Lyndon's tired light model as described in his preprint paper works as follows:

• A photon is absorbed by an electron initially at rest, giving the electron a boost in velocity.
• The electron is brought to rest again.
• The electron emits a red-shifted photon, along the line of the original photon.
• The recoiling electron is brought to rest again.
• The electron is brought to rest by interactions within the plasma, and these decelerations emit CMB radiation.

This is physically impossible. Electrons don't absorb photons unless they are part of an atom. A very easy proof of impossibility is energy momentum analysis; and this is why Lyndon has been asked repeatedly for an energy momentum analysis for his reaction. It is also why he has repeatedly refused to supply one. -- he can't; and above all he can't admit that he can't.

Instead, we get a series of red herrings. The latest red herring involves reference to a paper that gives an analysis for motions of a charged particle in an electromagnetic wave. Such a wave corresponds to a stream of photons; so it's got nothing to do with Lyndon's reaction. The paper refers to oscillations only exist while a whole stream of photons is passing through to maintain the oscillations; and this has nothing whatsoever to do with finding a place for the missing energy in Lyndon's photon absorption reaction.

This paper has no absorption; no redshift; no plasma. Lyndon gives no quantified connection to his photon absorption. He gives no energy momentum balance in which we can see where the energy of an absorbed photon ends up. He has no answers; only red herrings with yet another paper he does not understand.

But just for the sheer humour of it; let's plug in some numbers anyway. It's a good exercise to get a feel for the new bit of physics Lyndon is making a hash of. Perhaps we can make a party game around how many orders of magnitude there are in Lyndon's errors this time.

Equation (7) of the paper allows us to infer a peak momentum "p" for the electron oscillating in a passing wave as being E0.e/ω, where E0 is the field strength of the electromagnetic wave, e is the charge on the electron, and ω = 2*π*c/λ is the angular frequency of the wave in rad/sec.

The energy of oscillation will be p^2/2.m, where p is this maximum momentum, so the energy of the oscillating electron is E0^2.e^2/2.m.ω^2

Lyndon's paper has a photon being absorbed, and this is the energy Lyndon has never accounted properly. We'll plug this in and see what it means for oscillations of an electron in an electromagnetic wave to have this much energy.

Energy = h.c/λ = E0^2.e^2.λ^2/8.π^2.m.c^2
Therefore
E0^2 = 8.π^2.m.h.c^3/λ^3.e^2
Plug in the wavelength λ = 500 nm, and we can get
E0 = 2.00e10 J/C

This is the peak field strength of the electromagnetic wave with wavelength 500 nm required to give the electron oscillations with energy equivalent to one photon; the missing energy that Lyndon still has to quantify.

Now the irradiance of an electromagnetic wave (power per unit area) is
I = c.ε.E0^2/2 = 5.31e17 Joules/m^2/sec
The constant ε is permittivity, which is 8.85e-12 Farads/meter. Since the energy of a photon is 3.97e-19 J, we require a flux of
1.34e36 photons per meter squared per second to maintain this oscillation.

That, my friends, is a big number. For comparison, starlight is roughly 10^10 photons/m^2/s, and daylight about 10^18 photons/m^2/s. It is, in fact, so big that the weak wave approximations used in the cited paper are not valid.

This rather suggests Lyndon will never try to give a balanced energy momentum budget based on the actual numbers or formulae of the cited paper. He will continue to pretend that just tossing off the reference to a different reaction stands as an adequate answer to the requests for energy momentum budgets of his photon absorption reaction.

I would very much appreciate anyone with a calculator taking the time to check my figures for me. But I think they are in the right ball park. As a double check for myself, I scaled the numbers down for dimensions roughly corresponding to a single photon, and ended up within an order of magnitude or so of the momentum transferred to an electron in Compton scattering.

Cheers -- Sylas

PS. Added in edit. I have used unicode for the Greek letter pi, and it ends up looking a lot like lower case N ("n") in my browser. I have no variable "n" in the above analysis, and pi appears as "π".