Related papers: A Historical Method Approach to Teaching Kepler's …
Kepler's laws of planetary motion are deduced from those of a harmonic oscillator following Arnold. Conversely, the circular orbits through the Earth's center suggested by Galilei are consistent with an $r^{-5}$ potential as found before by…
The view that the laws of nature produce later states of the universe from earlier ones (prominently defended by Maudlin) faces difficult questions as to how the laws produce the future and whether that production is compatible with special…
In a recent paper, PNAS, 118, e1921529118 (2021), it was argued that while the standard definition of conservation laws in quantum mechanics, which is of a statistical character, is perfectly valid, it misses essential features of nature…
We study the evolution of the universal area law of entanglement entropy when the Hamiltonian of the system undergoes a time dependent perturbation. In particular, we derive a general formula for the time dependent first order correction to…
This recreational paper investigates what happens if we change quantum mechanics in several ways. The main results are as follows. First, if we replace the 2-norm by some other p-norm, then there are no nontrivial norm-preserving linear…
We apply Feynman's principle, ``The same equations have the same solutions'', to Kepler's problem and show that Newton's dynamics in a properly curved 3-D space is identical with that described by Einstein's theory in the 3-D optical…
This paper is a sequence of the work presented in [1], where, the principles of the general relativity have been used to formulate quantum wave equations taking into account the effect of the electromagnetic and strong interactions in the…
In this paper we clarify and generalise previous work by Moser and Belbruno concerning the link between the motions in the classical Kepler problem and geodesic motion on spaces of constant curvature. Both problems can be formulated as…
Lorentz covariance imposed upon a quantum logic of local propositions for which all observers can consistently maintain state collapse descriptions, implies a condition on space-like separated propositions that if imposed on generally…
Boltzmann's principleS=k*ln W is generalized to non-equilibrium Hamiltonian systems with possibly fractal distributions in phase space by the box-counting volume. The probabilities P(M) of macroscopic observables M are given by the ratio…
Kepler's orbits with corrections due to Special Relativity are explored using the Lagrangian formalism. A very simple model includes only relativistic kinetic energy by defining a Lagrangian that is consistent with both the relativistic…
The Kullback-Leibler inequality is a way of comparing any two density matrices. A technique to set up the density matrix for a physical system is to use the maximum entropy principle, given the entropy as a functional of the density matrix,…
We study the long time motion of fast particles moving through time-dependent random force fields with correlations that decay rapidly in space, but not necessarily in time. The time dependence of the averaged kinetic energy and…
In classical general relativity described by Einstein-Hilbert gravity, black holes behave as thermodynamic objects. In particular, the laws of black hole mechanics can be interpreted as laws of thermodynamics. The first law of black hole…
Assorted questions: Time as a parameter in Quantum Mechanics. No-Go theorems for a time operator. Localization, time and causality. Causality violation. Localization again. Lesson 1: Evading the troubles: Im E finite. Lights and shadows of…
It is shown that the force in relativistic mechanics is not only the cause of acceleration of particle relative to an inertial frame of reference, but also the cause of change of the course of time along the particle's trajectory. Therein…
This paper frames calculus as a global, centuries-long development rather than a subject that began only with Newton and Leibniz. Drawing on ideas from Greek, Indian, Islamic, and later European mathematics, it highlights how concepts like…
A classical and quantum mechanical generalized second law of thermodynamics in cosmology implies constraints on the effective equation of state of the universe in the form of energy conditions, obeyed by many known cosmological solutions,…
Based on recent data about the history of the Hubble factor, it is argued that the second law of thermodynamics holds at the largest scales accessible to observation. This is consistent with previous studies of the same question.
The lecture explains the geometric basis for the recently-discovered nonholonomic mapping principle which specifies certain laws of nature in spacetimes with curvature and torsion from those in flat spacetime, thus replacing and extending…