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3. Programming cosmic microwave background parameters for Planck scale Simulation Hypothesis modeling

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1 method of Planck scale Simulation Hypothesis modeling has the programmer God using geometrical objects for the base units such that particle to particle interactions result from geometrical imperatives. Described in this article is a method for programming the cosmic microwave background parameters at the Planck scale. A Planck size micro black-hole is defined as the minimum discrete entity and comprises the Planck units. The simulation clock-rate is measured in units of Planck time whereby for each unit of time a 4-axis hypersphere (the universe space) expands by 1 Planck step which constitutes the addition to the sum universe of a micro black-hole. This constant expansion is the origin of the speed of light. The mass-space parameters increment linearly, the electric parameters in a sqrt-progression, thus for electric parameters the early universe transforms most rapidly. The velocity of expansion is constant and is the origin of the speed of light, the Hubble constant becomes a measure of the universe radius and the CMB radiation energy density correlates to the Casimir force. A peak frequency of 160.2GHz correlates to a 14.624 billion year old universe (sans-particles). The cosmological constant, being the age when the simulation reaches the limit, approximates $t$ = 10$^{123} t_p$.
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Planck scale cosmic microwave background
3. Programming cosmic microwave background parameters for Planck scale
Simulation Hypothesis modeling
Malcolm Macleod
e-mail: maclem@platoscode.com
1 method of Planck scale Simulation Hypothesis modeling has the programmer God using geometrical objects
for the base units such that particle to particle interactions result from geometrical imperatives. Described in
this article is a method for programming the cosmic microwave background parameters at the Planck scale. A
Planck size micro black-hole is defined as the minimum discrete entity and comprises the Planck units. The
simulation clock-rate is measured in units of Planck time whereby for each unit of time a 4-axis hypersphere
(the universe space) expands by 1 Planck step which constitutes the addition to the sum universe of a micro
black-hole. This constant expansion is the origin of the speed of light. The mass-space parameters increment
linearly, the electric parameters in a sqrt-progression, thus for electric parameters the early universe transforms
most rapidly. The velocity of expansion is constant and is the origin of the speed of light, the Hubble constant
becomes a measure of the universe radius and the CMB radiation energy density correlates to the Casimir
force. A peak frequency of 160.2GHz correlates to a 14.624 billion year old universe (sans-particles). The
cosmological constant, being the age when the simulation reaches the limit, approximates t=10123tp.
Table 1 Black-hole Cosmic microwave background
Age (billions of years) 14.624 13.8 [4]
Age (units of Planck time) 0.4281 x 1061
Cold dark matter density 0.21 x 1026kg.m3(eq.1) 0.24 x 1026kg.m3[6]
Radiation energy density 0.417 x 1013kg.m3(eq.7) 0.417 x 1013kg.m3[4]
Hubble constant 66.86 km/s/Mpc (eq.10) 67.74(46) km/s/Mpc [5]
CMB temperature 2.7269K (eq.3) 2.7255K [4]
CMB peak frequency 160.2GHz (eq.12) 160.2GHz [4]
Entropy CEH 2.3 x 10122kB(eq.13) 2.6 x 10122kB[7]
Casimir length 0.42mm (eq.8)
keywords:
cosmic microwave background, CMB, cosmological constant, black-hole universe, white-hole universe, Planck
time, arrow of time, dark energy, Hubble constant, expanding universe, Casimir, Simulation Hypothesis;
1 Introduction
The simulation hypothesis is the proposal that all of real-
ity, including the Earth and the rest of the universe, could
in fact be an artificial simulation, such as a computer sim-
ulation. In this article we look at a mathematical universe
approach [1] that uses geometrical objects for mass, length,
time and charge [2] to determine the potential for applying
this approach to the cosmic microwave background parame-
ters, the only variable required being the universe age t, thus
the simulation may begin at any chosen unit of time, updating
in real-time as the simulation proceeds.
A Planck-size ‘micro black-hole’, defined as an entity that
embeds the Planck units, is initialized. The simulation begins
with a single micro black-hole, time t=1. A second micro
black-hole is added, t=2 and so on ... tas the clock rate
of the simulation and measured in units of Planck time tp,
the simulation universe (defined here as the sum black-hole)
growing in Planck steps accordingly.
The velocity of the universe expansion is constant and is
the origin of the speed of light. It is also this outward ex-
pansion of the simulation (black-hole) universe that gives an
omni-directional (forward) arrow of time. When the simula-
tion has reached the limit of its expansion (when it is 1 Planck
step above absolute zero), the simulation clock will stop.
2 Mass density
For each expansion step, to the black-hole is added a micro
black-hole which includes; a unit of Planck time tp, Planck
mass mPand Planck (spherical) volume (Planck length =lp),
such that we can calculate the mass, volume and so density
of this sum black-hole for any chosen time by setting tage; the
age of the black-hole universe as measured in units of Planck
time or tsec the age of the black-hole universe as measured in
seconds.
tp=2lp
c(s)
mass :mbh =2tagemP(kg)
volume :vbh =4πr3/3,r=4lptage=2ctsec (m)
mbh
vbh
=2tagemP.3
4π(4lptage)3=3mP
27πt2
agel3
p
(kg
m3) (1)
1 1
Planck scale cosmic microwave background
Via the Friedman equation, replacing pwith the above mass
density formula, λ=r=2ctsec reduces to the black-hole
radius (G=c2lp/mP);
λ=3c2
8πGp =4c2t2
sec (2)
3 Temperature
Measured in terms of Planck temperature =TP;
Tbh =TP
8πtage
(3)
The mass/volume formula uses t2
age, the temperature formula
uses tage. We may therefore eliminate the age variable tage
and combine both formulas into a single constant of propor-
tionality that resembles the radiation density constant.
Tp=mPc2
kB
=shc5
2πGkB2(4)
mbh
vbhT4
bh
=253π3mP
l3
pT4
P
=283π6k4
B
h3c5(5)
4 Radiation energy density
From Stefan Boltzmann constant σS B
σS B =2π5k4
B
15h3c2(6)
4σS B
c.T4
bh =c2
1440π.mbh
vbh
(7)
5 Casimir formula
The Casimir force per unit area for idealized, perfectly con-
ducting plates with vacuum between them, where dc2lp=dis-
tance between plates in units of Planck length;
Fc
A=πhc
480(dc2lp)4(8)
if dc=2πtagethen eq.7 =eq.8, equating the Casimir force
with the background radiation energy density.
Fc
A=c2
1440π.mbh
vbh
(9)
fig.1 plots Casimir length dc2lpagainst radiation energy den-
sity pressure measured in mPa for dierent tagewith a ver-
tex around 1Pa, fig.2 plots temperature Tbh. A radiation en-
ergy density pressure of 1Pa gives tage0.8743 1054tp(2987
years), length =189.89nm and temperature Tbh =6034 K .
6 Hubble constant
1 Mpc =3.08567758 x 1022m.
H=1M pc
tagetp
(10)
Fig. 1: y-axis =mPa, x-axis =dc2lp(nm)
Fig. 2: y-axis =mPa, x-axis =Tbh (K)
7 Black body peak frequency
xex
ex13=0,x=2.821439... (11)
fpeak =kBTbh x
h=x
8π2tagetp
(12)
8 Entropy
SBH =4πtage2kB(13)
9 Cosmological constant
Riess and Perlmutter (notes) using Type 1a supernovae cal-
culated the end of the universe tend 1.7 x 10121 0.588 x
10121 units of Planck time;
tend 0.588x10121 (14)
The maximum temperature Tmax would be when tage=1.
What is of equal importance is the minimum possible tem-
perature Tmin - that temperature 1 Planck unit above absolute
zero, for in the context of this model, this temperature would
signify the limit of expansion (the black-hole could expand
no further). For example, if we simply set the minimum tem-
perature as the inverse of the maximum temperature;
Tmin
1
Tmax
8π
TP0.177 1030 K(15)
2 3 Temperature
Planck scale cosmic microwave background
This would then give us a value ‘the end’ in units of Planck
time (0.35 1073 yrs) which is close to Riess and Perlmutter;
tend =T4
max 1.014 10123 (16)
The mid way point (Tmid =1K) becomes
T2
max 3.18 1061 108.77 billion years.
10 Rotation
By expanding according to a Theodorus spiral pattern (fig.
3) the universe can rotate with respect to itself dierentiating
between an L and R universe without recourse to an external
reference. The integer dimensions (mass, volume) follow a
linear progression (spiral circumference), the radiation com-
ponents a sqrt progression (spiral arm).
tage=number of points.
Fig. 3: spiral lattice geometry
11 Comment
In a geometrical model of the universe operating at the Planck
scale, it is the geometries of Planck units for mass, space and
time as well as the geometries of the particles that would dic-
tate the interactions between them. These interactions would
then be guided by geometrical imperatives.
As particles dictate the frequency of the Planck units, a
Planck unit scaolding can be used as a backdrop to which
particles are then embedded. Particle mass for example could
therefore be the absence of particle, exposing the underlying
Planck (mass) scaolding. It would not therefore be neces-
sary for the particle to have a physical unit of mass.
12 Notes
1. In comparing this black-hole with the CMB data, I took
the peak frequency value at exactly 160.2 GHz as my ref-
erence and used this to solve tageeq(12) and from there the
other formulas. This gives a 14.6 billion year old black-hole
sans particles (see table, page 1). As tage=number of expan-
sion steps is the only variable required, the simulation may be
started at any selected age tage.
2. ... in 1998, two independent groups, led by Riess and
Perlmutter used Type 1a supernovae to show that the universe
is accelerating. This discovery provided the first direct evi-
dence that is non-zero, with 1.7 x 10121. This re-
markable discovery has highlighted the question of why
has this unusually small value. So far, no explanations have
been oered for the proximity of to 1/tu21.6 x 10122,
where tu8 x 1060 is the present expansion age of the uni-
verse in Planck time units. Attempts to explain why 1/tu2
have relied upon ensembles of possible universes, in which all
possible values of are found [3].
References
1. Macleod, Malcolm J. ”The source code of God, a pro-
grammed approach”
http://platoscode.com (2020 edition)
2. Macleod, Malcolm J., Programming Planck units from a
virtual electron; a Simulation Hypothesis
Eur. Phys. J. Plus (2018) 133: 278
3. J. Barrow, D. J. Shaw; The Value of the Cosmological Con-
stant
arXiv:1105.3105v1 [gr-qc] 16 May 2011
4. https://en.wikipedia.org/wiki/Cosmic microwave back-
ground (2009)
5. https://en.wikipedia.org/wiki/Hubbles law (2016-07-13)
6. https://map.gsfc.nasa.gov/universe/uni matter.html (Jan
2013)
7. Egan C.A, Lineweaver C.H; A LARGER ESTI-
MATE OF THE ENTROPY OF THE UNIVERSE;
https://arxiv.org/pdf/0909.3983v3.pdf
3 10 Rotation
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The source code of God
  • Malcolm J Macleod
Macleod, Malcolm J. "The source code of God, a programmed approach" http://platoscode.com (2020 edition)
  • J Barrow
  • D J Shaw
J. Barrow, D. J. Shaw; The Value of the Cosmological Constant arXiv:1105.3105v1 [gr-qc] 16 May 2011