Dynamics of Current, Charge and Mass Bob Eisenberg Department of Applied Mathematics Illinois Institute of Technology USA Department of Physiology and Biophysics Rush University USA
[email protected] Xavier Oriols Departament d’Enginyeria Electrònica, Universitat Autònoma de Barcelona, SPAIN
[email protected] David Ferry School of Electrical, Computer, and Energy Engineering Arizona State University USA
[email protected] Available on arXivhttps://arxiv.org/abs/1708.07400 at September 6, 2017 ABSTRACT Electricity plays a special role in our lives and life. The dynamics of electrons allow light to flow through a vacuum. The equations of electron dynamics are nearly exact and apply from nuclear particles to stars. These Maxwell equations include a special term, the displacement current (of a vacuum). The displacement current allows electrical signals to propagate through space. Displacement current guarantees that current is exactly conserved from inside atoms to between stars, as long as current is defined as the entire source of the curl of the magnetic field, as Maxwell did. We show that the Bohm formulation of quantum mechanics allows the easy definition of current without the mysteries of the theory of quantum measurements. We show how conservation of current can be derived without mention of the polarization or dielectric properties of matter. We point out that displacement current is handled correctly in electrical engineering by ‘stray capacitances’, although it is rarely discussed explicitly. Matter does not behave as physicists of the 1800's thought it did. They could only measure on a time scale of seconds and tried to explain dielectric properties and polarization with a single dielectric constant, a real positive number independent of everything.