Programming a Virtual (Mathematical) Universe

Our external physical reality is a mathematical structure. That is, the physical universe is mathematics in a well-defined sense, and in those [worlds] complex enough to contain self-aware substructures SAS [they] will subjectively perceive themselves as existing in a physically 'real' world (- Max Tegmark's MUH).

Summary:

Calculates equivalent cosmic microwave parameters for a black-hole universe expanding in Planck unit increments. The best fit is for a 14.6 billion year old black hole.

Premise:

Let us suppose that there is an expanding black-hole universe with a contracting white-hole universe twin. Let us further suppose that discrete Planck 'drops', defined as that 'entity' which is the source of the Planck units (a Planck size black-hole for example), are transferred one by one from the white-hole universe to the black-hole universe thereby forcing an expansion of the black-hole universe at the expense of the contracting white-hole universe in incremental Planck unit steps.

The constant expansion steps are the universe clock-rate and thus the origin of Planck time. 

The constant rate of this expansion is the origin of the speed of light.

It is the incremental addition of these Planck 'drops' that forces the expansion of the black-hole, and so an independent dark energy is not required.

As the fabric of a black-hole is the black-hole itself, an independent cold dark matter may not be required.

This constant outward expansion of the black-hole in discrete steps gives an omni-directional (forward) arrow of time.

This black hole universe forms a 'Newtonian' absolute background upon which a Mach principle relativistic 3-D 'physical' universe can be projected.

The calculator below solves the following parameters for such an expanding black-hole. At 14.624 billion years, these parameters compare with the WMAP measured cosmic microwave background.


This black hole universe model is described in the following article;

Input temperature
(0 = 2.7272K default):
x10^

Input age seconds
(0 = 1 Planck time, big bang):
x10^

Input age years
(0 = 14.624 billion):
x10^


Gives (CMB equivalents)
Dark matter density kg/m3:
x10^

Peak frequency Hz:
x10^

Radiation density kg/m3:
x10^

Hubble:
x10^

Casimir wavelength:
x10^

Black hole parameters:

The calculator (left) uses age to calculate these black hole parameters.
Input in temperature K (Kelvin), or age in seconds or age in years. The calculator will then convert to age in units of Planck time to determine the following parameters:
- cold dark matter density
- blackbody frequency
- radiation density
- Hubble parameter
- Casimir wavelength

A best fit for the CMB values of our universe can be found for a 14.624 billion year old black hole (table above). 


Notes:
Planck units, see black hole electron calculator
max temp = Planck temperature/8.pi
min temp = 8.pi/Planck temperature
min age = 1 Planck time
conversion to years = 3600*24*365.252