Press Release. 5th November. 2003

The Paradox Of The Electron And The Hubble Constant

Has the secret of the universe been lying unrecognised on the keyboard of your schoolchild’s scientific calculator all the time?
Physics teacher Lyndon Ashmore believes that this relatively simple instrument contains three very common physical constants which, when combined, explain much about the age and nature of the cosmos.
Ashmore, whilst playing with a few ideas on how light might travel through space, found a very remarkable coincidence concerning the Hubble constant, H and the electron. That is, a highly regarded measurement of the Hubble constant is identical to the combination of three very common physical constants – so common that they appear on just about every schoolchild’s scientific calculator!
Edwin Hubble showed that distant galaxies were receding at a rate proportional to their distance from Earth, the constant of proportionality being the Hubble constant, H. Having found this constant, the approximate age of the Universe or ‘Hubble time’ is then just its reciprocal. If you know the value of the Hubble constant, then you know, approximately, how old the Universe is.
Values of the Hubble constant seem such strange numbers because astronomers and astrophysicists like to be different. Instead of using the standardised SI system of units they use their own units to make the numbers ‘nice’. Parsec is used as a unit of distance as stars are then a few parsecs away and galaxies a few megaparsecs away (
one megaparsec = 3.086exp(22) metres).
A value of the Hubble constant that is often cited is that of
Riess, Press and Kirshner (1996) who found it to have the value 64 km/s per Mpc. To put it simply, (and ignoring local gravitational effects) a galaxy one megaparsec away will recede at a speed of 64 km/s, a galaxy 2 megaparsec away will recede at a rate of 128 km/s and so on. Ned Wright, a cosmology teacher at UCLA, describes Reiss’s results on his web page ‘Ned Wright’s Cosmology Tutorial’ as providing “dramatic confirmation of the Hubble law”. If we convert the Hubble constant into SI units, 64 km/s per Mpc becomes 2.1exp(-18) per sec.
But what Ashmore found was that the quantity ‘hr/m per cubic metre’ (h is the planck constant, m is the mass of the electron and r is the classical radius of the electron) is also equal to 2.1exp(-18) per sec! Or, to put it another way, ‘hr/m  per cubic metre’ in astronomical units is 64 km/s per Mpc – the Hubble constant.
So this measured value of the Hubble constant is exactly the same as ‘hr/m in each cubic metre of space’. Furthermore, on this basis, the age of the Universe has the same value as the mass of the electron divided by both the planck constant and the radius of the electron. Recalling these numbers from your calculator memory and combining them gives a Hubble time of 16 billion years (and in a much shorter time than it took to measure it).
However, in an expanding Universe, it is not simply a case of distant galaxies moving away from us, it is that space itself is expanding carrying the galaxies with it. Just how remarkable a coincidence this result is can best be judged by considering a ruler of length one metre. According to the ‘Big Bang’ theory, as the Universe expands the ruler will get longer and longer, stretching at a rate equal in magnitude to the Hubble constant. But as Ashmore points out, if the Universe is expanding as cosmologists tell us it is, then they are asking us to believe that this metre ruler is stretching at a rate of (hr/m) metre per second. H could have had virtually any value so can it be purely coincidental that the measured value of H is so closely related to the electron? 
There is no known relationship between the electron and the Hubble constant and, if this is the case, it must be a very remarkable coincidence indeed. Scientists are taught to be very suspicious of coincidences between two numbers if there is no known relationship between them. Should we now be suspicious of the Hubble constant?
It should be noted that the three constants h, m and r  feature greatly in the theory of the scattering of light and it is the light from distant galaxies that is under scrutiny in measurements of the Hubble constant. This makes the coincidence even more remarkable.
Of course other researchers have found different values for the Hubble constant. In his book ‘The Extravagant Universe’ Kirshner states that the most recent measurements of the Hubble constant put it within the range of 60 to 80 km/s per Mpc. Consequently, recent values of H lie between 0.95 and 1.23 times ‘hr/m in each cubic metre of space’. Perhaps cosmologists should use ‘hr/m  per cubic metre’ as a unit for H (instead of using km/s and the parsec) so the values of H would all be around unity, and nicer still!
The ideas Ashmore was playing with when he found this match were an extension of ‘tired light’ theories first proposed by Zwicky in 1929. In Ashmore’s theory, photons of light travelling through space gradually lose energy by interacting with the electrons in the plasma of intergalactic space. As the energy of the photons reduces, the frequency reduces and the wavelength increases. It is 'redshifted'.
There will still be a great deal of debate on our understanding of the Universe and his theory is still under review in the academic press, but this paradox between the Hubble constant and the electron will remain. As Ashmore points out “It will be a very strange thing indeed if, after all this time, effort and money spent in finding the Hubble constant, all that we had been measuring was the planck constant and the parameters of the electron. Especially when all we had to do was borrow our schoolchild’s calculator”!

Lyndon Ashmore, aged 53 years, graduated from York University, England, with an honours degree in Physics in 1971,holds an M.Phil. research degree carried out at Preston Polytechnic (now University of Central Lancashire), England, and is Head of Physics and Science at Dubai College, Dubai, an 11 to 18 secondary school following the British Curriculum.
Ned Wright’s Cosmology Tutorial.
R.P. Kirshner “The Extravagant Universe” 2002 Princeton University Press. Princeton N.J. (ISBN 0-691-05862-8)
Reiss, Press, Kirshner. ApJ. 473. 88. 1996
Scientific calculator used. Casio fx-570s. Cost - around 10 dollars.
© 2003 Lyndon E Ashmore. All rights reserved Last Modified 7th November. 2003