Derivation of The Hubble Flow | ||||||||||||||||||||||

We can use this tired light theory to predict a value for the 'Hubble Flow'. Nearby galaxies, ones with in our local cluster do not obey the Hubble redshift relation, v = Hd. Followers of the Big Bang say that 'local gravitational effects' are greater than the effects of expanding space. For the Hubble relation to hold, galaxies must be millions of light years away. Some say 5 or 6 million, others say 50 million light years away. Galaxies at these distances and more obey the Hubble law and are said to be in the 'Hubble flow'. In Tired light, I say that there are insufficient collisions between photons and electrons to make the statistics work. That is, in order to have a sufficiently large enough sample to produce reliable redshifts the galaxies have to be sufficiently far enough away. By comparing space to a piece of glass it should be possible to use the theory to predict a value for the start of the Hubble flow. |
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When light travels through a transparent medium such as glass it does so by the photons firstly being absorbed by the electrons in the medium, and then the electron reemits a ‘new’ photon. There is a delay between absorption and reemission (Feynman says the electron ‘scratches its head’ in between) and it is this delay that causes wave to travel at a slower speed in the glass than it does in a medium. This reduction in speed by the photons being absorbed and reemitted leads us to the refractive index of the medium and Snells law (sin i/sinr and all that). Let me ask you a question. Is there a minimum thickness of a piece of glass such that the light passing through the glass film does not collide with any of the electrons within it? This would mean that refraction and Snell’s law would no longer hold for this thin film of glass. The answer is that it is highly likely, but if this is so, the thickness must be very small. We know that a layer of glass 10-7m thick has a refractive index and so reliable interactions must take place between the photons and electrons. This is the basis of ‘blooming’ on camera lenses and this works extremely well. Here is a reference to this process: http://www.newscientist.com/lastword/article.jsp?id=lw1046 This layer is 1000 atoms thick. Take care here, because this is where two areas of Physics overlap. The symbol ‘n’ I use in this calculation, tells us how many electrons there are in each cubic metre of space. It is NOT the symbol often used for the refractive index of glass! Accepted Physics tells us that the mean free path of a particle/photon is given by [(electron density, n)x(collision cross section,?)]-1 = (n ?)-1 Number of ‘interactions’, that is how many times a photon collides with an electron in passing through the glass = (the distance travelled, d)/(mean free path) = nd? In a solid there are about 1030 atoms per cubic metre, so lets assume that each atom contributes one electron to the effect (‘n’ glass should be of this order of magnitude at least). So for glass nd = (1030)x(10-7) which is 1023 That is, in going through this thin layer of glass, where we know that the number of collisions leads to repeatable and demonstrable refraction effects, the photons make (1023) ? collisions (where ? is the collision cross section between photon and electron. This tired light theory treats intergalactic space as a transparent medium, and so if we have this many photon-electron interactions in intergalactic space then we would expect to have repeatable and demonstrable effects i.e. would should see reliable redshifts and Hubble’s redshift distance law should hold. That is, we should be in the ‘Hubble flow’ for at least this number of collisions and above. For intergalactic space, measured and published values of the Hubble constant H (where v = Hd) are not very precise and vary between 0.1 and 10 electrons per cubic metre. As a test of this theory let us use the relation H = 2nhr/m to predict the electron density, n. According to this tired light theory the Hubble constant H can be thought of as a measure of the electron density of intergalactic space, n. Supernovae data gives H = 64km/sec per Mpc and this tells us that the electron density of intergalactic space is given by, n = 0.6 m-3. What thickness of IG space is equivalent to our non-reflective lens coating that produces reliable interactions between photons and electrons? In this case nd? for glass should equal to nd? for intergalactic space. That is (1023) ? = 0.6d?, where d is the thickness of intergalactic space (IG) equivalent to our thin film of glass. The value of d is 1.7x1023 metres. This is 18 million light year. So, for IG distances above 18 million light years we would expect the effect to work and for distances less than this we would expect to find a point where it stops working. As stated earlier. it is known that for nearby galaxies, we don’t get recession velocities. Followers of the Big Bang say that ‘local gravitational’ effects cancel the effects of expansion and so we measure only their peculiar motions. To show an expanding universe, galaxies have to be in the ‘Hubble flow” and it is known that this starts at about 6 or 7 million light year away (some say 50 million light years away). In my tired light theory I say that it is only at 6 or 7 million light year away or so that the statistics start to work and the number of collisions is sufficient to form a large statistical sample. Blooming on camera lenses is equivalent to 18 million light years of IG space. Experiment tells us that galaxies have to be millions of light years away to get the effect. Lets think about this. 18 million ly of IG space is equivalent to a layer of glass 1000 atoms thick. A layer of glass 100 atoms thick is equivalent to a distance in IG space of 1.8 million ly. This does not get us to the Andromeda galaxy, which is known not to be in the Hubble flow but is blue shifted. A layer of glass 10 atoms thick would be equivalent to a thickness of IG space of 180,000 ly which is about twice the diameter of the Milky way. Would we expect a layer of glass 10 atoms wide to refract light? Tired light passes another test, as it predicts the Hubble flow. |
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Now see how this Tired Light theory predicts the wavelength at which the intensity of the CMB radiation reaches a maximum! | ||||||||||||||||||||||

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Wavlength at which CMB peaks |
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Download preprint of paper |
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© Lyndon E Ashmore. All rights reserved. September 2004 |