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 Originally published 4 may 1999  J.E. Martin
This is a revised version of an earlier publication. The above site has been disconnected. This paper has not been revised since the above date.


In nature the fractional sequence 1/3  2/5  3/7  4/9 etc works in an unusual manner that is-

In a radius the distance between A and B is 1/3 of the distance A to X where X is the centre.
                 the distance between B and C is 2/5 of the distance B to X .
                 the distance between C and D is 3/7 of the distance C to X .
and so on.

Below 1/3 (to the left of the main sequence) the continuation is  1/9  1/7  1/5  1/3 so far I have only found one instance of 1/5 (see planetary waves) and none of the others; although years ago when I did a graph of a graviton by hand, I found 1/9 and 1/7, but I have not been able to repeat that using Excel.

This fractional sequence can be found in electrons and in the magnetic wave structure of large bodies. This leads me to propose that perhaps there is an underlying wave structure in the structure of the universe and that within each wave system, the amount of force carrier on each wave is equal to the amount of force carrier on any other wave.
On the Particle and Charge pages I proposed that charge is determined by the particle nucleons and binding field density. This means that the density of the field holding the 1/3 charge in the FQHE should be the same as the density of the quark binding field.
The questions that arise is what determines the wave structure and why does the bodies within universe have a common wave structure? I suggest that the only force that affects all bodies equally is vacuum.

Electron fractional charges (found by experiment )

The main sequence of fractional charges found in TFQHE  is:

1/3  2/5  3/7  4/9  5/11 etc

As reported in Scientific American, Jan 1999 page 9.
The work on Fractional Charged Electrons was done by  Horst L.Stormer of Bell Laboratories, Daniel C.Tsui of Prince Town University and Robert B.Laughlin of Stanford University winners of the 1998 Nobel Prize for Physics.

Now for the larger bodies-

Fractional wavelengths of Hale-Bopp comet (observed)

On the NASA photograph of comet I took the measurements of the dust bands (white) shown in red marks on fig W-2, these are listed as 'actual' distances in the table below. Removing the fraction shown in blue type gives a predicted distance for the next dust band towards the centre; these can be compared with the next row of actual distances. (The actual photograph cannot be reproduced for reasons of copyright. In all cases measurements are taken to the centre of the white bands).


fig W-2


Band   A B C D
4 Actual 38 39 60 48
3 less 1/3 25.3 26 40 32
3 Actual 25 27 40 32
2 less 2/5 15 16.2 24 19.2
2 actual 16.5 16 23 19
1 less 3/7 9.5 9.1 13 10.9
1 Actual 9.4 9 12 10

The measurements are within 10% of the predicted figures and less in most cases. Given the poor quality of the photo (taken from an inset in a larger photo) and the violent activity being photographed, I submit this is not to far out to be an acceptable prediction.

Planetary fractional wavelengths (observed)



distance to

Pluto 39.5 1/5      
Neptune 30.1 1/3 Neptune 31.6 +1.5  
Uranus 19.2 2/5 Uranus 20.06 +0.86  
Saturn 9.54 3/7 Saturn 11.52 +1.98  
Jupiter 5.2 4/9 Jupiter 5.45 +0.25  
Asteroids 2.9 5/11 Asteroids 2.89 -0.01  
Mars 1.52 6/13 Mars 1.58 +0.06  
Earth 1 7/15 Earth 0.82 -0.1  
Venus 0.72 8/17 Venus 0.38 -0.01  


0.39   Mercury 0.38 -0.01  

The vast differences in force and time scales plus the addition of satellites leads to planetary wave bands being more erratic than comet wave bands; even so the average error in the above table is less than one tenth of the average error (for all planets) in any other planetary distance formula. The 18% error for planet Earth could be due to the collision that lead to the creation of the Earth/Moon system. There does seem to be some relationship between the size of the error and the mass of satellites.

Formation of a solar system begins with a large dust cloud that has a weak gravity field due to a lack of concentrated mass. But an even spread of dust also means an even spread of EM force carrying quantum and therefore the dust cloud has a strong EM wave structure. The dust cloud also has spin, a relic from the creation of the universe.

As shown by the comet structure, the wave action divides the dust cloud into rings. Gravitational action with each dust ring collects the dust together in rock like lumps. Movement of the system as it orbits the galactic centre causes acceleration and deceleration of the rocks as they orbit the nucleus and allows the gravitational action to draw the boulders together.

As the dust cloud thins out and the planetoids grow bigger, the electromagnetic wave action weakens and eventually looses control of the planets which then have their orbits controlled by gravity. Whether a planet orbits inside or outside its magnetic wave orbit depends on whether the planet was accelerating or decelerating at the time of the changeover from wave to gravity. As the odds are 50/50 the split between inner and outer should also be 50/50 and there are 5 plus and 4 minus in the above table.

The BBC broadcast a program on planets in 2002 in which one of the astronomers said that at present no theory of planetary evolution accounts for the existence of the two outermost planets. If that is true then the discovery of a magnetic wave system in the early soar system could point the way to a solution to that problem.

The figures for planetary distances are taken from Astrophysical Quantities by  C.W.Allan Third edition, page 139.



Galaxy fractional wavelengths (theoretical)


The grey/black portion of fig W-4 is taken from page 83 of 'The structure of Spiral Galaxies' by Berlini and Linn. It shows the theoretical structure of a perfect spiral galaxy.
A spiral is superimposed in red. The distance between the red spiral arms at A is 1/3 of the outer arm radius and the distance at B is 2/5 of the inner arm radius,
The theoretical structure is, in the opinion of the authors the shape spiral galaxies would reach if they were not torn apart by gravity.


fig W-4

The uniformity of the wave structure cannot be explained by Newton's or Einstein's gravity because neither correctly explains the indirectly observed gravity of galaxies (as calculated from observed stellar orbits).