Natural Science Forum / Physics / General Physics / March 2007

Another justification for physicists' doing away with probability and
force (not to mention logic) in Quantum Field Theory is the claim that
vector fields do not allow point masses or point particles, which
seemed to them to eliminate forces and probability since points had
played an important role in them.

Vector fields are a branch of vector analysis, but vectors really are
a branch of calculus which in turn was developed by Newton and Leibniz
almost entirely on a point mass or particle basis.   It is true that a
field of vectors seems to be "distributed", but only in the sense that
a Plurality of people looks distributed even though it is composed of
nothing but Individuals.   Take away the Individuals, and you have
nothing.

But how do you formulate a point particle in vector analysis when most
of the equations do not explicitly refer to points?   First of all,
you've already chosen equations that refer to points by definition, so
you're already using garbage in-garbage out.  Secondly, you don't have
to regard vector analysis as the ONLY tool in your repertoire.
Physicists who get obsessed on one branch of mathematics often forget
that many mathematical quantities are defined piecewise, that is to
say differently on different intervals or regions.   Combinations of
different types of quantities have even been found very valuable in
Clifford algebra and Grassmann Algebra.   The same people who regard
superposition as vital cannot draw the line at particles as distinct
from fields!

Osher Doctorow