but not ultrarelativistic) particle. In a wide range of conditions, the energy transferred by the radiation to a particle to be accelerated is determined by the electric area of the laser pulse, i.e., by the integral of the electric field strength over the pulse time. This indicates that it is promising to develop schemes for generation of quasi-unipolar radiation laser pulses, in which the strength of the dominant component of the electric field does not change its sign during the main pulse duration.