Re: [Phys-l] Equations (causal relationship)

[Jack Uretsky <jlu@hep.anl.gov>]

Hi all-
	This thread seems to disclose a basic lack of understanding of the 
concept of a "vector".  Perhaps the confusion will be lessened if we write
N2 as (LaTeX notation)
		\vec{F}_{net) = m\vec{a}_{net}
or, in words,
	"the vector representing the net force = the mass times the
vector representing the net acceleration"
	The projection of this vector equation along any direction remains 
a (correct) scalar equation.
	It is possible to decompose a vector into a sum of any number of 
other vectors; such a decomosition is not unique, so it is meaningless to 
speak of a (net) vector as being "composed" of a particular set of other
vectors.
	There are many ways to represent a vector.  One instructive way, 
in 3-space, is to represent a vector as a set of 3 numbers:
	\vec{V} = [x,y,z]  You may, if you like, write each member of the
set as a sum of n other numbers.  Doing so, corresponds to an n-fold 
decomposition the the vector \vec{V}.
	Exercise: Show that there exist n-fold decompositions of vectors 
F and a leading to n scalar N2 equations, where n is an arbitrary number.
Argue that this n-fold decomposition can be spoken of as the result of
"n forces acting on the mass m".
				Regards,
					Jack








On Sun, 30 Apr 2006, Bernard Cleyet wrote:

> This reminds me of linear polarization, of which there are two not one
> in each case.  This is shown by inserting a polarizer at 45 deg. (w/
> crossed source and detector.)  So a linear polarized EM wave will cause
> two accelerations on a charge.
>
> bc, who suspects newton's laws, applied macroscopically, don't
> completely describe the Physics.
>
> John Denker wrote:
>
> > Michael Edmiston wrote:
> >
> >
> >
> > > What do the equations say about the superposition of three electric
> > > fields.  Do the equations say there are three fields at that point, or
> > > one?
> >
> > Before I answer the question, let me point out that the answer
> > cannot possibly provide evidence in favor of the notion that
> > "forces cause accelerations and not vice versa".
> >  -- Electric field at a point is a vector.
> >  -- Force is a vector.
> >  -- Acceleration is a vector.
> >
> > The math is the same.  The physical interpretation is the same.
> >
> > The laws of physics do not give any preference to forces relative to
> > accelerations.
> >
> > ==========
> >
> > To answer the question:  The equations are silent on the issue.
> >
> > To be specific, suppose
> >    Etot = E1 + E2 + E3
> >
> > Then there is *no* equation that can tell the difference between Etot
> > and (E1 + E2 + E3).  This cuts to the core of what "equals" means.
> >
> > This is the "substitution property of equality"
> >   http://en.wikipedia.org/wiki/Substitution_property_of_equality
> >
> > This answer has nothing to do with the physics of forces or accelerations.
> > This comes from the uttermost foundations of arithmetic.
> >
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