Related papers: Axioms for Mach's mechanics
Mechanics can be founded on a principle relating the uncertainty delta-q in the trajectory of an observable particle to its motion relative to the observer. From this principle, p.delta-q=const., p being the q-conjugated momentum,…
The analyses of high precision astrometric surveys, such as Gaia, implicitly assume a modern version of Mach's Principle: the local inertial frame of our Solar System should be non-rotating in the frame of distant quasars. On the contrary,…
We present a new test for a possible Mach-Sciama dependence of the Gravitational constant G. According to Ernst Mach (1838-1916), the gravitational interaction depends on the distribution of masses in the universe. A corresponding…
We apply the algebraic theory of infinite classical lattices from Part I to write an axiomatic theory of measurements, based on Mackey's axioms for quantum mechanics. The axioms give a complete theory of measurements in the sense of Haag…
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…
Formal definition of the reference frame is given. This definition is valid for nonrelativistic and relativistic cases. Proposed definition allows using wide classes of reference frames without restriction to inertial, uniformly accelerated…
Riemann's principle "force equals geometry" provided the basis for Einstein's General Relativity - the geometric theory of gravitation. In this paper, we follow this principle to derive the dynamics for any static, conservative force. The…
We propose a reformulation of gravitation in which the gravitational interaction is treated as a genuine force rather than an inertial effect arising from spacetime geometry. Within this framework, the difference between the affine…
We show that non-relativistic Quantum Mechanics can be faithfully represented in terms of a classical diffusion process endowed with a gauge symmetry of group Z_4. The representation is based on a quantization condition for the realized…
The force exerted by an electromagnetic body on another body in relative motion, and its minimal expression, the force on moving charges or \emph{Lorentz' force} constitute the link between electromagnetism and mechanics. Expressions for…
The logical line is traced of formulation of theory of mechanics founded on the basic correlations of mathematics of hypercomplex numbers and associated geometric images. Namely, it is shown that the physical equations of quantum, classical…
This note is an extended version of "A note on the foundations of Mechanics", arXiv: 1404.1321 [math-ph]. A presentation of its contents was given in a talk in memorial homage to the professor Juan B. Sancho Guimer\'a. For this reason, it…
We show that the dragging of the axis directions of local inertial frames by a weighted average of the energy currents in the universe is exact for all linear perturbations of any Friedmann-Robertson-Walker (FRW) universe with K = (+1, -1,…
This paper elaborates on relationalism about space and time as motivated by a minimalist ontology of the physical world: there are only matter points that are individuated by the distance relations among them, with these relations changing.…
The problem of axiomatization of physics formulated by Hilbert as early as 1900 and known as the Sixth Problem of Hilbert is nowadays even more topical than at the moment of its formulation. Axiomatic inconsistency of classic, quantum, and…
We adopt a 'thermodynamical' formulation of Mach's principle that the rest mass of a particle in the Universe is a measure of its long-range collective interactions with all other particles inside the horizon. We consider all particles in…
In the present work we propose a generalization of Newton's gravitational theory from the original works of Heaviside and Sciama, that takes into account both approaches, and accomplishes the same result in a simpler way than the standard…
In this paper we generalize the ideas of de Broglie and Bohm to the relativistic case which is based on the relativistic Schr\"odinger equation. In this regard, the relativistic forms of the guidance equation and quantum potential are…
The gap between classical mechanics and quantum mechanics has an important interpretive implication: the Universe must have an irreducible fundamental level, which determines the properties of matter at higher levels of organization. We…
Consider the configuration space Q for some physical system, and a continuous group of transformations G whose action on the configurations is declared to be physically irrelevant. Implement G indirectly by adjoining 1 auxiliary g per…