Related papers: Full Nexus between Newtonian and Relativistic Mech…
Strictly speaking, Newton's second law of motion is only an approximation of the so-called relativistic dynamics, i.e., Einstein's modification of the second law based on his theory of special relativity. Although the approximation is…
It is shown that Newtonian mechanics is not appropriate to compute approximate individual trajectories with small velocities in chaotic scattering. However, some global properties of the dynamical system, such as the dimension of the…
The three well-known forms of relativistic dynamics are unitarily equivalent and the problem of constructing the current operators can be solved in any form. However the notion of the impulse approximation is reasonable only in the point…
We study the role of acceleration in the twin paradox. From the coordinate transformation that relates an accelerated and an inertial observer we find that, from the point of view of the accelerated observer, the rate of the differential…
We have constructed a non-relativistic theory of quantum mechanics based on local modulus symmetry. The resulting connection in the covariant derivative is identified as the escape velocity of the gravitational field. A new real and…
This paper concerns the absolute versus relative motion debate. The Barbour and Bertotti 1982 work may be viewed as an indirectly set up relational formulation of a portion of Newtonian mechanics. I consider further direct formulations of…
Modified Newtonian dynamics can be considered as an effect derived from a squeezable extra dimension space. The third law of Newtonian dynamics can be managed to remain valid in the 5-space. The critical acceleration parameter $a_0$ appears…
The shortening of bodies in the direction of motion, Lorentz contraction, follows from the solution of Maxwell's equations. Moving light clocks will tick slower than those at rest because the speed of light does not depend on a source of…
I argue that in the Lagrangian formulation of standard, Galilei-invariant Newtonian mechanics there are subtle but concrete signs of {\em Lorentz} invariance. In fact, in a specific sense made explicit in the paper, Newtonian mechanics is…
We begin with a scenario that involves point-like observers starting at t=0 from the origin O of an inertial reference frame. They move with all possible proper accelerations in the positive direction of the OX axis. Equipped with light…
According to Newton's law of gravitation the force between two particles depends upon their inertial, as well as their active and passive gravitational masses. For ordinary matter all three of these are equal and positive. We consider here…
In relativistic mechanics the energy-momentum of a free point mass moving without acceleration forms a four-vector. Einstein's celebrated energy-mass relation E=mc^2 is commonly derived from that fact. By contrast, in Newtonian mechanics…
In the description of \emph{relative} motion in accelerated systems and gravitational fields, inertial and tidal accelerations must be taken into account, respectively. These involve a critical speed that in the first approximation can be…
Relativistic cosmological perturbation analyses can be made based on several different fundamental gauge conditions. In the pressureless limit the variables in certain gauge conditions show the correct Newtonian behaviors. We consider the…
Contrary to recent claims in the literature, Newtonian N-body simulations of collisionless Dark Matter in a LambdaCDM background are compatible with general relativity and are not invalidated by general relativistic effects at the linear…
A precise formulation of the strong Equivalence Principle is essential to the understanding of the relationship between gravitation and quantum mechanics. The relevant aspects are reviewed in a context including General Relativity, but…
Recently there have emerged an assortment of theorems relating to the 'absoluteness of emerged events,' and these results have sometimes been used to argue that quantum mechanics may involve some kind of metaphysically radical…
Physical theories must stem from observation. The possibility that perceived events are simulated, not real, raises a crucial dilemma about the credibility of known physics, known as the simulation hypothesis. To analyze this hypothesis in…
We consider transformations between uniformly accelerated systems, assuming that the Clock Hypothesis is false. We use the proper velocity-time description of events rather than the usual space-time description in order to obtain linear…
We consider the Newtonian limit of modified theories of gravity that include inverse powers of the curvature in the action in order to explain the cosmic acceleration. It has been shown that the simplest models of this kind are in conflict…