Relating the Hamilton Canonical equations and the Evans Eckardt Equations

This will be the next step. The Hamilton canonical equations of 1833 are fundamental equations of motion, and can be written in generalized coordinates as q dot = partial H / partial p, and p dot = – partial H / partial q where p and q are independent conjugate variables. The Hamilton Principle of Least Action also leads to partial H / partial r = – partial L / partial r, where L is the lagrangian. In Note 425(2) some consequences of this we developed, and it was found that dm(r) / dr is a small quantity proportional to angular momentum and inversely proportional to c squared. So the first task is to relate partial H / partial r to partial H / partial t in m space. The latter is zero but the former is not zero. The hamiltonian H is a function of p and r. Quantum mechanics depends on the hamiltonian. The quantum Hamilton equations were developed in the classic UFT175, which is also a definitive refutation of the Copenhagen dogma based on indeterminacy, rejected by Einstein and de Broglie and their School of Thought. Hamilton was made Andrews Professor of Astronomy at Trinity College Dublin when still a twenty one year old undergraduate, and was given accommodation at Dunsilk Observatory, now part of the Dublin Institute for Advanced Studies (DIAS) founded by de Valera, who invited Schroedinger to be its first Director. Dunsilk is just outside Dublin. However Hamilton had essentially no experience in observation and soon lost all interest in astronomy but kept his job and accommodation. This is lucky for the rest of physics. In 1826 Hamilton received an optime in both science and classics, a feat that had never been equalled, and I do not think it has been equalled to date. At that time TCD was reserved for the protestant ascendancy, and for the sons of the Irish nobility and gentry and similar. It is described in the second volume of my autobiography. I had given an invited lecture at DIAS and was invited to walk over to TCD by Bill Coffey, who was a Catholic, so by that time TCD was interdenominational, admitting both men and women. It has a lavish life style, with Commons off silver plates with servants, and Latin Grace to its founder, my ancestral cousin Elizabeth Tudor: “Laudamus te, benegnissime Pater, pro sernissimis, regina Elizabetha hujus Collegii conditrice, …” I sat at high table with the Fellows, one of whom would talk interminably, never stopping, of how unwise it is to be a republican. Naturally he was a unionist. There were portraits all around the walls. I was a long haired yob from Aberystwyth, known in Dublin as a muck turtle. Michael Collins, the Big Fella, for example was the muck turtle from West Cork, thus named by the Dublin jackeens. On one occasion Garett Fitzerald the Taoiseach dined at the College. Usually I was hungry after athletics and the serving of the food off silver plates was interminably slow, so I stopped this gabbing fella with a quote from Oscar Wilde, who was educated at Trinity College Dublin : “Work is the enemy of the drinking classes”, at which point the monologue was drowned by republican laughter. Coffey dragged me off to senior common room for rich coffee, and then to his drinking clubs. The fact that I did not drink made no difference to Coffey, whose consumption of alcohol was as remarkable as that of Hamilton.


%d bloggers like this: