![]() Now, physicists and astronomers have always been very detail-oriented people. ![]() A greatly exaggerated example of precession is shown below: Specifically, it precessed at a rate of 1.555 degrees per century. Mercury makes an ellipse that precesses - or rotates - ever so slightly. ![]() But Mercury (above) doesn't quite do that. Kepler's Laws (which can be derived from Newton's Gravity) said that all the planets should move in ellipses around the Sun. You see, there was a tiny, tiny problem with the planet Mercury. But one of them would change our view of the Universe forever. But other than that - and Einstein's new Theory of Special Relativity, there were very few mysteries about the Universe in 1909. There were the first hints that the Universe was made up of quantum particles, such as the photoelectric effect, Rutherford's first hints at the existence of the nucleus, and Planck's view that energy was quantized. The Universe was static, governed by two laws only: Newton's Gravity and Maxwell's Electromagnetism. The night sky, with stars, planets, comets, asteroids, nebulae, and the Milky Way, was viewed to make up the entire contents of the Universe. Its application results in dissipative Schrodinger equations, as well as in a new form of dissipative Liouville equation in classical mechanics.100 years ago, the way we viewed our Universe was vastly different than the way we view it now. A new projector operator is proposed for the collapse of the wave function of a quantum particle moving in a classical environment. In the case of a free quantum Brownian particles, a new law for the spreading of the wave packet it discovered, which represents the quantum generalization of the classical Einstein law of Brownian motion. Its equilibrium solution in the exact canonical Gibbs density operator, while the well-known Caldeira-Leggett equation is simply a linearization at high temperature. A nonlinear master equation is proposed by proper quantization of the classical Klein-Kramers equation. Considering the Brownian dynamics in the frames of the Bohmian mechanics, the density functional Bohm-Langevin equation is proposed, and the relevant Smoluchowski-Bohm equation is derived. A stochastic Lorentz-Langevin equation is proposed to describe the underlaying Brownian-like motion of the point particles in quantum mechanics. Thus, electrons and other point particles are no waves and the wavy chapter of quantum mechanics originated for the force carriers. The Schrodinger equation is explained via collisions of the target point particles with the quantum force carriers, transmitting the fundamental interactions between the point particles. The model of Brownian emitters is theoretically studied and the relevant evolutionary equations for the probability density are derived. A time-acting temperature operator is introduced for the quantum Klein-Kramers and Smoluchowski equations, accounting for the effect of the quantum thermal bath oscillators. Download a PDF of the paper titled Classical and Quantum Brownian Motion, by Roumen Tsekov Download PDF Abstract:In the frames of classical mechanics the generalized Langevin equation is derived for an arbitrary mechanical subsystem coupled to the harmonic bath of a solid.
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