Black-hole (Planck)
Programming cosmic microwave background parameters for Planck scale Simulation Hypothesis modeling
Universe simulation hypothesis models operating at the Planck scale can use the Planck units as the scaffolding upon which particle structures are embedded ^{[1]}. Data address in universe 'space' are represented by a Planck micro black-hole defined as a discrete entity that comprises the Planck units for mass m_{P}, length l_{p} and time t_{p}. The simulation clock-rate can therefore be measured in units of Planck time (or equally Planck mass or Planck length ...). Consequently, from 1 variable, the age of the universe for example, the other variables can be calculated.
Parameter | Calculated | Calculated | Observed |
---|---|---|---|
Age (billions of years) | 13.8 | 14.624 | 13.8 |
Age (units of Planck time) | 0.404 10^{61} | 0.428 10^{61} | 0.404 10^{61} |
Mass density | 0.24 x 10^{-26} kg.m-3 | 0.21 x 10^{-26} kg.m-3 | 0.24 x 10^{-26} kg.m-3 |
Radiation energy density | 0.468 x 10^{-13} kg.m-1.s-2 | 0.417 x 10^{-13} kg.m-1.s-2 | 0.417 x 10^{-13} kg.m-1.s-2 |
Hubble constant | 70.85 km/s/Mp | 66.86 km/s/Mp | 67 (ESA's Planck satellite 2013) |
CMB temperature | 2.807K | 2.727K | 2.7255K |
CMB peak frequency | 164.9GHz | 160.2GHz | 160.2GHz |
Casimir length | 0.41mm | 0.42mm |
Mass density[edit | edit source]
For each expansion step of universe 'space', to the sum (black-hole bh) universe is added a Planck micro black-hole which includes; a unit of Planck time t_{p}, Planck mass m_{P} and Planck (spherical) volume (Planck length = l_{p}), such that we can calculate the mass, volume and so density of this sum black-hole for any chosen time by setting t_{age}; the age of the black-hole universe as measured in units of Planck time or t_{sec} the age of the black-hole universe 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;
Temperature[edit | edit source]
Measured in terms of Planck temperature = T_{P};
The mass/volume formula uses t_{age}^{2}, the temperature formula uses √(t_{age}). We may therefore eliminate the age variable t_{age} and combine both formulas into a single constant of proportionality that resembles the radiation density constant.
Radiation energy density[edit | edit source]
From Stefan Boltzmann constant σ_{SB}
Casimir formula[edit | edit source]
The Casimir force per unit area for idealized, perfectly conducting plates with vacuum between them; F = force, A = plate area, d_{c} 2 l_{p} = distance between plates in units of Planck length
if d_{c} = 2 π √t_{age} then the Casimir force equates to the radiation energy density.
A radiation energy density pressure of 1Pa gives t_{age} = 0.8743 10^{54} t_{p} (2987 years), Casimir length = 189.89nm and temperature T_{BH} = 6034 K.
Hubble constant[edit | edit source]
1 Mpc = 3.08567758 x 10^{22}.
Black body peak frequency[edit | edit source]
Entropy[edit | edit source]
Cosmological constant[edit | edit source]
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 ~ 10^{71} 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/t_{univ}^{2} ~ 1.6 x 10^{-122}, where t_{univ} ~ 8 x 10^{60} is the present expansion age of the universe in Planck time units. Attempts to explain why Ω ~ 1/t_{univ}^{2} have relied upon ensembles of possible universes, in which all possible values of Ω are found ^{[2]} .
The maximum temperature T_{max} would be when t_{age} = 1. What is of equal importance is the minimum possible temperature T_{min} - 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 10^{73} yrs);
The mid way point (T_{universe} = 1K) would be when (about 108.77 billion years);
Spiral expansion[edit | edit source]
By expanding according to a Spiral of Theodorus pattern where each triangle refers to 1 step (additional micro black-hole), we can map the mass and volume components as integral steps of t_{age} (the spiral circumference) and the radiation domain as a sqrt progression (spiral arm). A spiral universe can rotate with respect to itself differentiating between an L and R universe without recourse to an external reference.
If mathematical constants and physical constants are also a function of t_{age} then their precision would depend on t_{age}, for example when t_{age} = 1, π^{2} = 6;
External links[edit | edit source]
- [1] - A Planck unit universe according to a geometrical electron formula and the magnitude of the fine structure constant alpha (overview)
- the Source Code of God; a programming approach -online resource
- Simulation Argument -Nick Bostrom's website
- Our Mathematical Universe: My Quest for the Ultimate Nature of Reality -Max Tegmark
- Micro black hole
- Planck particle
- Simulation hypothesis
- Mathematical electron
- Relativity in the Planck level
- Gravity and Planck mass
- Digital time in a simulation hypothesis
References[edit | edit source]
- ↑ Macleod, Malcolm J.; "Programming cosmic microwave background parameters for Planck scale Simulation Hypothesis modeling". RG. Feb 2011. doi:10.13140/RG.2.2.31308.16004/7.
- ↑ J. Barrow, D. J. Shaw; The Value of the Cosmological Constant, arXiv:1105.3105v1 [gr-qc] 16 May 2011