Lattices, vacuum, Plank,Pauli,Higgs and Shannon

Lattice scientists need to use Shannon. Lets try it out.

We have three vacuum shapes, distinguishable up to Plank. What is the density?

In the complete sequence, out SNR is Plank.  Assume the vacuum are spheres of r1,r2,r3 radius,  R1 and R3 occur with the same frequency, they are negative and positive phase. We do not know the density of free Null, the r2.

There is some density over which the -2iLog(i) and  -jLog(j) are within an integer, that makes a counting system. The -Log(x) give you the volume of each sphere when the condition is met. Plug them into the Shannon condition, using the Plank SNR, find the j (number of Nulls), and you have it, the density of free Nulls in space, and you can compute the relative vacuum sizes, in units of Plank. You need, then, to adjust the Log(i) into two volumes that occupy the same space. The number of vacuum that meet the condition gives you the Higgs size, at the Pauli under sampling angle.

Let -Log(i) = r**2, then dividing up the phase by volume gets: r1**2 + r3**2 = r**2, the Euclidean right angle. 

Pauli is the nearest exact 'multiply' in the system, I think. It tells us how to under pack Nulls so that a multiply moves from the Shannon condition at one scale to another.  Work the problem at two different scale and see if underpacking results.

This method should work on most lattice structures. For example, the problem of finding the integer set used for Fourier analysis given the separation of samples. That is exactly what the vacuum does, that number is given by the golden angle.

Work the problem for quarks and gluons the same way. I need to set up dual counting systems, and find the common multiples, within Shannon, from Higgs on down. These are the stable groups. They are the sets where waves and mass coexists. Kinetic energy is still a work in process for me at these huge quant levels.

At the range of gravity, the quant sizes are so small that one can use a single counting system, and ignore Pauli packing of gravitrons.  But at Black Hole compaction ranges, that approximation breaks down because all the packed masses get squeezed. The same approximation distance holds for Newton physics. The difference is when 'multiply' becomes stable over a wide range. In our world, the magnetic seems to be a sharp boundary when that occurs.

Shannon, Pauli and Fibonacci are at the heart of any counting system, including group theory, because it defines the maximum entropy solution for a given spacial separation.