Promote the Doing Physics with Quaternions Project, and look cool :-)
These 5 buttons represent a visual presentation of some of the key ideas behind my efforts to unify gravity and electromagnetism.
Fine cuisine depends on starting with the best ingredients. Great physics depends on using new powerful math. An event in space-time 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.