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Ashmore's Paradox

"Experimental results show that the  Hubble constant, H is the same as hr/m for the electron in each cubic metre of space. Therefore the Universe is not expanding".

Measurements of supernovae redshifts give a value for the Hubble constant as 64 km/s per Mpc. However, since astrophysicists use these strange units of kilometres per second per Megaparsec it has little meaning outside of cosmology. Let us convert this value to SI Units (metre, seconds etc) - one Megaparsec = 3.1x10²² m.

In SI units 64 km/s per Mpc has the value 2.06x10^-18 s^-1

Let us now look at the expression hr/m in each cubic metre of space, where 'h' is the Planck constant, 6.626x10^-34 Js, 'm' is the rest mass of the electron, 9.1x10^-31 kg and 'r' is the classical radius of the electron (the effective radius of the electron when it is interacting with other particles or photons), 2.82x10^-15 m.

hr/m = 2.05x10^-18 m³s^-1.

So we see that, in magnitude, they have the same value. However, for them to have both the same value and units (an essential for all realtionships in Physics) then we must look at the quantity, hr/m for the electron in each cubic metre of space.

hr/m per cubic metre of space = 2.05x10^-18 s^-1.

Consequently, recently found experimental values of the Hubble constant are exactly equal to hr/m for the electron in each cubic metre of space.

H = hr/m

 for the electron in each cubic metre of space - Ashmore's Paradox!

FAQ's

1) So, What's special about this, it may just be a coincidence? 

As scientists we must always be suspicious when 'coincidences' occur as they often (but not always) signify a relationship between the two. The point I make here is that these quantities (h, r and m) are not just any numbers as they are all significant in the interaction of light with matter. The planck constant, h, is the constant of proportionality between the energy of a photon anf its frequency (E = hf). The Hubble constant is concerned with the increase in wavelength, or decrease in frequency and energy of a photon. To measure the Hubble constant we look at absorption or emission lines in the spectra of distant galaxies and these are formed by electrons jumping from one energy level to another. In other words, we have used the electron and the planck constant in determining the Hubble constant and then we find that the value of H that we end up with is actually equal to a combination of the things we used to measure it! In the Big Bang theory they put this down to pure coincidence, but it is asking too much for us to believe that. In Tired Light Theory, we say that the redshift is due to electrons being absorbed and re-emitted by the electrons in the plasma of intergalactic space and so we expect some sort of relationship between H and h, r and m for the electron. More information can be found Here.

2) Why the 'per cubic metre of space? 

For two quantities to be equal to each other, they must have the same magnitude and the same units. The Hubble constant is a 'per sec' (s^-1) and so our function of the electron must also be a 'per sec' (s^-1). For this to be so we must look at 'hr/m in each cubic metre of space' as this has the same units i.e. 'per sec' (s^-1). What we are saying in Tired Light is that the Hubble constant is equal to 'this much of an electron in each cubic metre of space'. In actual fact when we work it out from first principles, we find that H = 2nhr/m where 'n' is the number of electrons in each cubic metre of Intergalactic space. This is where the 'per cubic metre of space' comes from - it is the number density of electrons, the more electrons we have the more collisions and so (up to a point), the greater the value of H. 

3) Why does 'H = hr/m per cubic metre of space' mean the Expanding Universe Theory is wrong?  

Apart from the final answer being equal to a combination of the quantities used to determine it, there are other implications. For one thing it is just too much of a coincidence that each cubic metre of space is expanding at a rate of 'hr/m for the electron' when they are not supposed to be related at all. Secondly, the age of the Universe is related to the Hubble constant. The 'Hubble time' is the 'time' used to determine the age of the Universe. This means that the age of the Universe is related to the electron and equal to m/hr!

4) H = 64 km/s per Mpc is only one value. Other workers use other techniques and obtain other values. 

True, it must be said that the value of the Hubble constant of H = 64 km/s per Mpc cited above is just one of many values found by different workers using various techniques. Many scientists choose to use a value for H found by an international group of scientists who spent eight years using the Hubble space Telescope (HST). They came to the conclusion that the Hubble constant had a value of 72 +/- 8 km/s per Mpc. This means that the ‘best guess’ for the value of His 72 but it could lie anywhere between 64 and 80 km/s per Mpc. Consequently, this value of the Hubble constant, found by an international team of scientists using the Hubble Space telescope over a period of many years, it is still consistent with the value that our schoolchild could have pulled up on their calculator in a matter of seconds! In SI units this value of H is (2.33 +/- 0.26) x10^-18 s^-1 compared to the value of hr/m per metre cubed of space of 2.07x10^-18 s^-1. In order to simplify things perhaps it would be a good idea to name the quantity “hr/m per cubic metre of space” as a constant in its own right and give it its own symbol. Lets assign the symbol ‘A’ to this quantity, ‘A’ for Ashmore’s constant (apologies for this but it has to be done!).

Let A = hr/m per cubic metre of space.

The constant ‘A’ has units of ‘per sec’ or s^-1. Consequently, the value of the Hubble constant from the supernovae results is just ‘A’. The HST result cited above is H = (1.1 +/- 0.1)A. But which is the correct value? The answer is that they are both correct; we often get different values when we measure things in different ways. One way around this is to find the average value of all the most recent results and to get an unbiased sample, the title words "Hubble AND constant AND measurement" were fed into the ADS database search engine and 'return 100 items' chosen (this database contains just about all of the scientific papers of note). Of these, all the papers giving an actual value for H are listed above. In theory, all the most recently measured values of H over the last 5 years (at the time of writing) should be listed. The values are given in terms of ‘Ashmore’s Constant, A’. The ‘Bib. code’ refers to the reference where these papers can be found if anyone should want more information. In finding the average, I have neglected the uncertainties and, where a range of values is given, I have taken the mean. We can see that the average of the values of the Hubble constant from twenty six of the latest measurements give a value equal to ‘hr/m for the electron per cubic metre of space’. That is, the average value of H is equal to ‘this much of an electron in each cubic metre of space’ where ‘this much of an electron is ‘hr/m’. Since the electron is not supposed to have anything  to do with H at all, are you still convinced that the Universe is expanding?

The honest answer is that H having the same magnitude as hr/m is a 'quirk' of the SI system of units. The expression of H = 2nhr/m works in any system of units and is perfectly valid. The paradox, H = hrm in magnitude is a 'coincidence' because the value of 'n' (the number of electrons in each cubic metre of space) is approximately unity. The reason the paradox is important is down to probabilities. If, in the Big Bang Theory, the Hubble constant is not related to the electron then it is highly improbable that at the first time we measure the value of H accurately, it just happens to be hr/m for the electron in each cubic metre of space. However, in Tired Light, since the full expression for H is: H = 2nhr/m, it is no big deal when H and hr/m have the same value since we expect something along these lines/ It just means n is about 0.5 per cubic metre and observation shows this to be true. For those of you who don't like coincidences, stick to the full theory and H = 2nhr/m. This works all the time!

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© Lyndon E. Ashmore. 2003. All rights reserved. Last modified 15/11/2003, 23 February, 2005