Setting some terms for Shannon and Quantum Mehanics

The way this model specifies quantum mechanics solutions is to use a finite sequence that contains the system at minimum phase.  We need to mostly set some standard units with regard to SNR and to define some terms that are reusable through out. Then we can go on t look at atomic orbitals more. I had to get back into this because of the Zeeman effect, this theory needs to get that right and I wanted to clarify stuff before I dig into that math.

One point. What phase resolution is used to balance phase in the quantum sequence? Since the system is already under sampled, the only phase left is the original Nyquist phase values.

For a Compact System:

If the vacuum ignored the Pauli requirements, and measured the phase imbalance completely at the Nyquist rate, then it will measure a unit of phase for every two Nyquist samples. In this case the sequence will be 2*N Nyquist samples, divided into N/2 phase measurements. The N/2 phase measurements are again divided into N/4 and N/8. We get a binary system. Working the theory the way Shannon did, then, the whole thing is 1 - (bit error).  Any Complete sequence (the shortest sequence over which phase is balanced), will be 2**N, where N is the order, including Nyquist. In this case, it is 2**3. The Nyquist is order 1. That is a change I have made from previous posts. Take note.

In this binary system, working with two mass M1 + M2, then, and Nyquist gets 1/2*(M1+M2), that is the phase left over when the other two masses are phase balanced. In our 2/3 system, Nyquist gets 1/3 *(M1+M2). The total sequence will be 1.5**N. The bits counts as N**1.5,(N-1)**1.5, and so on. And Nyquist always gets N/3 of the sequence in a compact system.

For Sparse system:

We need to add signal for the kinetic and wave motion. Note, in quantum mechanics, the mass is decomposed into a standing half wave in compact systems,which is the whole point.

Adding kinetic or wave motion requires we ad a pseudo orders, for each axis of simultaneity along which waves or mass can move. We increase the bits of precision.

Consider the electron to proton mass using our base 1.5 system.  1/Log(1.5,1836) = 18, and that is the sparsity ratio, the number of orders needed to make the compact sequence. And that is the number of electron quantum states available, including kinetic energy. But that is only one axis of simultaneity on the Bohr atom. In terms of mass equivalent, this kinetic energy is just a bit smaller than the mass of the electron. The compact mass of the electron is 2/3 the mass of the proton. Such a world does not exist except a bare moment after the big bang. But adding the kinetic energy order, then, the kinetic energy is 2/3 the mass of the proton in units of relative mass.  In the complete sequence, Nyquist is order 1, proton is order 2, kinetic energy is order 1 thru 17, and the electron is order 18. The kinetic energy is really a 17 bit number, base 1.5, or a three digit number base ten.

 This  tells us the frequency with which the electron will have appear along the radius.

This sequence corresponds to the first picture to the left. We can call that cloud the region of simultaneity, and the total complete sequence is 1836 + 1836/3; the last part is Nyquist samples needed to balance phase along the sequence.  The subdivision of sample space goes as follows.

Of the rest, we can balance by order or balance by mass. Since mass is equivalent to wavelength (in the compact order), and 1/wavelength is frequency of appearance along the sequence, the two should match.  I will try to get this right in a moment, then look at setting quant levels by SNR.

We have 19 orders, one for Nyquist, one for proton, 16 for the kinetic and 1 for the electron, listed from small to large. 2/3 of the Nyquist makes hash marks, basically the Pauli separation.  The other one third is available for phase equalization. Our counting system, in fractions, is:

(2/3)**i, and i is the order, which is .666, .44, .297, and so on. Our 'digits' should match the order in the compact version. These are the masses of each order, and thus the relative frequency.

Our ratio is 2/3, so it converges to 3, which can be seen here. To get the fraction for a pseudo order with a series from 2-17, for example, use S-2/3 * S = T, so S = T/(1-2/3).    So for the kinetic, which is the sum from order 2 to 17, use 2/3**2 - 2/3**18, or .418.

This method then breaks down the sequence into sample rates per order, and the wave function can be laid out.  The Nyquist samples appear at their sample rate and minimize phase.

Then break up the kinetic energy into more moments by taking off the first order, and calling that different spheres of  simultaneity.  Each time a new kinetic moment is introduced you are essentially adding energy.

Make sure the proton has a charge field and its standing wave has it variations. Then lay out the nyquist to minimize phase along the sequence. The variations in the Nyquist function along the sequence should have multiple modes which tell you how to rotate the kinetic axis to minimize phase.  The third and fourth orbitals should be defined by some rotation that removes the Nyquist phase variation.  This alway generates the maximum entrop encoding of the atom, and the minimum phase moments along the Nyquist phase equalizer shouold be correct.

SNR Method:

SNR.  The SNR method lets you skip the hassle of compact systems. Just take the mass ratios as SNR, then use Shannon to get the number and level of quants, as I did in some previous posts.

Now, I haven't tried any of this, so warning, the first experimenter will change details.