Related papers: Hilbert's 6-th Problem and Axiomatization of Dynam…
The constraint distribution in non-holonomic mechanics has a double role. On one hand, it is a kinematic constraint, that is, it is a restriction on the motion itself. On the other hand, it is also a restriction on the allowed variations…
In this paper, we investigate the validity of the generalized second law of thermodynamics of the universe bounded by the event horizon. Here we consider homogeneous and isotropic model of the universe filled with perfect fluid in one case…
Hilbert's sixth problem calls for the axiomatization of physics, particularly the derivation of macroscopic statistical laws from microscopic mechanical principles. A conceptual difficulty arises in classical probability theory: in…
Among theoretical issues in General Relativity the problem of constructing its Hamiltonian formulation is still of interest. The most of attempts to quantize Gravity are based upon Dirac generalization of Hamiltonian dynamics for system…
Newtonian dynamics is derived from prior information codified into an appropriate statistical model. The basic assumption is that there is an irreducible uncertainty in the location of particles so that the state of a particle is defined by…
A new approach to relativistic mechanics is proposed, suitable to describe dynamics of different kinds of relativistic particles. Mathematically it is based on an application of the recent geometric theory of nonholonomic systems on fibred…
The Hamiltonian defines the dynamical properties of the universe. Evidence from particle physics shows that there is a different version of the Hamiltonian for each direction of time. As there is no physical basis for the universe to be…
In this paper we use the framework of generalized probabilistic theories to present two sets of basic assumptions, called axioms, for which we show that they lead to the Hilbert space formulation of quantum mechanics. The key results in…
In this paper I propose a new principle in physics: the principle of "finiteness". It stems from the definition of physics as a science that deals (among other things) with measurable dimensional physical quantities. Since measurement…
The principle of relativity is extended to accommodate finite-mass observers with quantum properties by introducing two operational requirements: (i) equivalence of observers at the level of transition amplitudes, and (ii) the impossibility…
This article is an attempt for a new vision of the basics of Physics, and of Relativity, in particular. A new generalized principle of inertia is proposed, as an universal principle, based on universality of the conservation laws, not…
We describe how geometrical methods can be applied to a system with explicitly time-dependent second-class constraints so as to cast it in Hamiltonian form on its physical phase space. Examples of particular interest are systems which…
In a previous paper [1] we considered the question, "What underlying property of nature is responsible for the second law?" A simple answer can be stated in terms of information: The fundamental loss of information gives rise to the second…
This work is basically about the general form of Newton's second law for variable mass problems. We develop a model for describing the motion of the one-dimensional oscillator with a variable mass within the framework of classroom physics.…
We relate Newton's Second Law with the Second Law of Thermodynamics through the analysis of a simple model introducing a dynamic pressure concept. From this analyses we can clarify some conceptual problems resulting from several concepts of…
We report on recent developments towards a relativistic quantum mechanical theory of motion for a fixed, finite number of electrons, photons, and their anti-particles, as well as its possible generalizations to other particles and…
Since Newton, all classical and quantum physics depends upon the "Newtonian Paradigm". Here the relevant variables of the system are identified. The boundary conditions creating the phase space of all possible values of the variables are…
This paper considers systems subject to nonholonomic constraints which are not uniform on the whole configuration manifold. When the constraints change, the system undergoes a transition in order to comply with the new imposed conditions.…
Theory of Newtonian dynamical systems admitting normal shift of hypersurfaces was first developed for the case of Riemannian manifolds. Recently it was generalized for manifolds geometric equipment of which is given by some regular…
The problem of the dynamical stability of anistropic systems is studied, by proposing a criterion in terms of the adiabatic local index $\gamma$. The result has general validity and can be applied to several physical situations.…