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}.

This seems to tells us that the there is an intrinsic lossss of energy with distance. The '-' tells us that the rate of change dE 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.

Some observable facts:

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

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