
Fine cuisine depends on starting with the best ingredients. Great physics
depends on using new powerful math. An event in spacetime has one
dimension for time and three dimensions for space, the most powerful tool
would be a generalized number that can be added, subtracted, multiplied
and divided, but has four parts to it. There is one such number called
a quaternion, shown here. Time is t, and x, y, and z are the values the
event may have in the three directions, i, j, and k. Quaternions
are the mathematical foundation for all my efforts in theoretical physics. 

A person standing on a scale in a closed box could not tell the difference
between the box sitting on the surface of the Earth or the box accelerating
at the same rate as the Earth's gravity in a rocket ship as depicted here.
Einstein called this the equivalence principle, but it only applied to
mass, not charge. The General Equivalence Principle extends this idea of
fooling observers to cover any measurement. The box mathematically
means "all the changes in time and space." One can ask, what are all the
possible changes in the direction rulers (I) and the potential (A), or
Box IA? The usual answer is the rulers are fixed and it is the potential
that changes, I Box A. However, the answer could also be the potential
is the same, but the rulers are changing, A Box I. 

A unified field theory describes light and gravity in the same equation.
Einstein spent the last half of his life looking for one, but did not
succeed. The equation on the right reads in mathlish, "The change in the
change in the potential equals some constants times the source."
The stars are involved in games with plus and minus signs. It takes
work to see that the signs are correct. A unified field theory must
be able to describe all forms of change. The graphic tries to depict this:
changes in a square grid, changes moving straight out from the center,
changes that are circular ripples, and changes that are spirals. The graphic
does not show changes in time or the third dimension. It is only
a graphic after all. 

The standard model is used to quantify why there are this many of that
kind of subatomic particle, and that many of those particles.
A vast amount of exquisite detail is explained. No one has justified
why the standard model should be this way. The standard model is
constructed from what are called symmetry groups which go by the names
U(1), SU(2), and SU(3). The quaternion unified field theory can be
written in a way that lines up perfectly with two of these symmetries.
The connection to the SU(3) symmetry is unclear now, although technically
it has the right number of fingers and toes (eight in this case). 

Newton's law of gravity works to explain the rotation of the Moon around
the Earth. Newton's law of gravity works to explain the velocity
of stars near the center of a galaxy, but fails to explain why stars further
from the center maintain that same velocity. One hypothesis is called
dark matter, stuff that cannot be seen but makes the velocities work out
just so. All physics laws must respect relativity and the rules of
calculus. These rules create the second term which has a constant
velocity and accurately describes the distribution of mass with respect
to the radius, no dark matter required. 