Thursday, November 5, 2015
Mechanical and Electrical Analogy: deriving of mass from charges, posted to talk page in wikipedia
I would love to see a theoretical physics discussion of the origin of the analogy between electrical and mechanical components. On the surface, you could say we find it easy to think in terms of linear systems, so we think of components that act linearly. This leads directly to the same simple differential equations for different systems, especially when conservation of energy is a natural focal point for optimizing engineering applications. The most natural of the possible analogies is the impedance analogy which is the one most commonly used and first cited in the Wikipedia article. The reason for this is that charge in electrical components is simply replaced with meters in the mechanical components. There are no other changes. Capacitors allow charge to build up for a fixed dielectric distance and the analogous spring allows meters to build up for a fixed number of charges (which are the source of resisting compression). For small compressions and non-saturating amounts of charge, both are linear. The same direct relation exists for inductors and mass: inductance (magnetism) from a classical view (pre-quantum) is a relativistic effect of charge build up per unit length, not a thing unto itself. See Schwartz, Feynman, and Wikipedia. For small changes, it is again linear so V=L*di/dt instead of having to resort to full-blown relativistic equations. So it seems mass could be viewed from a pre-quantum perspective as the relativistic effect of (quark?) charges being brought closer together as a result of length contraction. Again, it's linear for small changes in velocity so F=ma instead full-blown relativistic calculations. In short, linear electrical components control charge/length where length is held constant by the component, and mechanical systems do the same but hold the charge constant and allow lengths to change. This is simple enough that there should be some references out there that delve into the source of the analogies and thereby allow it to be included in the article.