ON THE GENERALIZATION OF EINSTEIN’S IDEA OF THE PHOTOELECTRIC WORK FUNCTION: EXAMPLE FROM SCANDINAVIAN CLIMATE DATA
A linear law, with a nonzero intercept c, of the type y = hx + c = h(x – x0), is often observed when we analyze our (x, y) observations on a number of complex systems. The climate system data is considered here for illustrative purposes. The nonzero c in such a law is like the nonzero work function W, conceived by Einstein, in 1905, to explain the photoelectric effect. Einstein’s law was thus able to explain the cut-off frequency observed experimentally by Lenard. Likewise, there is a cut-off x0 = -c/h. The photoelectric law implies a movement of the empirical observations along a family of parallel lines. A similar movement along parallels is observed if we analyze our (x, y) observations carefully. The method of deducing the existence of such parallels is also discussed and is traced to the method used by Millikan to determine the two universal constants: the absolute magnitude on the charge q on a single electron and the Planck constant h.
In the attached I have discussed how nonlinearity arises as we analyze the Russian data for precipitation reported by several weather stations (184 total). This also been posted in response to a question on nonlinearity posed by Prof. Derek Abbott, which is reproduced below.
The paradox of infinity: where does the nonlinearity come from?
The principle of linear superposition holds for the integers, eg. 3 + 4 = 7. However, when we take the integers out to infinity we now obtain nonlinear behaviour. Infinity plus any amount is still infinity, so linearity has broken down.