This sampling method needs a name, let's call it the Pauli sampler because it is sampling to make Pauli exclusion true.
Pauli says the probability of two quants arriving and the probability of one quant not arriving must be equal. As a ratio of that normal curve, we want the tails left over from two quants equal to the size of the quant.
Q must be equal to the tails of 2*Q.
100-2*Q = Q. Q =33%. For Nyquist that would be 50%. The effective quant rate is .33 per sample. Nyquist samples 2 times per Q. 2* .33/.5 = 1.32 is the Pauli rate, the Nyquist rate is 2. The system is under sampled at the Pauli rate, gets more Q, but they are deliberately erroneous. So in any complete sequence that equalizes phase, the Nyquist sampler gets 33%. These are the extra samples the vacuum keeps to maintain Pauli exclusion. However, the Pauli samples are taken at Nyquist rate. Which means two samples gets one Pauli sample, or, using Shannon,
1.32/2= .66 = log2(1+SNR) or SNR = .58. This is the accuracy of all the mass measurements, including the vacuum, all taken at Nyquis and meeting the Pauli exclusion. Any sample that is weak, the electron for example, will be quantized down to meet this accuracy.
We break the system up into the vacuum, the proton and the electron. If the total system requires 150 samples, then the vacuum gets 50, the proton might get 30, and the electron 2. Convert these to rates: Vacuum, 1/3, proton, 1/5, and electron 1/75. Wavelength is the inverse of rate.
Quantization levels:
The electron has the longest wavelength. 75 samples are needed to complete one wave. So 1/75 is the rate taken taken at the Pauli SNR, how many partial quants?
(B/75) = .66 or B = 75 * .66 = 49. The electron has to be measured to 49 quantization levels. For the proton: 5 * .66 = 3.3. This means that the uncertainty of the electron field has to be much less than the uncertainty of the proton field. The vacuum handles this by creating more samples of the field, mainly 49 more. So the electron, with the longest wavelength ends up with a greater number of samples in its side lobes, the advanced and delayed fields.
Energy states
This is the ground state. The number of Nyquist samples is sufficient to balance phase, if I did the numbers right. Increasing the energy state is equivalent to removing Nyquist samples. I would think the energy states can be increased by removing the Nyquist samples three at a time. As they are removed, at some point a phase inversion occurs and a dimension of simultaneity is introduced. At that point, the system equilibriates back to a state where the Nyquist rate is again 1/3, and the excess Nyquist samples are the kinetic energy of the emitted particle.
But since the length of the sequence was measured in the dimensionality of the scientist, the system reaches a limit which should be two more dimensions, in our case. When that limit is reached, the wave contribution from the proton collapses, and the proton particle goes back to its ground state, it requantizes from wave to particle.
As long as phase inversion is not breached, the modeler is free to add chunks of inert vacuum along an axis of dimensionality to distribute the wave. The modeler introduces simultaneity back, within the energy holding capacity of the volume from which the sequence was taken.
Time and space dialation
Time is the ration of Nyquist samples to the length of the sequence. Space dialation are the samples along the axis of dimensionality.
Low SNR fields need greater numbers of field samples to balance phase.
Phase delay in sampling and field curvature.
This is important. Why do most quantizations end up with fewer field samples holding more phase advanced and more field samples holding more phase delay? The electron seems phase imbalanced, always negative, but that cannot be so, phase rebalancing still occurs at Nyquist. The number of sub quantized samples around the electron is fixed by the wavelength, so the balance is in fewer field samples having large phase advance and more field samples having less delay. The answer is relative sparsity, the electron is relatively sparse to the proton, and longer wavelength, so it extends more samples to the proton, all of one phase sign, and fewer in the other direction. Hence the delayed phase is smaller per sample than the phase advance. The longer delayed field is the short end and the advanced field the long end, mainly because of the wavelength of the sparse is longer relative to the dense.
Sparse regions have stable quants, unbalanced phase, more simultaneity, more kinetic energy and more vacuum.
I(n our compressed sun center we should expect a slightly more dens electron region, a slightly less dense nuclear region and a slightly more dense boson region. On the outs shell, the magnetic region is dens, the gravitational regions sparse. The vacuum as been redistributed to provide the balance, the nuclear getting a bit more, the electron getting a bit less.
Wave action between the electron and magnetic would be slightly multimodal, containing sjorter nuclear modes. An unstable quasar wave would requantize into component, including galaxy size quants near the edge. Galaxaies would be dispersed around the quasar, kep in orbit by far flung blackhoeltron, and compressed by random appearance of galaxy size quant near the quasar the have requantized momentarily.
Compaction is the process of move the vacuum out from the center as the center cools. Thermal energy increases the density mis match between orders, radiation restores the balance. The shorter the wavelength of emission, the larger the phase mis match, and so the greater the density mismatch.
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