Overview of the theory.
In the tired light theory, photons of light from distant galaxies interact with the electrons in the plasma of Intergalactic Space. Here they are absorbed and the electron set into oscillation before being re-emitted as a new photon. On absorption and re-emission, the electron in the plasma recoils meaning that some of the energy of the photon has been transferred to the electron. Since the energy of the photon is less, the frequency is less and the wavelength is greater. It has been redshifted. The theory shows that:
H = 2nhr/m for the electron.
The electron is brought to ‘rest’ (by ‘rest’ we mean its initial condition) by interactions with the other electrons in the plasma and the energy transferred to the recoiling electron is radiated as a secondary photon by bremsstrahlung. This radiation forms the CMB.
The theory shows that the wavelength of the emitted secondary CMB photon is given by:
Lambda (CMB) = 2mc(lambda)^2/h
where lambda is the wavelength of the original photon. Nb (lambda)^2 means 'lambda squared'.
Since the microwave radiation is produced in IG space it will collide with dust which will absorb the radiation and re-emit it (thus smoothing out the kinks in the already microwave radiation) to give the Black Body curve.
In considering scatter, we assume that the particle is originally at rest, since any affects of the random thermal motion cancel out over the large number of interactions a photon makes on its journey from a distant galaxy to the earth. In fact a photon of light on its way from a galaxy with redshift 0.1 will make about 25,000 interactions on its way.
The paper has been accepted for publication and a preprint is available here
Effects Of The Thermal Velocity Of The Electrons On The Tired Light Process.
In the theory we have considered low energy photons such as light interacting with the electrons in the plasma. However, we know that X rays and Gamma rays interact by a process known as the Compton effect. We must ask the question, at what photon energy does the tired light effect stop and the Compton effect begin? This critical photon energy must depend upon the thermal energy of the electrons in the plasma.
If the photon energy is much less than the average kinetic energy per particle of the plasma then the absorption of the photon only increases the electrons total energy slightly. The motion of the electron receives a slight ‘tweak’ and thermal motion is still dominant.
The electron is set into oscillation (superimposed on top of the thermal motion), the oscillations die down and a new photon is emitted. The electron recoils, is brought to rest and secondary radiation emitted. All this, according to the tired light theory.
But if the photon energy is greater than the average Kinetic energy per particle in the plasma, then the situation changes. The energy of the individual electron increases greatly and the effects of the energy absorbed by the photon become dominant. The motion of the electron is now determined by the photon impact and the interaction will be Compton.
Clearly the temperature of the plasma affects the point at which the tired light theory breaks down and the Compton effect takes over. There must be a critical photon energy, below which tired light occurs and above which Compton scatter takes over. This critical photon energy is where the photon energy (hf) is equal to the average kinetic energy per electron in the plasma (3kT/2). This critical photon energy has a corresponding ‘critical frequency, fc’ and a ‘critical wavelength, lambda 'c’.
Let us calculate this critical wavelength, Lambda 'C'.
Handbook of Space Astronomy and Astrophysics gives the electron temperature for the plasma of IG space as 10^5 – 10^6 K.
http://ads.harvard.edu/cgi-bin/bbrowse?book=hsaa&page=286
Average kinetic energy of each electron is given by 3kT/2 and gives a range for the average energy of each electron as 2.1x10^-18 J to 2.1x10^-17 J.
For photons of light from distant galaxies to have this energy,
hfc = 2.1x10^-18 J to 2.1x10^-17 J
where fc is the critical frequency of the incoming photon.
Substituting for h gives fc as 3.2x10^15 Hz to 3.2x10^16 Hz. ie the critical frequency is in the UV.
Using c = (frequency)x(wavelength) gives the critical wavelength as:
Lambda 'c' = 9.4x10^-8 m to 9.4x10^-9 m
We would expect the intensity of the CMB to ‘fall off’ when the wavelength of the incoming photons becomes less than the critical wavelength (ie for higher photon energies).
Since Lambda (CMB) = 2mc(Lambda)^2/h
When an incoming photon has energy equal to the average kinetic energy of the electrons in the plasma, we would expect the intensity of the CMB to peak. The wavelength at which this intensity will peak, Lambda (peak), can be found using the above formula and the range of critical wavelengths. The range in which the CMB peak wavelength will occur is therefore:
Lambda (peak) = 7.3x10-3 m to 0.73x10-3 m
The CMB is known to peak at a wavelength of:
Lambda (peak) = 2.1X10-3 m
Experiment is once again in agreement with this tired light theory.
Ashmore’s Second Paradox.
The Hubble constant can be calculated from the number density of the electrons in the plasma in IG space and the wavelength at which the CMB intensity peaks can be determined from the temperature of the plasma of IG space. Therefore, the Universe is not expanding.
