### “Listening to the Logos rather than to me, it is wise to agree that all things are in reality one thing and one thing only”

–Heraclitus (Greek philosopher 500BC)

## The Physics of Plato's Cave

In brief, this theory could be described as a Planck-unit Mathematical Universe Hypothesis where the Planck units (mass, space, time, charge, temperature) are geometrical forms constructed according to 2 mathematical constants and a dimensioned unit. It is the geometry of the physical constant which confers the function of that constant, the dimensioned unit becoming a mathematical rather that physical construct.

The universe is presumed to be an expanding black-hole fed by a contracting white-hole twin in integer Planck steps (incremental units of Planck mass, Planck time and Planck length) giving us the universe clock-rate and the origin of physical time.
Comparing the cosmic microwave background
CMB data from NASA with an equivalent black-hole gives a best fit for a 14.6 billion year old black hole universe, NASA estimates our universe at 13.8 billion years.

The electron is constructed around a Dirac Kerr-Newman rotating black-hole electron. We could envisage this electron as a magnetic-monopole cloud that surrounds and covers a Planck-size micro black-hole center. The electron oscillates between this electro-magnetic magnetic-monopole (AL ampere-length) wave-state and an M = Planck mass T = Planck time mass point-state (1 rotation of the micro black-hole center). As our measured mass is the average occurence of mass units per second, and v = wave state frequency per second then E = hv (wave-state) = mc2 (point state) as every electric wave-state has a corresponding mass point-state.

Gravity becomes a point-state (black-hole to black-hole) interaction.

The electric force is a wave-state (magnetic-monopole to magnetic-monopole) interaction. However in this model forces are replaced with physical links, orbitals are units of momentum resembling photons, they are the source of orbit momentum and they are the orbit path. There is no empty space within the atom, electrons do not jump between atomic orbitals, rather the orbitals themselves are exchanged. This orbital model resembles the de Broglie-Bohm pilot wave model.

The dimensions of mass, space, time, charge, temperature are not independent but overlap and cancel within a defined ratio; units = M^9 T^11 / L^15 = (AL)^3/T = 1. This ratio is found in the electron, the electron frequency function is thus a dimensionless mathematical constant constructed from 2 mathematical constants; the fine structure constant alpha and a proposed Omega. The dimensional units mass, space, time, charge and temperature can be defined as exponents of a hypothesized unit denoted "u".

Via these 2 fixed mathematical constants alpha and Omega and unit "u" and 2 scalars derived from the SI ampere, the SI dimensioned physical constants (G, h, c, e, me, kB ...) can be derived and solved to a 10-digit precision, results consistent with CODATA 2014.

The (square root) sqrt of Planck momentum is used as the link between mass and charge.

The universe topology is expressed as a dimensionless 4 axis hyper-sphere black-hole expanding in integer incremental steps, giving the universe clock rate (a time reference). As this expansion is a constant, this hyper-sphere is a Newtonian absolute background upon which a Mach's principle relativistic 3-D space is projected.

As the sum universe is dimensionless (the dimensions of mass, space, time and charge cancel), and as the universe is neutral; matter + antimatter = zero, sum energy = 0 and as it can be structured using only the 2 dimensionless constants; the fine structure constant alpha and an Omega, it resembles by definition both Tegmark's Mathematical Universe and a Virtual (Programmed) Universe.

In the article "Surprises in numerical expressions of physical constants", Amir et al write ... In science, as in life, `surprises' can be adequately appreciated only in the presence of a null model, what we expect a priori. In physics, theories sometimes express the values of dimensionless physical constants as combinations of mathematical constants like pi or e. The inverse problem also arises, whereby the measured value of a physical constant admits a 'surprisingly' simple approximation in terms of well-known mathematical constants. Can we estimate the probability for this to be a mere coincidence? (Ariel Amir, Mikhail Lemeshko, Tadashi Tokieda; Surprises in numerical expressions of physical constants; arXiv:1603.00299 [physics.pop-ph]).

The reader must debate; do the formulas presented in this model pass the Amir test?

For the mathematics of this model go to planckmomentum.com (link below)