Method for programming Planck Black-hole Cosmic Microwave Background parameters for use in Simulation Hypothesis models
A primordial Planck size micro black-hole that incorporates the Planck units (units of Planck mass, Planck time, Planck length ... ) as fundamental (non-divisible) discrete units is premised . Computer Simulation Hypothesis models that use digital time instead of analog (continuous) time where the time variable (tage) is measured in units of Planck time can calculate comparable cosmic microwave background parameters (see table) with good approximation at low computational cost by modelling the scaffolding of the universe as expanding in Planck size micro black-holes per increment in tage. .
|Age (billions of years)||14.624||13.8|
|Age (units of Planck time)||0.428 1061|
|Mass density||0.21 x 10-26 kg.m-3||0.24 x 10-26 kg.m-3|
|Radiation energy density||0.417 x 10-13 kg.m-1.s-2||0.417 x 10-13 kg.m-1.s-2|
|Hubble constant||66.86 km/s/Mpc||67 (ESA's Planck satellite 2013)|
|CMB peak frequency||160.2GHz||160.2GHz|
|Entropy CEH||2.3 x 10122kB||2.6 x 10122kB|
For each increment to time tage, to the sum black-hole is added a Planck black-hole comprising a unit of Planck time tp, Planck mass mP and Planck (spherical) volume (Planck length = lp), such that we can then calculate the mass, volume and so density of the sum black-hole for any chosen unit of time, (tsec as the age of the black-hole as measured in seconds).
Gravitation constant G as Planck units;
From the Friedman equation; replacing p with the above mass density formula, √(λ) reduces to the radius of the universe;
Measured in terms of Planck temperature = TP;
The mass/volume formula uses tage2, the temperature formula uses √(tage). We may therefore eliminate the age variable tage and combine both formulas into a single constant of proportionality that resembles the radiation density constant.
Radiation energy densityEdit
From Stefan Boltzmann constant σSB
The Casimir force per unit area for idealized, perfectly conducting plates with vacuum between them; F = force, A = plate area, dc 2 lp = distance between plates in units of Planck length
if dc = 2 π √tage then the Casimir force equates to the radiation energy density.
A radiation energy density pressure of 1Pa gives tage = 0.8743 1054 tp (2987 years), Casimir length = 189.89nm and temperature TBH = 6034 K.
1 Mpc = 3.08567758 x 1022.
Black body peak frequencyEdit
Riess and Perlmutter using Type 1a supernovae to show that the universe is accelerating. This discovery provided the first direct evidence that Ω is non-zero giving the cosmological constant as ~ 1071 years;
- units of Planck time;
This remarkable discovery has highlighted the question of why Ω has this unusually small value. So far, no explanations have been offered for the proximity of Ω to 1/tuniv2 ~ 1.6 x 10-122, where tuniv ~ 8 x 1060 is the present expansion age of the universe in Planck time units. Attempts to explain why Ω ~ 1/tuniv2 have relied upon ensembles of possible universes, in which all possible values of Ω are found  .
The maximum temperature Tmax would be when tage = 1. What is of equal importance is the minimum possible temperature Tmin - that temperature 1 Planck unit above absolute zero, this temperature would signify the limit of expansion (the black hole could expand no further). For example, taking the inverse of Planck temperature;
This then gives us a value for the final age in units of Planck time (about 0.35 x 1073 yrs);
The mid way point (Tuniverse = 1K) would be when (about 108.77 billion years);
- Programming Planck units via a mathematical electron, a simulation hypothesis model, (wiki: Mathematical electron)
- Programming the Matrix via a Mathematical Electron, a Simulation Hypothesis Overview
- 1. Method for programming a Planck black-hole universe, a simulation hypothesis model
- 2. Method for programming Relativity as the mathematics of perspective in a Planck Simulation Hypothesis Universe
- 3. Method for programming gravitons as units of orbital momentum ħc, a simulation-hypothesis model, (wiki: Quantum gravity (gravitons))
- Digital time in simulation models
- Macleod, Malcolm J. "Programming Planck units from a virtual electron; a Simulation Hypothesis". Eur. Phys. J. Plus 113: 278. 22 March 2018. doi:10.1140/epjp/i2018-12094-x.
- Macleod, Malcolm; "Programming a Planck Universe Black-hole CMB and the Cosmological constant, a Simulation Hypothesis". SSRN. 21 June 2018. doi:10.2139/ssrn.3333513.
- Egan C.A, Lineweaver C.H; A LARGER ESTIMATE OF THE ENTROPY OF THE UNIVERSE; https://arxiv.org/pdf/0909.3983v3.pdf
- J. Barrow, D. J. Shaw; The Value of the Cosmological Constant, arXiv:1105.3105v1 [gr-qc] 16 May 2011