Quantum explanation of Brownian motion

Thomas Nordstrom PhD

In this paper the concept random is investigated, for the notable reason that it is based on probability rather than determinism. Is the question relevant Can there be an alternative explanation Are experiments biased by the theory The random movement of particles in fluids is called Brownian motion. When particles in a fluid collider with fast-moving molecules the result is a random motion of these particles. The motion is not deterministic, i. e. the particles have what is called a random walk. At the fundamental level there are flows of packages, e. g. rivers or winds that carry the smaller particles from one place to another, i. e. aRb. The validity of the random theories cannot be proven in any experiments, since the circumstances are manipulated according to the theory. Within aRb it is Nature that decides, i. e. at the fundamental level, while at the surface level chaotic motion is admitted. Imagine sliding down a helter-skelter, wobbling from side to side, but still on your way down. The conclusion: 1. The Brownian motion, i. e. why particles move, depends on the flow of packages in nature.2. The question concerning Brownian motion is not relevant.3. The Kinetic Theory has to be discussed.

Vinay Ambegaokar

Alexey A. Kryukov

The motion of a ball through an appropriate lattice of round obstacles models the behavior of a Brownian particle and can be used to describe measurement on a macro system. On another hand, such motion is chaotic and a known conjecture asserts that the Hamiltonian of the corresponding quantum system must follow the random matrix statistics of an appropriate ensemble. We use the Hamiltonian represented by a random matrix in the Gaussian unitary ensemble to study the Schrödinger evolution of non-stationary states. For Gaussian states representing a classical system, the Brownian motion that describes the behavior of the system under measurement is obtained. For general quantum states, the Born rule for the probability of transition between states is derived. It is then shown that the Schrödinger evolution with such a Hamiltonian models measurement on macroscopic and microscopic systems, provides an explanation for the classical behavior of macroscopic bodies and for irreversibility of a measurement, and identifies the boundary between micro and macro worlds.

Aniello Lampo, Miguel Ángel García March, Maciej Lewenstein

Alexey A. Kryukov

Abstract The motion of a ball through an appropriate lattice of round obstacles models the behavior of a Brownian particle and can be used to describe measurement on a macro system. On another hand, such motion is chaotic and a known conjecture asserts that the Hamiltonian of the corresponding quantum system must follow the random matrix statistics of an appropriate ensemble. We use the Hamiltonian represented by a random matrix in the Gaussian unitary ensemble to study the Schrödinger evolution of non-stationary states. For Gaussian states representing a classical system, the Brownian motion that describes the behavior of the system under measurement is obtained. For general quantum states, the Born rule for the probability of transition between states is derived. It is then shown that the Schrödinger evolution with such a Hamiltonian models measurement on macroscopic and microscopic systems, provides an explanation for the classical behavior of macroscopic bodies and for irreversibility of a measurement, and identifies the boundary between micro and macro worlds.

Mikio Namiki