The Minimum Universe .
2 Dec 2014
We calculate the minimum necessary sufficient size for a Universe . (r=2.645 x 10^(-20) meters)
1.A handy view is the holographic principle :
“The holographic principle is a property of string theories and a supposed property of quantum gravity that states that the description of a volume of space can be thought of as encoded on a boundary to the region”
2.While the boundary of a volume can be mathematically regarded as two-dimensional , in reality it has to be at least one Planck-length deep . At least one particle of matter .
3.The Shell Principle :
A Universe of Radius R(0) has all it’s information encoded in a shell of depth b around it .
VolShell = 4/3*pi [ (R(0) + b)^3 – R(0)^3]
This means that VolShell = 4/3*pi*R(0)^3 from an information viewpoint . All the data in the sphere is packed into the shell .
This gives b= (2^(1/3) -1) * R(0)
= 0.259921049 *R(0)
4. We iterate this .
Every shell has another shell around it , and this decreases by the above factor of 0.26 .
We iterate until b is equal to one Planck length .
This gives about 26 iterations .
5.What does this mean ?
The 26 shells are in one-to-one correspondence with the minimum necessary sufficient Arith I systems to describe any universe .
The “bubbles” of numbers or space-time correspond to the shells .
6.The minimum necessary sufficient size for any universe with a Planck length .
From above , n = 25.62 + ln(R(0)) / 1.343773
N is 26 as a minimum .
This gives 2.6458 x 10^(-20) meters as the minimum size of a universe , but it still has to have at least 26 dimensions .
7.This would translate as the pre-inflationary size of the Universe .
Why does it inflate then ?
The Schwinger limit is exceeded in the shells http://en.wikipedia.org/wiki/Schwinger_limit
The system goes chasing it’s own tail in a wild , non-linear feedback .
8. What does it mean ?
8.1 Creating universes is much easier than we thought .
But your kernel must include iron or a multiple atomic number . See 8.2 below .
No mass concentrations . Only exceed the http://en.wikipedia.org/wiki/Schwinger_limit
8.2 Stable transuranics
The system is fractal , so expect islands of stability at beats of 26 .
Why iron is at the bottom of the nucleonic packing curve .
It is the simplest way of describing this universe .
Expect Stability at
9. Minimum self-sustaining biospheres .
We use the Shell principle in para 3 above .
Biosphere volume for Earth = = 4/3*pi [ (R(0) + b)^3 – R(0)^3]
Here R(0) = 6371 km b = 23 km
After 14 iterations we can pack the whole of Earth’s biosphere into a sphere of 2 cm radius ..
You can measure a civilization’s level by the concentration of it’s biosphere .
For instance , Earth is a level 0 civilization .
The whole biosphere (6371 km) is packed into itself .
9.1 How big a spaceship do you need for your biosphere , given your level of knowledge ?
Levels : radius of a spaceship to accommodate the whole biosphere .
0. 6371 km Earth .
1. 1410 km a big spaceship .
2. 366 km Better bio knowledge
5. 6 km
6. 2 km
7. 400 m
8. 104 m
9. 27 m
10 . 7 m
11. 2 m
12. 24 cm
13. 7 cm
14. 1.9 cm
10. How to do this ?