In bits: (hv/kT) = log(1+hv/E)/log(2)
This is the quant size of the vacuum noise. Einstein and Stern added a term:
Both quant and SNR look like energy? Yes, but the exponents of the base have a factor (1/2) which represents twice the sample rate, and thus, the square root of energy. So they are normal. They both use frequency to quantize light. They use Boltzmann's constant and set bandwidth by that, the sample rate becomes Temperature. But fell free to dump those units and replace speed of light with sample rate of light.
kT really takes a probability function multiplied by the number of elements to give you a band limit, and means: Sampled at twice that rate.
Kinetic energy is noise, signal is potential energy. Einstein added enough noise so it fails the Shannon test. When it passes the Shannon test, then it can be broken up into sub channels and make a twos system. Otherwise we can make it a natural log digit system, but group operations are a bit complicated. I need to look into stochastic algebras, but no doubt they mean that numbers have to tiny little matrices, which I expected.
I have a hard time finding my error here
- We know we operate at maximum (Shannon) or near maximum (Hyperbolic) entropy functions.
- My quant ratios seem to be fitting all the major constants of physics, they define the Shannon potential boundaries.
- Group theory tells us what are the valid integer sets along out invariant frame axis.
- I can mark any subset of integers with my Shannon operator and the boundaries, my Hamiltonian is my SNR.
- I can sub select the integers that meet group theory.
- I can substitute my hyperbolic for the Shannon and draw my orbitals.
Where have I gone wrong?
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