Error and correction of Brownian motion research method

• 1、Department of Precision Instrument,Tsinghua University

Abstract：In this paper, a series of abnormal problems in Brownian motion theory, such as "Brownian particle displacement obeys normal distribution", "Brownian particle displacement is proportional to the square root of time" and "Brownian particle instantaneous velocity is infinite", are analyzed, and it is pointed out that the probability analysis method assumes that the displacement of Brownian particle at a certain time obeys a certain probability distribution, Virtually changing the research object from a Brownian particle to a set of a large number of Brownian particles, and describing the individual behavior of a Brownian particle with the statistical law describing the collective behavior of a large number of Brownian particles, is the fundamental reason for a series of abnormal problems in Brownian motion theory. In this paper, the quantitative relationship between Brownian particle displacement and time is reduced to a time function, the Brownian motion law of "the instantaneous velocity of Brownian motion is equal to white noise" is proposed, and the Brownian particle kinematics equation which can correctly describe the phenomena, characteristics and laws of Brownian motion is given.

Keywords： Brownian motion；probabilistic analysis；function analysis