Tired Light and the CMB
Introduction
We have already seen how light is redshifted as it passes through the plasma of Intergalactic space. Photons are absorbed and re-emitted by the electrons as they pass through the plasma, the main energy of the photon being stored in the oscillations of the electron. Both on absorption and re-emission of the photon, the electron will recoil.
Thus, some of the energy of the photon is lost to the recoil of the electron.
Since the photon has lost energy, its frequency must also reduce (E = hf).
Since the frequency of the photon is now less, the wavelength, λ, will increase (c = fλ).
The photon has been redshifted.
But what of the energy 'lost' by the photon as the electrons recoil? This is given off as secondary photons and forms the CMB (Cosmic Microwave Background radiation). The CMB is often cited as being the 'proof' of the Big Bang theory, the radiation left over as the 'echo' of the Big Bang. But it is not as easy as that. Regardless of your beliefs as to how the Universe started, one piece of experimental observation has to be explained - that is, in redshift, the photons of light have a longer wavelength on arrival at the Earth, than when they set off from the distant galaxy. This means that photons of light have less energy on arrival than when they set off.
Where did this energy go?
In the theory of the expanding universe you will get all sorts of nonsense in an attempt to explain it, but you will never get a satisfactory answer.
In Tired Light we say that the energy lost by the photons in being redshifted is given out as the cosmic microwave background (CMB). The CMB is a vast amount of low energy microwave photons that are all around us. When your T/V is 'off tune' quite a number of those little white dots that you see on the screen are CMB photons picked up by your T/V aerial.
What evidence do we have for this?
Firstly, we can calculate the expected wavelength of this radiation and find that it is microwave.
Secondly, rather than the electrons being spread evenly throughout Intergalactic space, we would expect the plasma to be in the form of clouds. This would introduce some degree of quantization in the redshifts of distant galaxies. The plasma clouds will be of similar size and so we would expect to see certain redshifts appear more than others as the light travels through one, two, three plasma clouds and so on.
Thirdly, we expect these plasma clouds to show up as 'clumps' in the CMB with the nearer of the clouds appearing bigger than those further away. When we look at the CMB we find that there are small variations in it. In the Big Bang Theory, these 'clumps' are said to be at the beginning of the Universe and form the 'seeds' from which the galaxies and so on are formed. However, a team of international scientists have found that the larger of the clumps in the CMB are positioned at strategic positions in relation to our galaxy. This means that it is highly unlikely that they are at the 'beginning of the Universe' - as stated in the Expanding Universe theory but they must be 'local'. However. this is what one expects in Tired Light. The nearer the plasma cloud, the larger it looks and we will see why some of these local plasma clouds are linked to the motion of our galaxy as found from observation.
And lastly, there are some interesting 'coincidences' between the temperature of the plasma clouds and the CMB which are perhaps a little too much to be just 'coincidences'!
Lets look at this in more detail. If you have not seen the redshift Tired Light Theory, then it may help to do so first. We will start by showing mathematically how it works.
i) Calculation Showing That The Wavelengths of the Secondary Photons Are In The Microwave Region.
Momentum of the incoming photon = h/λ where h is the Planck constant and λ the wavelength of the incoming photon. This photon is absorbed by an electron of mass, m that oscillates due to the incoming electric fields of the photon. The electron also recoils when it absorbs the photon and does so with a velocity, v.
By the principle of conservation of momentum:
h/λ = mv or v = h/mλ
The Kinetic Energy (KE) transferred to recoiling electron is mv2/2 = h2/(2mλ2)
This is the energy radiated by bremsstrahlung (radiation emitted by an electron whenever it accelerates) and forms one of our CMB photons.
Energy of CMB photon = h2/(2mλ2) Since E = hf, and c = fCMBλCMB
The wavelength of the CMB photon is given by:
λCMB = 2mc λ2/h
Photons of light have a wavelength of 5x10-7 m. When a photon of light is redshifted the wavelength of the CMB photon emitted is 21cm, ie it is in the microwave region. For the CMB, the wavelength of the majority of photons is 2.1mm. This is produced by photons with a wavelength of 5x10-8 m, ie by photons in the Ultra Violet part of the spectrum.
A 'spin off' from this is an explanation of the question, 'just why are there so many CMB photons?'
Each time a photon is absorbed and re-emitted, its wavelength increases by an amount 'h/mc' or 2.42x10-12 m. In travelling to us from a galaxy with a redshift of 'one' (z = 1), a single photon of wavelength 5x10-8 m will make over 20,000 collisions and thus produce over 40,000 CMB photons. Is it surprising that there are so many CMB photons around us?
We see that the Tired Light theory is consistent with the CMB in that the energy lost by the photons in being redshifted is given off by the recoiling electrons and this radiation is in the microwave region.
However, the overall spectrum of the microwave radiation is the same as that of a 'black body' with temperature 2.7K. How do we get this? Well up to now we have treated the plasma as being evenly spread out throughout Intergalactic space. Whilst this works very well when considering the vast distances involved there will be local variations. In particular, there are vast clouds of Hydrogen atoms. Cosmic rays (mainly protons) streaming through IG space will collide with the nuclei of the Hydrogen atoms in these clouds and the products of these proton - proton collisions will eventually decay into electrons to give us plasma. These clouds are sparsely occupied and so the electrons in the plasma will still be able to recoil and give us our Tired Light Effect. High redshift galaxies are known to have strong Hydrogen absorption lines showing that this light has passed through large amounts of Hydrogen on its way to us. As the light is redshifted CMB photons will be given off with the overall effect that these clouds will 'glow' in the microwave. Furthermore, the plasma clouds are in thermal equilibrium where the rate at which they receive energy from the light being redshifted is equal to the rate at which they radiate energy due to the CMB. The radiation will be black body.
The diagram below sets out the situation as explained by Tired Light.
The above diagram shows how it works. The distant galaxy is in the top right corner, the earth in the bottom left corner and two of the many plasma clouds are shown in Intergalactic space. Light emitted by the distant galaxy travels to Earth and is redshifted as it passes through the plasma cloud. As the light is redshifted, the photons lose energy and this energy is emitted as two CMB photons - one on absorption and one on re-emission of the original photon. When we add up all this secondary radiation due to all the plasma clouds and galaxies in the Universe, we get the CMB. It is for this reason that the CMB is homogeneous - basically the same everywhere we look.
(ii) Clumps in the CMB
Whenever a photon is redshifted by the absorption and re-emission of a photon the electron recoils twice and two CMB photons are given out. For photons redshifted within these plasma clouds, the clouds will glow in the microwave region and provide the CMB. Whilst the laws of averages tell us that the microwave radiation given off by each cloud will be very similar there will be slight 'temperature' variations from cloud to cloud. These will appear as clumps in the CMB. These clumps are known to exist but, in the Big Bang Theory they are said to be the 'seeds' from which the galaxies etc grew. In the BB Theory, these clumps are said to be at the very edge of the Universe and seen when we look back in time at the Big Bang itself.
It would seem to be an easy dispute to settle. In the BB, these clumps are very distant. In Tired Light the CMB is 'local' formed by nearby plasma. If the clumps are distant then there will be no relationship between our galaxy and the 'clumps' in the CMB. If the clumps are 'local' then there could well be some alignment that puts us somewhere 'special' in the Universe.
In 2005, a team of international scientists found that the larger of the clumps in the CMB were aligned with our Solar System. In astronomy, large means close and so we are not surprised when we find that it is the larger or closer here we have our apparent motion as predicted by the Tired Light Theory. Furthermore, galaxies such as ours are known to be surrounded by Hydrogen clouds and these are thought to be the remnants left over from the formation of our local galaxy. The Tired Light Theory says that cosmic rays in the form of protons passing through these Hydrogen clouds collide with the Hydrogen Nuclei and create plasma. Photons of light passing through the plasma created by this plasma is redshifted and the energy lost is re-radiated as the CMB. The clouds give us the 'clumpiness' and since these clouds are the 'left overs' from the formation of the galaxies in our local cluster, is it any wonder that the larger and nearer of the clouds are linked to the galactic plane of the Milky way?
(ii) Quantized Redshifts.
So, we have a sparsely populated plasma in Intergalactic space with a clumpy denser plasma in the Hydrgen clouds. What this means in observational terms is that when measuring the redshifts of distant galaxies, we should see the usual continuous spread in redshifts but superimposed on top of this we should see certain preferred redshifts caused by the light passing through these clouds. That is, light passing through one of these clouds will receive a boost in redshift. Furthermore, these 'boosts' in redshift will be quantized as the light passes through an integral number of these clouds on its way to us. The further away the galaxy, the greater the distance travelled by the photons of light and thus the more plasma in the clouds of Hydrogen the photons will pass through.
A galaxy - redshift frequency distribution should have a continuous spread but with spikes corresponding to one cloud, two clouds, three clouds and so on.
This is what we find. Below is shown the results* of the 2dF Galaxy Redshift Survey and can be found in this paper by Colless et al. Mon. Not. Roy. Astron. Soc. 328 (2001) 1039.
The Redshift Survey is designed to measure
the redshifts of around 250,000 galaxies. By
inspection of this distribution we see that on
top of the continuous distribution 'spikes'
appear in intervals of redshifts of about z = 0.025.
Are these spikes caused by the plasma in the
intervening Hydrogen clouds?
The Hydrogen clouds in IG space are vast and there is evidence to show that these clouds extend for up to 1022 m. In order to produce a redshift of 0.025 in travelling a distance of 1022 m through one of these clouds would require the value of the Hubble constant to be 6.6x10-15 s-1 in these regions ( using The Tired Light expression for redshift of z = exp(Hd/c) - 1). Using H = 2nhr/m, we can calculate the electron density within these clouds and this comes out to be 2800 electrons per cubic metre. This number is feasible - especially when one considers that in IG space the collision products from the proton - proton collisions always decay into electrons as the collision length is greater than the decay length. In the Earth's atmosphere etc. the collision products collide into other particles before decaying and so the end products is not necessarily electrons.
Heavenly Happenstances.
i) The 'coincidence' between the Plasma temperature and the Wavelength at Which the Intensity of the CMB Curve Peaks.
We know that the temperature of the plasma clouds in Intergalactic space is between 105 and 106 Kelvin and we know that the average kinetic energy of an electron at these temperatures is given by 3kT/2 - where k is the Boltzmann constant (1.38x10-23 JK-1). The point where the energy of the incoming photon is equal to the initial kinetic energy of the electron that it interacts with is of interest and should mark a watershed in the CMB curve. If the energy of the incoming photon is much less than the kinetic energy of the electron then the electron's motion will not change drastically but will only be modulated by the effects of photon absorption. If the energy of the incoming photon is much greater than the initial kinetic energy of the electron the the effects of photon absorption will dominate. The point where the photon energy is equal to the electron kinetic energy marks the point where one effect finishes and the other starts. We will now work out the wavelengths of the CMB photons emitted at this watershed and see if it shows up in the observed CMB curve.
energy of incoming photon = hf
Kinetic energy of plasma electron = mv2/2 = 3kT/2.
For this temperature range (105 to 106 Kelvin) the range of frequencies of incoming photons having the same energy as the Kinetic Energy of the electrons in the plasma is 3.1x1015 Hz and 3.1x1016 Hz.
When these photons are redshifted, the wavelength of the CMB photons given off will be in the range 0.076mm to 7.6mm - and it is in this range of wavelengths where the intensity of the CMB curve should peak. Again, this is consistent with observation as the wavelength at which the intensity of the CMB peaks is found to be 2.1mm. The uncertainty is due to the uncertainty in determining the temperature of the plasma clouds. However, here we have introduced a new parameter - the temperature of the plasma clouds, and yet the Tired Light Theory is still consistent with observation.
ii) The 'coincidence' between the point at which Compton Scatter ceases and the Wavelength at Which the Intensity of the CMB Curve Peaks.
There are other interactions between photons and electrons and one of the more common ones is the Compton effect. Here, the photon is scattered at an angle to the original direction in which the photon was moving. There is an exchange in energy between the photon and the electron but the photon is scattered. It does not arrive at Earth since the direction of the photon has changed.
As to 'which way the energy goes' in the Compton Effect depends upon the energy of the photon compared to that of the electron. If the photon has more energy than the electron then the electron gains energy and the photon loses it. This is what is normally known as 'Compton Scatter'. However, if the energy of the photon is less than the energy of the electron then the photon gains energy from the electron. The electron slows down and the photon gets a boost in frequency. This is known as 'Inverse Compton Scatter'.
When the energy of the photon is equal to the energy of the electron it collides with then there is no exchange of energy. As we have shown above, this is the point in the Tired Light Theory where virtually the whole of the CMB spectrum is formed! Photons with energies equal to the kinetic energy of the electrons they interact with produce the microwave CMB - and yet this is the very same point at which Compton scatter is no longer having an effect. Is it because because the two effects, Compton and Tired Light, are competing for electrons to collide with? At the point where the photon energy is equal to the kinetic energy of the electron in the plasma cloud, there is no exchange of energy between the photon and electron fields by the Compton Effect. Tired Light Effects dominate.
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© Lyndon Ashmore. June 2005. All rights reserved.