'at present no candidate theory in physics is able to calculate the fine structure constant or the electron mass'
A Mathematical Universe Hypothesis
This website introduces the physics from the book Plato's Cave; - it is a description of a Mathematical Universe Hypothesis in which the Planck units are geometrical shapes constructed from 2 dimensionless constants; alpha the fine structure constant and a proposed Omega, and 2 dimensioned units; mass and time. The geometries of mass and time suggests they are linked to (or a function of) rotation. The units for length (space), charge, temperature... are defined in terms of this mass and time. The basic structure is a black-hole electron which oscillates between a dimensioned magnetic monopole wave-state and a dimensionless Planck black-hole point state. Our 3-D space is seen as the surface of an expanding dimensionless 4-D hyper-sphere, the time axis however does not equate to our notion of time. There is no relativity.
1. Sqrt of Planck momentum
The sqrt of Planck momentum (denoted Q) is proposed as a link between the mass and the charge domains. As we can define both the mass constants such as G, h and the charge constants; e, me, kB in terms of Q, we can reduce the number of fundamental constants required to; Q, c, fine structure constant alpha, vacuum of permeability μ0. We can then rewrite Q in terms of the Rydberg constant R and thus solve the fundamental constants in terms of the 4 most accurate constants; c and μ0 (exact values), R (12-13 digit precision), α (11-12 digit precision). Results table left.
3. Dimensioned mass, time and dimensionless fine structure constant alpha and Omega
The Planck units are defined in terms of 5 universal physical constants in such a manner that these constants take on the numerical value of 1 when expressed in terms of these units; G* = h* = c* = ke* = kB* = 1. To revert back to SI values will require 5 scalars, i.e: c = c* x 299792458. What I suggest here is that the physical constants G, h, c, e, me, kB ... can be solved in terms of geometrical shapes constructed according to 2 dimensionless constants; the fine structure constant alpha and a proposed Omega such that only 2 scalars (2 dimensions) are required to revert back to SI equivalents. In the table (left) I define the Planck units (in terms of alpha and Omega) as dimensionless geometrical shapes associated with a mass unit k and time unit t. To solve the physical constants as SI units we set k to Planck mass (kg) and t to Planck time (s). If we meet aliens, we need only their k and t to solve their G, h, c, e, me, kB ... read more...
2. Magnetic monopole black-hole electron
A formula for a magnetic monopole constructed from alpha, e (elementary charge) and c is proposed. From this monopole and Planck time we can construct a formula for the frequency of the electron. This monopole resembles the quark in that it is also 1/3 unit of an electric charge. continued...
5. Physical orbitals and (gravitational) orbits
In this model the fundamental forces (strong, electric, gravity) are replaced with standing wave orbitals (i.e.: wave functions are replaced by physical waves of momentum) resembling photons albeit of opposite phase. This suggests the planets are not orbiting via an abstract force but are instead being pulled by waves of momentum (gravitational orbitals akin to atomic orbitals) around the sun. These orbital waves of momentum are both the track and the locomotive. continued...
4. Cosmological constant and an expanding black-hole contracting white-hole universe
Postulates an expanding black-hole universe linked to a contracting white-hole universe twin. Discrete Planck units, the universe clock-rate, are transferred from the white-hole to the black-hole universe forcing this expansion. This gives us Planck time, the arrow of time and corresponding dark energy and the speed of expansion as the speed of light. Solving for a black-hole whose temperature equates to the temperature of the CMB cosmic microwave background (see table), gives a set of parameters that correlate with the CMB parameters (wikipedia) for a 14.64 billion year old black-hole (calculated). The cosmological constant becomes the age of the black-hole when it reaches absolute zero and this correlates with the estimated cosmological constant for our universe. An online calculator demonstrates this relationship. continued...