Simulation argument (coding cosmic microwave background)
Programming cosmic microwave background parameters for deep universe (Planck scale) Simulation Hypothesis modeling
The simulation hypothesis or simulation argument is an argument that proposes that the universe in its entirety, down to the smallest detail, could be an artificial simulation such as a computer simulation. Neil deGrasse Tyson put the odds at 50-50 that our entire existence is a program on someone else’s hard drive ^{[1]}.
Universe simulation hypothesis models operating at the Planck scale can use the Planck units as the scaffolding upon which particles are embedded ^{[2]}. A minimum structure that comprises discrete Planck units for mass m_{P}, volume (measured in length l_{p}) and time t_{p}, is proposed for use as a base structure, this can be defined as a Planck micro black-hole.
Simulation clock-rate[edit | edit source]
The simulation clock-rate would be defined as the minimum increment to the simulation. As an example;
FOR t_{age} = 1 TO the_end '1 = big bang generate 1 unit of Planck time t_{p} generate 1 unit of Planck mass m_{P} generate 1 unit of Planck volume (radius Planck length l_{p}) ........ NEXT t_{age} 't_{age} in an incrementing variable and not a dimensioned unit of time
A 14 billion year old universe would approximate 10^{62}t_{p}. In the absence of other factors (assuming only Planck units), the universe simulation would then have a mass and size commensurate with t_{age} = 10^{62} multiples of Planck mass and Planck length respectively as shown in this table:
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]
Setting bh as the sum universe and t_{sec} as time 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 formula.
The diagram (right) plots Casimir length d_{c}2l_{p} against radiation energy density pressure measured in mPa for different t_{age} with a vertex around 1PaA. A radiation energy density pressure of 1Pa occurs around t_{age} = 0.8743 10^{54} t_{p} (2987 years), with 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 ^{[3]} .
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; t_{age} = the_end (the 'universe' 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 increment to t_{age}, 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 (the 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 using this progression when t_{age} = 1, π^{2} = 6;
External links[edit | edit source]
- A Planck scale Simulation hypothesis
- Programming the Planck units for mass, length, time and charge
- Mathematical electron
- Programming gravity at the Planck level
- Programming relativity in the Planck level
- Micro black hole
- Planck particle
- Simulation hypothesis
- the Source Code of God; a Programming approach -online resource
- Simulation Argument -Nick Bostrom's website
- [1] - A Planck unit universe according to a geometrical electron formula and the magnitude of the fine structure constant alpha (overview)
- Our Mathematical Universe: My Quest for the Ultimate Nature of Reality -Max Tegmark
References[edit | edit source]
- ↑ Are We Living in a Computer Simulation? https://www.scientificamerican.com/article/are-we-living-in-a-computer-simulation/
- ↑ 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