# MATHEMATICAL UNIVERSE HYPOTHESIS

## A PLANCK-UNIT BLACK-HOLE-ELECTRON

### 'at present no candidate theory in physics is able to calculate the fine structure constant or the electron mass'

update pending (hopefully by early July) on relationship between geometrical and physical universe

-http://en.wikipedia.org/wiki/Theory_of_everything

This is a model of a Mathematical Universe in which the units (dimensions) such as mass, space, time and charge are geometrical aspects of a black hole electron. The electron is both a dimensioned and dimensionless natural constant. The model is divided into 6 parts:

• sqrt of momentum links mass & charge
• electron as a magnetic monopole
• natural constants alpha and Omega
• time & a black-hole white-hole universe
• physical atomic, gravitational orbitals
• why the universe doesn't use relativity

### 1. Sqrt of Planck momentum

The sqrt of Planck momentum is proposed as a link between the mass and charge domains. From this link we can derive formulas for the fundamental constants as geometrical shapes. This then gives the framework to solve these constants in terms of c (exact value), R (Rydberg 12-13 digits), vacuum of permeability (exact value) and the fine structure constant alpha (10-12 digits).

Results are consistent with CODATA 2014 (table left). There is an online calculator provided which uses alpha as the user input .

### 3. Dimensioned mass, time and dimensionless fine structure constant alpha and Omega

In part 1 I used the sqrt of Planck momentum to reduce the required number of dimensioned units to 3 Planck units; velocity c, (Planck) time and the sqrt of momentum Q. Here I replace these 3 units with 2; mass and time, and instroduce a 2nd natural (dimensionless) constant Omega. From the frequency of mass and time and from the Sommerfeld fine structure constant alpha and Omega we can solve the fundamental constants (see table below).

This is possible because the electron frequency is both dimensioned and dimensionless and therefore a natural constant. In other words, what we consider to be the units mass M and time T and length L are not independent of each other but rather overlap such that there is a particular ratio in which they cancel. This ratio appears in the electron.

As such we have the basis for a Mathematical Universe Hypothesis and Plato's theory of forms.

continued...

### 2. Magnetic monopole electron

A magnetic monopole has the units ampere-meter which can also be written as charge-velocity. The monopole of this model is constructed from alpha, e (elementary charge) and c. 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 charge.

### 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) resembling photons albeit of opposite phase. In other words, there is no empty space in the atom, the electron and proton are physically linked by an orbital and the moon does not orbit the earth.

### 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 14.6 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. The online calculator demonstrates this relationship. continued...

### 6. Relativity and the black-hole electron

...in summary, by including the unseen wavelength axis within the visible x-y-z axis, classical physics adopted 3-D space and 1-D time. This later created problems which Einstein patched over with space-time and relativity. Mathematically this was satisfactory but created conceptual problems, the mystery of relativity. Quantum mechanics also had to patch over classical physics with probabilities, for in the absence of the w-axis the electron is and so must be, but they could not find it, hence again mathematically satisfactory but it also creating conceptual difficulties...

### Plato's Cave (2015 edition)

This model is described in more depth in the book Plato's Cave (2015 edition)