相关论文: The physical heritage of Sir W.R. Hamilton

We give a simple and self contained introduction to quaternions and their practical usage in dynamics. The rigid body dynamics are presented in full details. In the appendix, some more exotic relations are given that allow to write more…

We consider a classical spinning particle in the frame of the relativistic physics by means of a covariant Hamiltonian and of a generalization of Poisson brackets which take into account the gauge fields. We obtain different equations of…

Quantum mechanics, one of the most successful theories in the history of science, was created to account for physical systems not describable by classical physics. Though it is consistent with all experiments conducted thus far, many of its…

The Dirac method is used to analyze the classical and quantum dynamics of a particle constrained on a circle. The method of Lagrange multipliers is scrutinized, in particular in relation to the quantization procedure. Ordering problems are…

A covariant Hamiltonian description was introduced in the dynamics of charges and electromagnetic interaction. By a canonical transformation this Hamiltonian formalism was transformed to obtain the Dirac generators for any form of…

In this work, we use the concept of quaternion time and demonstrate that it can be applied for description of four-dimensional space-time intervals. We demonstrate that the quaternion time interval together with the finite speed of light…

It is demonstrated that energy conservation allows for a straight derivation of Newtonian mechanics without an apriori definition of the concept of work. Furthermore it is shown that energy must be depicted as a function of position and…

The fact that mass has an effect on surrounding space is the first essential element of general relativity. This paper unifies this mass/space distinction of general relativity with Newtonian gravity at a subatomic scale and with reported…

A generalised canonical formulation of gravity is devised for foliations of spacetime with codimension $n\ge1$. The new formalism retains n-dimensional covariance and is especially suited to 2+2 decompositions of spacetime. It is also…

All measurable predictions of classical mechanics can be reproduced from a quantum-like interpretation of a nonlinear Schrodinger equation. The key observation leading to classical physics is the fact that a wave function that satisfies a…

Historically, Ehrenfest's theorem (1927) is the first one which shows that classical physics can emerge from quantum physics as a kind of approximation. We recall the theorem in its original form. Next, we highlight its generalizations to…

Despite the fact that it has been known since the time of Heisenberg that quantum operators obey a quantum version of Newton's laws, students are often told that derivations of quantum mechanics must necessarily follow from the Hamiltonian…

We discuss the use of the variational principle within quaternionic quantum mechanics. This is non-trivial because of the non commutative nature of quaternions. We derive the Dirac Lagrangian density corresponding to the two-component Dirac…

A simple formal procedure makes the main properties of the lagrangian binomial extendable to functions depending to any kind of order of the time--derivatives of the lagrangian coordinates. Such a broadly formulated binomial can provide the…

Two-spinor formalism for Einstein Lagrangian is developed. The gravitational field is regarded as a composite object derived from soldering forms. Our formalism is geometrically and globally well-defined and may be used in virtually any…

Quantum mechanics predicts many surprising phenomena, including the two-slit interference of electrons. It has often been claimed that these phenomena cannot be understood in classical terms. But the meaning of "classical" is often not…

The task of quantizing gravity is compared with Einstein's relativization of gravity. The philosophical and physical foundations of general relativity are briefly reviewed. The Ehlers-Pirani-Schild scheme of operationally determining the…

A system's apparent simplicity depends on whether it is represented classically or quantally. This is not so surprising, as classical and quantum physics are descriptive frameworks built on different assumptions that capture, emphasize, and…

It has been shown in the past century that the particle inertia against velocity change has increased at higher velocity values. This increase has been predicted in principle in the framework of special theory of relativity. However, any…

A theoretical scheme, based on a probabilistic generalization of the Hamilton's principle, is elaborated to obtain an unified description of more general dynamical behaviors determined both from a lagrangian function and by mechanisms not…