Vacuum friction that slows down light and produces the Hubble redshift thereby (in a STATIC universe):

"Indeed, Wilczek began his lecture by speaking of the profound analogy between materials and vacuum. What our naked senses perceive as empty space turns out to be a riotous environment of virtual particles fluorescing and dying away on extremely small scales of space and time, as well as fog-like fields and condensates, which permeate all space and dictate the properties of elementary particles. To give an analogy for this perplexing new picture of reality, Wilczek asks us to imagine intelligent fish in a world surrounded by water. Such creatures would perceive the water surrounding them as their version of empty space or a vacuum. "The big idea I want to convey is simply this: We're like those fish," he said. What our senses perceive as empty space is better understood as a substance, a material." https://asunow.asu.edu/20170208-finding-nothing-conversation-frank-wilczek

Paul Davies: "This leads to the prediction of vacuum friction: The quantum vacuum can act in a manner reminiscent of a viscous fluid." http://philpapers.org/rec/DAVQVN

New Scientist: "Vacuum has friction after all." https://www.newscientist.com/article/mg20927994.100-vacuum-has-friction-after-all

"So how can a vacuum carry force? One of the first things we learn in classical physics is that in a perfect vacuum - a place entirely devoid of matter - friction can't exist, because empty space can't exert a force on objects traveling through it. But, in recent years, quantum physicists have shown that vacuums are actually filled by tiny electromagnetic fluctuations that can interfere with the activity of photons - particles of light - and produce a measurable force on objects."

http://www.businessinsider.com/casimir-effect-vacuum-space-nanoparticles-2017-4

Assume that, as the photon travels through space (in a STATIC universe), it bumps into vacuum constituents and as a result loses speed in much the same way that a golf ball loses speed due to the resistance of the air. On this hypothesis the resistive force (Fr) is proportional to the speed of the photon (V):

Fr = - KV

That is, the speed of light decreases with time in accordance with the equation:

dV/dt = - K'V

Clearly, at the end of a very long journey of photons (coming from a very distant object), the contribution to the redshift is much smaller than the contribution at the beginning of the journey. Light coming from nearer objects is less subject to this effect, that is, the increase of the redshift with distance is closer to LINEAR for short distances. For distant light sources we have:

f' = f(exp(-kt))

where f is the initial and f' the measured (redshifted) frequency. For short distances the following approximations can be made:

f' = f(exp(-kt)) ~ f(1-kt) ~ f - kd/λ

where d is the distance between the light source and the observer and λ is the wavelength.

The approximate equation, f' = f - kd/λ, is only valid for short distances and corresponds to the Hubble law.

The original equation, f' = f(exp(-kt)), shows that, at the end of a very long journey (in a STATIC universe), photons redshift much less vigorously than at the beginning of the journey. It can be shown that this provides an alternative explanation of the observations that brought the 2011 Nobel Prize for Physics to Saul Perlmutter, Adam Riess and Brian Schmidt.

Pentcho Valev