I’ve been studying Classical Mechanics. Bui and Teetee wanted to know why I should be studying mechanics again if I had had physics in high school and college. So I had to explain to them that mechanics was reformulated a hundred years after Newton by the French mathematician Lagrange; and then yet again, another hundred years after Lagrange, by the Irish mathematician Hamilton. It is the mechanics of Lagrange and Hamilton that I am now after. I was thinking also that it might interest young people like Bui and Teetee to learn that the traditional statements of Newton’s Second Law (F=ma) and Third Law (action = reaction) are, strictly speaking, false --- the Third “Law” even more than the Second. The Second Law fails because mass keeps increasing with velocity, as we learnt from Einstein, and the way to preserve the sanctity of the Second is to reformulate it to say that force equals the rate of change of momentum. In that form the Second Law holds even at relativistic velocities. The Third Law however is hopeless, because Newton requires that at any instant of time action equals reaction. But the notion of simultaneity of two events does not survive relativity. Two events, simultaneous to one observer, need not be simultaneous to another. So the third law is no law at all. If this were to be mentioned casually to high school kids, even without getting into the failure of the notion of simultaneity in any detail, I think it would intrigue and fascinate them. Here, however, for those who would dwell a moment on it, is a nice paradox to think about. Suppose we have an electric charge X traveling along the x axis, and another charge Y traveling along the y axis. Let these charges move at non-relativistic speeds, so the third law we expect will hold. Show that the force on X due to Y is not equal and opposite to the force on Y due to X. Does the Third then fail even at non-relativistic velocities?
Posted on: Fri, 06 Jun 2014 04:36:35 +0000
Trending Topics
Recently Viewed Topics
© 2015