Could the Universe be a continuum with one light photon
following another in a never-ending succession?
We experience this process of energy exchange as Time with a
probabilistic future unfolding moment-by-moment, quanta by quanta. The
continuous absorption and emission of light, along with the repetition of the
quantum wave particle function collapsing and reforming would form a mechanism
for generating a probabilistic uncertain future.
Photon spherical oscillations or vibrations precedes
everything with the emerging spherical geometry forming greater degrees of
freedom for statistical entropy and the spontaneous irreversible processes of
classical physics. Such as heat energy always spontaneously flowing from hot to
cold and friction always changing motion into heat.
In this theory the mathematics of Quantum Mechanics
represent, the physics of time with Classical Physics represents processes over
a ‘period of time’ as in Newton's differential equations.
The wave particle duality of light and matter in the form of
electrons is forming a blank canvas that we, as atoms, can interact with
forming a future relative to the energy and momentum of our actions.
At the
smallest scale of this process, we have the Planck constant as a constant of
action. This constant is formed because when there is the absorption and
emission of light the energy levels cannot drop below the centre of the electron
sphere of probability that surrounds the nucleus of the atom. We have to square
the radius because the process is relative to the centre of sphere, formed by
the nucleus of the atom, and the spherical surface.
A repetition of this geometrical process will naturally form
the Fibonacci Spiral and fractal self-similarities we see in nature. Because of
this process of spherical symmetry forming and breaking the future is
probabilistic, but not totally uncertain. There is a built in potential for
greater symmetry to emerge, this formed the potential for the complexity of
cell life and emerges of built in geometrical patterns to our mathematic.
In this theory sporadic group, represent exceptional
symmetries describing the symmetries that remain after a high degree of initial
symmetry as in spherical symmetry that has been broken through a series of quantized
steps. This process of spherical symmetry forming and breaking could explain why
many sporadic group are linked to sphere-packing lattices, including the
Monster, are deeply connected to the symmetries of the Leech lattice, a key
structure in the study of dense sphere packing. Spherical lattice serves as a geometric
foundation for the construction and understanding of many of these exceptional
finite simple groups.
The centre of each sphere within the lattice is a discrete
set of points within a vector space.
In this theory, this is because of a geometrical process linked
to Huygens Principle that says each point on the light wave front acts as a
source of a secondary spherical wavelet. Each point on the wave front has the
potential for a new photon contributing to the probability amplitude and thus the
probability density squared at a future point. The weight of this modular form
is half the dimension of the lattice because the process is based on the radius,
that is squared, is half the diameter of the lattice. The spherical radiant
energy, radiating out from the centre of the sphere could explain the potential
for centralizers of an involution of rather smaller sporadic group. Now called
the baby monster and the slight variation of it centre of an involution in the
monster group.
A process of spherical symmetry forming and breaking can form
a simpler uniform construction of all the finite simple groups. Spherical
symmetry, a high degree of symmetry, is broken as part of a physical systems to
give rise to directional properties and structures explaining why sporadic
group are based on a few simple rules about how we are allowed to shuffle
things, or why very simple axioms are hiding such complexity and beauty in them.
We can think about this just in terms of pictures of a geometrical periodic
pattern on the surface of a sphere.
Something having positive curvature formed
by the outer spherical surface and sometimes having constant negative curvature
formed by the inner concaved spherical surface.
If you add a point at infinity
this fundamental domain is really a Riemann surface with a complex structure
and the mapping that takes a point in tau and maps it to a point on the Riemann
sphere is known as the modular j function.
Based on this dynamic geometry the modular J function, which
shows up in all sorts of number theory, is linked to the monster group the
largest sporadic group forming the idea that sounds so ridiculous that it was
called moonshine. The fundamental domain is the Riemann sphere but if you take
an arbitrary subgroup then the image of it will be some general Riemann surface,
it won't be a sphere, it might be a toroidal doughnut-like shape or something
more complicated formed out of broken spherical symmetry.
In this theory,
mathematics is discovered not invented.
The potential for this can be seen as Ford Circles emerging
naturally in our mathematics. Pascal's triangle is a good example of this; it
is constructed starting with a single '1' at the apex with increasing symmetry
and complexity as it cascades down.
The Fibonacci sequence is within Pascal's
triangle, appears along the shallow diagonals of the triangle where each number
is the sum of the two preceding ones.
Everything is based on the same geometrical
process forming the unity of mathematics and physics within three-dimensional
space with one variable in the form of time.
