Saturday, March 22, 2014

Efficient packing by Florets are Fibonacci and the symmetry issue is a conundrum

A model for the pattern of florets in the head of a sunflower was proposed by H. Vogel in 1979.[55] This has the form
\theta = \frac{2\pi}{\phi^2} n,\  r = c \sqrt{n}
where n is the index number of the floret and c is a constant scaling factor; the florets thus lie on Fermat's spiral. The divergence angle, approximately 137.51°, is the golden angle, dividing the circle in the golden ratio. Because this ratio is irrational, no floret has a neighbor at exactly the same angle from the center, so the florets pack efficiently.

I think we end up with a Fibonacci sequence, though I have not worked it out.
Here is the angle separation it uses, (The basic quant ratio). That large angle is: The golden angle is then the angle subtended by the smaller arc of length b. It measures approximately 137.508°, or about 2.39996 radians.

Split in half, at the larger angle, it becomes -1.94, and +1.94, in radians, which is less than  Pi * (-2/3 and +2/3) (-2.09,+2.09), (using the fraction instead of 3/2). I used 2/3, which is the fraction count of quant size, going from heaviest to lightest.

The Fibonacci sequence obeys the Shannon condition, I think, which is that each of the i*log(i) be within an integer.  The Floret is making the minimum phase packing of a positive and negative phase.

Nyquist would be sampling at -pi/2 and +pi/2, which is (-1.57,+1.57). If we went there, that makes the Pauli/Nyquist rate a bit more than we have assumed.

The difference is the asymmetry, I assumed the vacuum to be a bit more optimistic about nulls, assuming there are more of them than the phases, the universe is slightly unbalanced. . The Floret is symmetric.

In the standard model, the 2/3 ratio is used, and that is what they call symmetry breaking, and I do not believe the vacuum breaks symmetry, unless we assume some extra stress mode in the vacuum where Plank breaks down. How could that be, this symmetry breaking? That only occurs when something out of the model compresses energy beyond Plank, but the only thing that can compress more than Plank is the vacuum itself. I dunno? Still working the problem.

Anyway, lets summarize will quickly. 

(-1.57,+1.57). Is Nyquist, there are only waves.
(-1.94, and +1.94) is symmetric packing, nulls balance phase.
(-2.09,+2.09) is asymmetric packing, more null measured than phase.
 
When we have protons packed asymmetrically, and gravity packed symmetrically, then we have larger field strength in gravity, relative to null, then protons. The proton static field gets overwhelmed, and cannot dissipate gravity phase density, they break apart. We get a Universe that cycles.  When everything is packed asymmetrically, the universe reaches steady state, and cold (less phase more null).  When everything is packed symmetrically we get steady state and mildly warm(enough phase remains to warm the place). What a conundrum!

Consider the formation of gravity. It is removing the common mode phase from a pack of mass. If we are asymmetric, then gravity slightly underestimates the amount of imbalance in the negative and positive portions of that measurement. Hence, gravity accepts more nulls and less phase, the gravity phase surrounding the matter is a bit weaker than it should be. The universe never blows up.

Here is where the SpaceTime thing may work.  The vacuum elements can expand. The phase measured is relative to the vacuum size. a phase of -2.09 says the vacuum has shrunk, a phase of -1.94 says it expanded a bit, a phase of -1.57 says it has expanded a bit more. We get the Einstein's gravity stopping point, Nyquist, and there are no gravitrons. We have a universe where the sampling ratio, compared to Nyquist, can change. Gravity is the maximum sampling rate, and defines light speed as Nyquist. Then we have the Nyquist path determined by the density of the vacuum. There is no real quantization. But that cannot be because it does not explain impedance in EM wave. I am still stuck.

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