"We are all agreed that your theory is crazy. The question which divides us is whether it is crazy enough to have a chance of being correct" - Niels Bohr, Danish Physicist (1885-1962)
The Black-Hole Electron; A Mathematical Universe Hypothesis
Mathematical realism holds that mathematical entities exist independently of the human mind. Thus humans do not invent mathematics, but rather discover it, and any other intelligent beings in the universe would presumably do the same. Platonism is a theory that numbers or other abstract objects are objective, timeless entities, independent of the physical world and of the symbols used to represent them and echoes the Pythagoras quote; number is the ruler of forms and ideas. The mathematical universe hypothesis (MUH), also known as the Ultimate Ensemble, is a "theory of everything" proposed by the cosmologist Max Tegmark. The Matrix is a 1999 science fiction film in which reality as perceived by most humans is actually a computer simulated reality called "the Matrix" and is based around the mathematical universe of Pythagoras.
A charged rotating black hole is a black hole that possesses angular momentum and charge rotating about one of its axes of symmetry. If a black hole has the same mass and charge as an electron, then potentially it could share many of the properties of the electron including the magnetic moment and Compton wavelength.
This book Plato's Cave describes a model of a mathematical universe as being a universe of dimensionless geometrical forms to which a physical dimensionality (the dimensions of mass, space, time..) is added via rotation, the engine for this rotation is the expansion of the universe in discrete steps. The book proposes that a black-hole itself is a dimensionless entity (without mass, space or time) and that the dimensions of mass, space and time are embedded with the geometry of a black-hole electron. This website is a discussion of the physics behind this model.
The model is constructed around an electron which oscillates via this rotation between a dimensionless mathematical-state and a dimensioned physical (magnetic-monopole) electric-state. After each rotation the dimensions of the magnetic-monopole (ampere-meter AL) intersect with time T and cancel leaving a dimensionless geometrical torus (a torus whose radius is dimensionless).
The veracity of this model depends on its ability to derive and solve the dimensioned physical constants (G, h, c, e, me, kB...) in terms of mathematical forms, a principle requirement for any mathematical universe hypothesis. Results are consistent with latest experimental values known as CODATA 2014. At present physics has no model which can do this.
The model uses 2 dimensionless constants (1 is the fine structure constant alpha) and 2 dimensioned scalars whose numerical values depend on the system of units being used, if we were to met an alien for example, we merely need adjust these 2 scalars in order to solve his physical constants (G, h, c, e, me, kB...) in terms of his units and using his numerical values. The model is 'galaxy-independent'.
If our physical dimensions are constructs of dimensionless mathematical forms; then mass, space and time are themselves constants. Relativity then becomes the means to translate from our geo-centric 4-D spacetime to the topolgy of a black-hole universe.
In summary, this is a geometrical model of a non-relativistic expanding black-hole universe (with a contracting white-hole universe twin) whose information content is stored by Planck-unit micro black-holes defined as particles. Photons are the means of data exchange.