Related papers: A Historical Method Approach to Teaching Kepler's …

The appearance of a geometric flow in the conservation law of particle number in classical particle diffusion and in the conservation law of probability in quantum mechanics is discussed in the geometrical environment of a two-dimensional…

A new interpretation of quantum mechanics, similar to the Copenhagen interpretation, is developed from time-symmetry arguments and commonly held principles concerning time and causality. These principles, which are grounded in ideas outside…

We comment on two issues in quantum cosmology, in the context of the Wheeler-De Witt equation and wave function of the Universe: (i) arrow of time and interpretation of the wave function in the classically allowed regions; (ii) stability of…

Angular momentum is traditionally taught as a (pseudo)vector quantity, tied closely to the cross product. This approach is familiar to experts but challenging for students, and full of subtleties. Here, we present an alternative pedagogical…

Transition to a nonrelativistic Pauli equation in Riemann space of constant positive curvature for a Dirac particle in presence of the Coulomb field is performed in the system of radial equations, exact solutions are constructed in terms of…

We derive a simple analytical expression for the two-body force in a sub-class of MOND-like theories and make testable predictions in the modification to the two-body orbital period, shape, and precession rate, and escape speed etc. We…

Since the advent of quantum mechanics we have mainly been concerned with its predictions from the perspective of an external observer. This is in strong contrast to the theory of general relativity, where the physics is governed by the…

We study the motion of a particle in a 3-dimensional lattice in the presence of a Coulomb potential, but we demonstrate semiclassicaly that the trajectories will always remain in a plane which can be taken as a rectangular lattice. The…

We propose that in time dependent backgrounds the holographic principle should be replaced by the generalized second law of thermodynamics. For isotropic open and flat universes with a fixed equation of state, the generalized second law…

I briefly consider the Kuhnian notion of "paradigm shifts" applied to the history of mathematics and argue that the succession and intergenerational continuity of mathematical thought was undeservedly neglected in the historical studies. To…

Time is a parameter playing a central role in our most fundamental modeling of natural laws. Relativity theory shows that the comparison of times measured by different clocks depends on their relative motions and on the strength of the…

In this article, we review the main results of Volume I of Newton's Principia which relates Kepler's law of planets and universal gravitation. In order to clarify the reasoning of Newton, elementary and simple proofs are given to inspire…

The true and eccentric anomaly parametrizations of the Kepler motion are generalized to quasiperiodic orbits, by considering perturbations of the radial part of the kinetic energy in a form of a series of negative powers of the orbital…

In statistical thermodynamics the 2nd law is properly spelled out in terms of conditioned probabilities. As such it makes the statement, that `entropy increases with time' without preferring a time direction. In this paper I try to explain…

Hodographs for the Kepler problem are circles. This fact, known since almost two centuries ago, still provides the simplest path to derive the Kepler first law. Through Feynman `lost lecture', this derivation has now reached to a wider…

In this work, we introduce the Law of Closest Approach which is derived from the properties of conic orbits and can be considered an addendum to the laws of Kepler. It states that on the closest approach, the distance between the objects is…

Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum…

We give a short review of the recent developments of entropic cosmology based on two thermodynamic laws of the apparent horizon, namely the first and the second laws of thermodynamics. The first law essentially provides the change of the…

The Kepler problem concerns a point particle in an attractive inverse square force. After a brief review of the classical and quantum versions of this problem, focused on their hidden $\text{SU}(2) \times \text{SU}(2)$ symmetry, we discuss…

We investigate learning difficulties among second-year students on electromagnetism courses when they apply Amp\`ere-Maxwell's law. Using phenomenography, we analysed written answers from 65 undergraduate physics students to four questions…