[ExI] Fwd: Logical Proof of a Multiverse
Stuart LaForge
avant at sollegro.com
Sun Jan 23 21:18:23 UTC 2022
----- Forwarded message from Stuart LaForge <stuart.laforge at gmail.com> -----
Date: Sun, 23 Jan 2022 13:10:19 -0800
From: Stuart LaForge <stuart.laforge at gmail.com>
Subject: Fwd: Logical Proof of a Multiverse
To: Stuart LaForge <avant at sollegro.com>
---------- Forwarded message ---------
From: Stuart LaForge <stuart.laforge at gmail.com>
Date: Sun, Jan 23, 2022 at 1:00 PM
Subject: Logical Proof of a Multiverse
To: <extropolis at googlegroups.com>
Claim: Our causal cell or Hubble volume does not contain the information
storage capacity to compute the electron positions of a single gold (Au)
atom.
Proof: Let [image: S_i] represent the Shannon information capacity of our
Hubble volume as calculated by generally accepted parameters for the Hubble
volume applied to the formula for the Bekenstein bound as follows.
The equation for the Bekenstein bound is
[image: \mathbb{S}_i \leq \frac{2\pi c M R} {\hbar ln2}]
The mass of the Hubble volume (including dark components) can be adequately
represented by the product of the critical density [image: \rho_c] and the
spherical Hubble volume [image: V_H] as follows where H is the Hubble
parameter (constant).
[image: \rho_c = \frac{3 {H}^2}{8 \pi G}]
[image: V_H = \frac{4 \pi}{3} R_H^3]
Here [image: R_H = \frac{c}{H}] is the Hubble Radius. [image: M_H = \rho_c
V_H = \frac{c^3}{2 H G}] is the Hubble mass.
Substituting the Hubble mass and the Hubble radius into the Bekenstein
bound formula gives us the maximum total information content of our Hubble
volume:
[image: S_H \leq \frac{\pi c^5}{ln2 H^2 G \hbar} \approx 3.25 \times
10^{122} bits]
Remember our Hubble volume is the set of all space-time that is subluminal
and timelike relative to us; that is to say our causal cell is by one
definition our causally bounded universe.
Now let's try to compute the electron configuration of a gold atom. Gold
(AU) has an atomic number 79 with 79 protons and 79 electrons. Now let us
ignore the protons and simply try to compute the electron distribution
across the atom. Since the gold atom has a radius of 144 picometers (pm)
and a diameter of 288 pm then we could envisage a 3-dimensional
approximation of a gold atom in a 288 x 288 x 288 cubic grid with a total
of $288^3 = 23,887,872 voxels that any one or more of the 79 electrons
could occupy at any one time according to the multiparticle time-dependent
Schrodinger's equation.
[image: \Psi(\vec{r}_1, \vec{r}_2,...\vec{r}_{79};t)]
Since in order to determine a probability for each of the 79 electrons to
be in each of the 23,887,872 voxels, we would have to integrate over three
terms dx,dy, and dz for each of the 79 electrons to determine the
probabilities of each of the [image: 288^{3 \times 79} = 23887872^{79}
\approx 7.52 \times 10^{582}] possible states.
Since each of the [image: 7.52 \times 10^{582}] states will have to be
represented by a scalar probability value, and each such scalar value must
exceed 1 bit of Shannon entropy, and [image: 7.52 \times 10^{582} >> 3.25
\times 10^{122}], the claim is proved.
Q.E.D.
So logically either the multiverse exists and is so mind bogglingly big as
to be practically infinite OR the inner working of atoms is governed by a
universal wave function that is running on a computer that is causally
disconnected from and vastly larger than our observable universe. In either
case, there is much more to reality than meets the eye.
Stuart LaForge
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