Re: The Problem of (and Solution to) Time



Rock Brentwood wrote:

You don't need to go too far in exotic directions for any of this. In
fact, the 5-D geometry is a commonly used device in the representation
theory of the Galileii group and even finds application in such fields
as solid state physics (e.g. semiconductor and transistor physics,
where on is making use of the *non-relativistic* formulation of
quantum field theory; Dirac equation, path integrals, etc.)

As it is necessary to solve the problem of time, so it is necessary to
explain the fundamental interactions. Approaches based on Clifford
algebra and the concept of 16-D Clifford space seem to be very
promising. A by product is a possible resolution of the issue of time,
since a 5-D geometry is embedded in Clifford space.

Although the term "Clifford space" sounds very abstract mathematical, it
is just an extension of the space of points to the space of higher grade
objects -- oriented areas and volumes. The latter objects can be handled
mathematically by means of Clifford algebra, whereas physically they are
associated with extended objects living in space time. Once one extends
a vector space (which is a tangent space to the spacetime manifold) to
the corresponding Clifford algebra (which in turn is a tangent space to
the Clifford space) one finds that "miraculously" spinors enter the
game. Spinors are nothing but certain Clifford numbers, for instance the
sum of a time-like and a space-like vector acting on a special Clifford
number (a "vacuum"). This is a well known result in mathematical
physics.

In a curved 16-D Clifford space, one obtains not only the 4-D gravity,
but also other interactions ('a la Kaluza-Klein). It appears that a nice
and coherent picture is starting to emerge, the issue of time being just
a part of it.

.