Natural Science Forum / Physics / Relativity / October 2005

The I subscript is for inertia, not for an element. I didn't intend for
the equation to be in element notation. The equation
f = Ma
as I had inteded it means that the ordinary force as a vector is equal
to the Mass as a matrix times the acceleration as a vector. There is
nothing wrong with doing this and I think it was Steve Carlip that I
first heard suggest that it could be done. An addendum was added to the
relativity faq demonstrating that it could be done but he didn't work
out what the Matrix actually looked like in terms of its components.
Someone asked me what the matrix looked like so I wrote it out. The
only difference between what I wrote out and what he suggested could be
done was that he used it to say three component force is 3X3 matrix M
multiplying three component acceleration whereas to be more general I
extended the definitions of ordinary force and coordinate acceleration
to include a fourth element(not four-vectors). So my equation reads
four component ordinary force is 4X4 matrix M mutltiplying four
component acceleration. To visualise the product take the force and
acceleration to be columb vectors. It works out fine. In element
notation his would read
f^i = M^i_J*a^J
where the Matrix M elements are M^i_J
I didn't want to do that because someone will confuse f and a with
four-vector force F and four-vector acceleration A, but in element
notation mine would read
f^mu = M^mu_nu*a^nu

Well then perhaps you should explain to Steve Carlip why you think the
addendum should be removed. All I am saying is that someone wanted to
know what the matrix referred to in it looked like once written out and
so I am showing it to people at the link. I called it matrix mass
specifically to draw attention to the post. I see it did that, good.
Now if you'll visit the link you'll see that I don't hide the
underlying physics, nor do I think of this matrix as the mass. If
you'll read it you will see that I start out with a four-vector
equation where the mass m is an invariant and then from that work out
the relation between ordinary force and coordinate acceleration and
then mention that this result can be written as a matrix equation and
write out the matrix M. It isn't a fog of symbols, I work it out step
by step explicitly defining each term as I go. If you'll read it, you
will see that I think of the invariant m as the mass, not the matrix M.
I didn't think the i sucscript would be confused for an idex because
the rest of the equation was obviously not in element notation. I just
meant for it to mean inertia.

There aren't two different clocks for a. It isn't four-vector
acceleration.
a^0 = d^2x^2/dt^2
a^0 = (d/dt)(dx^0/dt)
a^0 = (d/dt)(dct/dt)
a^0 = (d/dt)(cdt/dt)
a^0 = (d/dt)(c)
a^0 = 0
Those wanting details:
http://s2.phpbbforfree.com/forums/modernscience-about22.html