Actually Stan Szygmunt, who is my physics conscience, reminded me that a
slightly different form of the law holds in General and Special
relativity. It is
f=dp/dt
where dp is the change in momentum. Now I can not find in the Principia
where Newton actually used this form of his law, it does hold in Newtonian
mechanics as well and is the general Newtonian form. This form is
necessary to derive the rocket equation:
F=(dm/dt)v+m(dv/dt)
>Even then, though, the meaning of the terms has changed significantly
> from a philosophical perspective. E.g., Newtonians would have taken
> the following as either axiomatic or self-evident (for those with a
> scientific background): (1) Absolute Space, (2) Absolute time, (3)
> Absolute mass, (4) Absolute Energy, (5) Causal Determinism, (6) No
> action at a distance (gravity warily excepted). According to our
> current understanding, which may itself be wrong (foundations of
> physics reads more like philosophy than physics), all of these
> foundations are wrong. (There are other things wrong, too, but I'm
> focusing on the fundamentals.) They're not -approximately- right,
> unless one has a -really- broad notion of approximately; they're
> simply wrong. Space is not absolute, it is relative. Time is not
> absolute, it is relative. Etc. The truth value of the Newtonian
> axioms is zero, not one. But the PREDICTIONS based upon them are
> approximately correct (NEVER [I believe] IN PRINCIPLE 100% right,
> except wrt tautologies; but often IN PRACTICE 100% right.)
>
Obviously I agree that Newton's definitions of time, space etc as
absolutes are not true. But in the purest form, physics is F=dp/dt.
Almost everything follows from this. I think a case can be made that if
this equation is called Newtonian mechanics, then Einstein is a subset of
Newton.
>So if Newton and Einstein both have F=ma, but F, m, and a have
> significantly different definitions (from a philosophical perspective;
> not wrt, say, civil engineering), I still think it's accurate to say
> that Newton, philosophically speaking, simply got it wrong. Even the
> brightest and most scientifically productive man who ever lived made
> mistakes in his conception of the ultimate nature of matter and the
> universe. But none of us would have done nearly as well, obviously.
> This is not a call to ridicule Newton -- not at all!!! -- but a call
> to realize the limits of science and our own intellects.
>
Granted. And here is another problem. General Relativity (GR) and
quantum mechanics appear to be mutually exclusive and yet within their
respected realms,they appear to be observationally verified. Gravity does
not easily quantize. Gravity within GR is curvature of space-time. How
is this curvature to be taken in small steps? So Einstein and Schrodinger
may both be wrong in their concepts of the ultimate reality.
I will stand corrected if Stan says so. :-)
glenn
Foundation,Fall and Flood
http://members.gnn.com/GRMorton/dmd.htm