相关论文: On the foundation of Mechanics

This short note is intended to review the foundations of mechanics, trying to present them with the greatest mathematical and conceptual clarity. It was attempted to remove most of inessential, even parasitic issues, which can hide the true…

In this article we study the nature of time in Mechanics. The fundamental principle, according to which a mechanical system evolves governed by a second order differential equation, implies the existence of an absolute time-duration in the…

The aim of this paper is twofold: First, we give a formal introduction to the basics of the mathematical framework of classical mechanics. Along the way, we prove a Hamiltonian and a Lagrangian version of Noether's Theorem, an important…

Despite its apparent simplicity, Newtonian Mechanics contains conceptual subtleties that may cause some confusion to the deep-thinking student. These subtleties concern fundamental issues such as, e.g., the number of independent laws needed…

This paper collects and extends the lectures I gave at the "XXIV International Fall Workshop on Geometry and Physics" held in Zaragoza (Spain) August 31 - September 4, 2015. Within these lectures I review the formulation of Quantum…

These lecture notes were prepared as a basic introduction to the theory of constrained systems which is how the fundamental forces of nature appear in their Hamiltonian formulation. Only a working knowledge of Lagrangian and Hamiltonian…

The axiomatic structure of the electromagnetic theory is outlined. We will base classical electrodynamics on (1) electric charge conservation, (2) the Lorentz force, (3) magnetic flux conservation, and (4) on the Maxwell-Lorentz spacetime…

This is the logical foundation for for Relativity Theory, Probability Theory, and for Quantum Theory. Contents is the following: 1 Introduction. 2 Classical logic. 3 Time and space. 3.1 Recorders. 3.2 Time. 3.3 Space. 3.4 Relativity. 4.…

Some aspects of the interpretation of quantum theory are discussed. It is emphasized that quantum theory is formulated in the Cartesian coordinate system; in other coordinates the result obtained with the help of the Hamiltonian formalism…

This paper expounds the relations between continuous symmetries and conserved quantities, i.e. Noether's ``first theorem'', in both the Lagrangian and Hamiltonian frameworks for classical mechanics. This illustrates one of mechanics' grand…

These notes provide an introduction to a number of those topics in Classical Mechanics that are useful for field theory.

Hamilton's principle of stationary action lies at the foundation of theoretical physics and is applied in many other disciplines from pure mathematics to economics. Despite its utility, Hamilton's principle has a subtle pitfall that often…

The paper shows the relationship between the major wave equations in quantum mechanics and electromagnetism, such as Schroedinger's equation, Dirac's equation and the Maxwell equations. It is shown that they can be derived in a striking…

As it is well known, classical mechanics consists of several basic features like determinism, reductionism, completeness of knowledge and mechanicism. In this article the basic assumptions are discussed which underlie those features. It is…

This contribution analyses the classical laws of motion by means of an approach relating time and entropy. We argue that adopting the notion of change of states as opposed to the usual derivation of Newton's laws in terms of fields a…

Classical, Quantum, Relativistic and Statistical: the four branches of mechanics. However, the Quattro Donna of Physics disagree even about the entities that are supposed to be fundamental, such as space, matter and time. In order to search…

In this paper we will present tha main features of what can be called Schwinger's foundational approach to Quantum Mechanics. The basic ingredients of this formulation are the \textit{selective measurements}, whose algebraic composition…

In 1834-1835, Hamilton published two papers that revolutionized classical mechanics. In these papers, he introduced the Hamilton-Jacobi equation, Hamilton's equations of motion and the principle of least action. These three formulations of…

This paper proposes a basic theory on physical reality and a new foundation for quantum mechanics and classical mechanics. It presents a scenario not only to solve the problem of the arbitrariness on the operator ordering for the…

We propose six principles as the fundamental principles of quantum mechanics: principle of space and time, Galilean principle of relativity, Hamilton's principle, wave principle, probability principle, and principle of indestructibility and…