Hologram alpha > 2/3 means space is fractal?

On Jan 25, 2015, at 9:12 AM, JACK SARFATTI <This email address is being protected from spambots. You need JavaScript enabled to view it.> wrote:

alpha = 2/3 comes most simply from

 

A/Lp^2 = A^3/2/(&L)^3

 

for a 2D horizon hologram screen of area A with quantum bit pixel area Lp^2

 

the bulk 3D hologram voxels have quantum volumes (&L)^3

 

However, if the horizon 2D screen is fractal with linear scale parameter y and the interior bulk is fractal with linear scale parameter x

 

A^(1 + y)/Lp^2(1 + y) = A^(3/2)(1 + x)/(&L)^3(1 + x)

 

(&L)^3(1 + x) = Lp^2(1 + y)A^3/2(1 + x)/A^(1 + y)

 

A^3/2(1 + x)/A^(1 + y) = A^3/2 A^3x/2/AA^y = A^1/2 A^(3x/2 - y)

 

(&L)  = [Lp^2A^1/2]^(1/3(1 + x) [Lp^2y A^(3/2x - y)]^1/3(1 + x)]

 

alpha = (2/3)(1 + y)/(1 + x)

Lp^2y A^(3/2x - y)]^1/3(1 + x)  is not a dimensionless pure number

 

If we use the non-fractal measures, it's no longer true that

 

A/Lp^2 = A^3/2/(&L)^3

 

that is the effective hologram mapping from screen to image is no longer 1 - 1 

 

this corresponds to a non-unitary S-Matrix I suspect.

 

to be continued

 

 

 

 

 

 

 

 

 

 

 

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