Black-hole (Planck)
Planck-unit Black-hole universe
A Planck-unit Black-hole universe defines the universe superstructure in terms of discrete Planck-units and is applicable to Simulation Hypothesis programming that use digital time where time is measured in discrete units of Planck time (the universe simulation clock-rate).
A base structure, a discrete and indivisible Planck micro black-hole is assigned the Planck-units ^{[1]}, forming the scaffolding for particle substructures.
Universe time t_{age} is defined by incremental additions of these Planck micro black-holes to the sum Planck Black-hole universe, as such for any chosen unit of simulation (Planck) time t_{age}, there can be calculated the equivalent cosmic microwave background parameters ^{[2]}.
In this table t_{age} = 0.428 10^{61} units of Planck time;
Parameter | Calculated | Observed |
---|---|---|
Age (billions of years) | 14.624 | 13.8 |
Age (units of Planck time) | 0.428 10^{61} | |
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 temperature | 2.727K | 2.7255K |
CMB peak frequency | 160.2GHz | 160.2GHz |
Entropy CEH | 2.3 x 10^{122}k_{B} | 2.6 x 10^{122}k_{B}^{[3]} |
Casimir length | 0.42mm |
Mass densityEdit
For each increment to time t_{age}, to the Planck Black-hole is added a Planck micro black-hole comprising a unit of Planck time t_{p}, Planck mass m_{P} and Planck (spherical) volume (Planck length = l_{p}), such that we can then calculate the mass, volume and so mass density of the sum Black-hole for any chosen unit of time, (t_{sec} if the age of the Black-hole is 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;
TemperatureEdit
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 densityEdit
From Stefan Boltzmann constant σ_{SB}
Casimir formulaEdit
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 constantEdit
1 Mpc = 3.08567758 x 10^{22}.
Black body peak frequencyEdit
EntropyEdit
Cosmological constantEdit
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 ^{[4]} .
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);
...
External linksEdit
- Mathematical electron
- Programming relativity and gravity in a Planck unit Simulation Hypothesis
- Programming the Matrix via a Mathematical Electron, a Simulation Hypothesis Overview
- Planck quantum gravity
- Digital time in simulation models
ReferencesEdit
- ↑ 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 relativity and gravity in a Planck unit Simulation Hypothesis". RG. 26 March 2020. doi:10.13140/RG.2.2.31308.16004.
- ↑ 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