Is there a connection between the quantum world and the large scale appearance of the universe?

Let's ask ourselves what is the smallest change in energy dE you can have with maximum wavelength w.

Taking the standard formula the links the energy and wavelength of a photon we have E = hc/w where w is the wavelength.

We differentiate E with respect to w to establish the
relationship dE/dw = -hc/w^{2}.

Re-arranging dw/w^{2} = - dE/hc. This tells
us that the rate of change of the wavelength per wavelength = -dE/hc. The '-'
tells us that the rate of change dE/hc decreases as w increases. It would appear that an apparent stretching of wavelength is an intrinsic property of
electromagnetic radiation rather than an expansion of space.

The lowest possible quantum of energy is one with a wavelength the size of the observable universe. E = hc/1.265*10^{26}m = 1.57*10^{-51}J or 1.57*10^{-44}ergs.

dw/w^{2} = 1.57*10^{-51}/hc = 7.9*10^{-27}m^{-1}

So, does perceived red shift have its basis in a quantum phenomenon rather than an expanding universe. There are some circular arguments. In actual fact, the only truly common parameter is the size of the observable universe as 'hc' cancels out and disappears. Here is a summary. The blue is existing knowledge which agrees with the expanding universe notion. The green is the alternative view.

The distance to the edge of
the observable universe is around 1.265*10^{26}m

The Red Shift Factor =
1/(1.265*10^{26}m) = 7.9*10^{-27}m^{-1}

Universal frequency =
c/(1.265*10^{26}m) = 2.37*10^{-18}Hz (s^{-1})

Universal time
=1/(2.37*10^{-18}Hz (s^{-1})) = 4.22*10^{17}s

There is a fundamental
wavelength to the universe being the length of the observable universe 1.265*10^{26}m.

There is therefore a fundamental frequency of c/(1.265*10^{26}m) = 2.37*10^{-18}Hz
(s)^{-1} or *2Pi to give 1.49*10^{-17}s^{-1}.

The fundamental quantum of energy = hc/(1.265*10^{26}m) = 1.57*10^{-51}J

The Red Shift Factor is also dw/w^{2} = - dE/hc = 7.9*10^{-27}m^{-1}
where dE = 1.57*10^{-51}J

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