Re: About absolute reference frame......

Mike wrote:
Tom Roberts wrote:
F = m a - m w x (w x r) - 2 m w x v
(F, v, and a are 3-vectors; w is the pseudo-3-vector rotation;
m is the mass of the object)
Here w is a frame-dependent violation. Now this example is obviously
rotating frames in Newtonian mechanics, but the point is that the
appearance of any vector describing the _frame_ is not allowed.

This does not constitute a violation of Newton's
law.

Sure it does! Newton's second law is F=ma, and in a rotating frame that simply does not hold -- one must _invent_ fictitious "forces" (called "centrifugal force" and "Coriolis force") in order to "save" the law. Those fictitious "forces" are special, are coordinate dependent (i.e. rotation dependent), and cannot possibly be real (because they are coordinate dependent).

And also: I was not discussing Newton's laws, this was an _example_ I used while discussing the PoR.


Still, the sum of all forces acting on a body is equal to ma.

Calling the last two terms in my equation above "forces" does not make them so. <shrug>


Since one needs to add those fincticious forces in non-inertial FoR,
some naive philosophers thought the law was violated. You can easily
correct that as D'Alembert did by eliminating the term "impressed" and
define: Sum(F) = dp/dt

That does not solve the problem.

This approach can solve the problem, but one needs differential geometry and a _covariant_ derivative (remember that p is a 3-vector).


Tom Roberts tjroberts@xxxxxxxxxx
.