These notes teach the mathematical basis of Aether Science theory


© Harold Aspden, 1997


It was in 1959, some 38 years ago, that I sent the manuscript of my short 48 pp. book entitled 'The Theory of Gravitation' to the printers. There on page 23, as equation (21), was that formula 144π(r/d) giving the value of hc/2πe2 and that followed the chapter on 'THE AETHER' where that (r/d) quantity was calculated by using the principles presented here as Tutorial No. 7 in these Web pages.

To know r/d, the orbital radius of the quantized activity of the aether in terms of the unit cell dimension of that aether, was shown to be sufficient for a determination of Planck's constant h in terms of the unit charge e of the aether action that was in quantized motion at the speed c/2 relative to the inertial reference frame.

To know Planck's constant and understand how the aether sets up the relationship E=hf between energy quanta E and electromagnetic wave frequency f, as explained in that book, takes us a long way forward in our efforts to decipher the secrets of the universe.

I could not have guessed at the time that, over the years which followed, there would be a major discovery in astronomical observation that could confirm my derivation of the precise value of that dimensionless quantity hc/2πe2.

Here I refer to an observation by Tifft as reported in THE TIMES, (U.K. newspaper), on October 14, 1996.


"The story began with the discovery in the 1970s by William Tifft, of the University of Arizona, that the speeds of the galaxies he studied were always multiples of 72 kilometres per second."

"Red shifts should be able to take any value, but Dr. Tifft seemed to show they were 'quantized' - restricted to certain values."

"This appeared impossible, but more recent research by Bill Napier at Oxford and Bruce Guthrie of the Edinburgh Royal Observatory confirmed it. Explaining why is very tricky, unless you assume that red shifts don't really tell us anything about speed or distance and that would undermine the whole basis of cosmology."


Now I have already, in Tutorial No. 8, explained how my theory developed to show that the aether has levels of energy density at which it becomes, as it were, locked into a quantum state corresponding to an integer value of the cube of (9/8) times (d/r)2. One can say that for each such integer step, which corresponds to the number of electrons and positrons that can be created as a group upon the annihilation of an aether particle and occupation of the aether space thereby vacated, there is the possibility of such a quantum state. It all depends upon the energy activity in the aether domain under consideration and there are many such different domain regions in the whole expanse of the universe.

What is so fascinating about this theory is the way in which it affords, for our local domain sector of the universe, the precise values of that quantity hc/2πe2 as found by measurement, namely 137.0359, and the proton-electron mass ratio of 1836.152, the latter being a little below that integer value of 1843 that prevails in our domain sector.

What promises to be equally fascinating is the scope for extending the theory to examine what happens in regions of outer space that are primed with far more energy activity than we see locally. If the r/d factor increases then that 1843 factor reduces and the proton mass will increase in terms of electron mass, but that then raises an interesting question. It is whether or not the 1843 factor in relation to the 1836 factor is fortuitous or whether it has real physical significance. My proton theory was developed by building the proton from muons rather than electrons, so my guess at this stage is that the similarity of these numbers is fortuitous, but this subject warrants some onward research.

Now, I am going to let you, the reader, take such research forward if that is your wish. For my part I am now going to document the text of something I have written and offered for publication on this topic and do no more, at least, until I have got much further ahead with my experimental endeavours on New Energy research. You see, I cannot compete with astronomers in interpreting astronomical observations. I can only point the way forward, where my theory offers an avenue of exploration. I may, however, be able to apply my electrical engineering skills to show that there is some technological potential for tapping aether energy and that keeps my sights locked on our immediate space locality where r/d has the value corresponding to that 1843 integer. In this quest I am not looking into outer space, but looking instead at the activity occurring within a ferromagnetic core. The aether interacts with that magnetic core by determining r as h/4πmec, whereas he/4πmec, with electron charge e here written in electromagnetic c.g.s units, is the unit we term the Bohr magneton. The aether also mediates in sustaining an energetic activity in flux switching in the magnetic domains of the ferromagnet conforming with quanta related to that Bohr magneton. See my paper reference [1978c] in the Bibliographic section of these Web pages.

As I say, I must now get back to my research interests in that field, but I will leave this 1843 topic and the Tifft's findings by noting that my specific interest here is restricted to one single question. Why, in the light of Tifft's findings, is the value of that integer not 1844, which is a lower energy state? Remember that at 1845 the energy state would become negative and that is impossible!

I do not know the answer to that question, but it may be connected with the need for the aether locally to store the energy that relates to the gravitational potential of stars in our local galaxy.

I will say no more here on this subject other than documenting below the copy of the paper I mailed to Physics Letters and the Editor's responses. I will let these Web pages do their work in disseminating that information.

This Tutorial No. 10 completes my plans for presenting this 'Educational Course'. I have sought to show students and others how easy it is to solve the key outstanding problems of physics, completing a task of deciphering the fundamental dimensionless physical constants as inspired by Sir Arthur Eddington. Now I shall get on with my experimental work in the New Energy field, the subject addressed in my earlier Energy Science Reports.

What now follows is the text of a manuscript I sent to Physics Letters A in October, 1996. Its receipt was acknowledged by Editor, Professor P.R. Holland on October 31, 1996.

Intergalactic Red Shift confirms Alpha-Theory
H. Aspden*
Energy Science Limited
P.O. Box 35, Southampton SO16 7RB, England
[* Retired. Formerly Visiting Senior Research Fellow, University of Southampton.]

The theoretical derivation of the dimensionless fine-structure constant α, giving α-1 as 108π(2)1/2/N1/6, where N is 1843, reported in Physics Letters 41A, 423 [1972], is shown to be confirmed by the 72.5 km/s steps observed by Tifft in the red shifts of closely-positioned galaxies. Spectral lines are shifted in proportion to (N1/3)(N1/3)1/3 or N4/9 and, with N decreasing in integer steps, 4c/9N is between 72.4 km/s and 72.6 km/s over a range from N=1841 to N=1828.

Recent media interest [1] has drawn attention to the discovery by Tifft [2] that the differences of recession speeds of galaxies in the pairs or small groups he studied were always a multiple of 72.5 km/s and the fact that this was later confirmed by independent observers.

Although it has been suggested that this is attributable to a cyclic variation in the constant of gravity G, which affects the cosmological red shift by introducing ripples in the rate of expansion of the universe, Tifft expressly noted that he could find no evidence of gravitational interaction between those galaxies. The following alternative explanation therefore warrants attention.

The combined spectral emission from the numerous stars in a galaxy will have its basic frequency components determined by the usual Rydberg formula. The derivation of this formula involves the fine structure constant alpha (here denoted A) and the frequency f of any spectral component at its source can be expressed as proportional to A2 and the Compton electron frequency fo. Thus, as equation (1), we can say that f is proportional to:

The primary question at issue, therefore, is whether A and/or fo can vary from galaxy to galaxy, because we should look first at the source of the radiation before elaborating the task by interpreting the phenomenon as G-dependent with G fluctuating over time. Doppler red shifts in steps of 72.5 km/s referenced on the speed of light are also far in excess of the gravitational red shifts of stars such as the Sun.

Petley [3] has reviewed theories for deriving A and the most recent entry in his Table 5.3 on page 161 of his book is the formulation (equation 2):

A-1 = 108π(8/1843)1/6
which has the value 137.0359. This theoretical value for A was reported by Aspden and Eagles [4], where 1843 was a variable determined as the odd integer which represented the least finite zero-point energy state in a cubic-structured representation of the vacuum field medium. Writing the formula as equation (3):
A-1 = 108π(8/N)1/6
it was shown that the zero energy state for electric displacement governing charges e quantized according to the Bohr magneton criteria which introduced Planck's constant, required N to be 1844.53. The advance in that paper was the realization that the transition between the sub-atomic vacuum charge form and materialization of electrons and positrons demanded an integer N relationship. As the zero-point vacuum energy per unit charge e increased, so N would reduce and least energy applicable to an odd integer indicated the value 1843. The odd integer relationship seemed necessary for charge parity conservation.

However, since the equilibrium between energy quanta is assured by a population of virtual muon pairs and state transitions occur at domain boundaries, one need not rule out energy fluctuations creating even integer states, resulting in different values of N prevailing in some domain sectors of a galaxy. As can then be seen, if N can reduce in integer steps, this will decrease the value of f and there will be a red shift in steps deducible from that proportional relationship (1).

Now, it is not intended here to introduce any new principles of physics. It is merely sought, using the theory as it stands in [4], to assess the bearing which Tifft's observations might have on physical constants seen from the perspective of different galactic domains. The full formal derivation of equation (3) is of record in several earlier works by the author, the most recent being [5], and the author now feels justified in drawing the following facts to the reader's attention.

Firstly, rest-mass energy of the electron mec2 is equal to hfo and the derivation of equation (3) shows that these also are linearly proportional to e2/d, where d is the lattice dimension of the cubic structure of the vacuum model used to derive the equation. All three of these energy terms are deemed to be universal constants in an intergalactic sense. Secondly, the model requires a universal uniformity of the vacuum lattice energy density, because energy has to be conserved in a spatial context, but the zero-point energy of each unit cell of volume d3 can still exceed the minimum value, corresponding to the decrease of N. The uniformity of the zero-point energy density is the dominant universal factor. Then, though this is not a mechanical fluid model subject to normal dynamics, one is led, from a physical dimensional analysis, to conceive the need for a constant speed parameter affecting perturbations or distortions of the lattice structure. Thirdly, therefore, since fo and d are the only physical parameters we can combine with a numerical quantity to define a speed parameter, we must be prepared to accept that fod is also a universal constant.

Note that, although the four terms mec2, hfo, e2/d and fod are all universal constants, if the value of N can differ in different galactic domains, this will change fo, d, h and e individually. However, here in this paper, we are only interested in how fo changes in (1).

To proceed, given that the mass-energy density of the structure forming the vacuum medium is uniform, we know that moc2/d3 is constant, where me3 is N times (2mo)3, because, as seen from [4] this is the fundamental basis on which the vacuum model was established, mo being the virtual mass of the lattice charge forming the vacuum structure. Therefore, we can write, as equation (4):

mec2(1/N)1/3/d3 = constant
and from this, since mec2 is a constant, we conclude, as equation (5) that:
(1/N)1/9/d = constant
Since fod is constant, equation (5) then tells us that fo is proportional to N1/9 and, introducing this fact and the relationship of equation (3) into expression (1), we see that the frequency f varies linearly in proportion to (N)1/3(N)1/9 or (N)4/9.

Remembering that the least energy condition for odd integer N sets Nmin at 1843, but admitting even integer values at higher energy states, balanced by fewer cells, we tabulate below the red shift factors applicable for increased cell energy in a space domain involving lower values of N.

		  N	 (N/Nmin)4/9 	km/s	  ~		 
		1843	 1.0000000	  0	  0
		1842	 0.9997588  	 72.3	 72.3
		1841	 0.9995176	144.6	 72.3
		1840	 0.9992762	217.0	 72.4
		1839	 0.9990348	289.4 	 72.4
		1838	 0.9987933  	361.8 	 72.4

The speed in km/s is calculated by determining the factor change in the second column and multiplying by the speed of light, thereby expressing the shift in the equivalent Doppler form corresponding to a recession velocity.

As can be verified, the 72.5 km/s steps reported from astronomical observation are in precise accordance with the theory under discussion, it being found that a further 10 steps take the increment through 72.5 km/s to 72.6 km/s. The author regards this as confirming his theory by which the fine-structure constant was first derived at the part per million level of precision [4]. The theory in its non-integer N form dates from early work published in the 1960-69 period.

The conclusion one reaches from this remarkable result is that galaxies can, so far as the different space domain origins of their primary radiation sources are concerned, lock into slightly different sets of fundamental physical constants, and this, particularly with regard to fo, has interesting implications in confining the range of action of gravity forces to interaction between matter within the same galactic domain. The author recognized the need to accept the existence of such 'space domains' even within our local galactic system in Chapter 16 of his 1972 book [6] but see also Chapter 8 in the 1980 work [7]. Such domains have bearing on geological events such as geomagnetic field reversals occurring as the solar system transits through boundaries separating adjacent space domains.


[1] N. Hawkes, 'Scientists hit Galactic G-spot', The Times, London, October 14, 1996, p. 18.
[2] W. G. Tifft, 'Discrete States of Redshift and Galaxy Dynamics II. Systems of Galaxies', The Astronomical Journal, 211, 31-46 (1977).
[3] B. W. Petley, 'The Fundamental Physical Constants and the Frontier of Measurement', Adam Hilger, Bristol, p. 161 (1985).
[4] H. Aspden & D. M. Eagles, 'Aether Theory and the Fine Structure Constant', Physics Letters, 41A, 423-424 (1972).
[5] H. Aspden, 'The Theory of the Proton Constants', Hadronic Journal, 11, 169-176 (1988).
[6] H. Aspden, 'Modern Aether Science', Sabberton, PO Box 35, Southampton, England (1972).
[7] H. Aspden, 'Physics Unified', Sabberton, PO Box 35, Southampton, England (1980).


It was some six weeks or so before I received the Editor's response to my paper submission. Professor Holland simply declared that "on the basis of the referee's report your paper is not suitable for publication in Physics Letters A."

Now, I want you to take note that my paper made explicit reference and, indeed, relied upon my original theoretical discovery as reported in quoted reference [4], which was deemed worthy of publication by Physics Letters A some 24 years previously. In this new paper I was saying that here, at last, was proof in support of the theory of that earlier contribution. I was referring to something topical, a recent confirmation of a major new discovery in astrophysical observation that had defied explanation for 20 years but yet had now been confirmed by others. Yet this was the anonymous referee opinion that Editor Professor Holland saw fit to pass on to me with his letter of rejection:-

I am afraid that I believe this paper to be of no scientific value. It is based on a collection of unfounded numerological relations of Aspden's. It is unfortunate that he seeks to use them to explain some peculiar astronomical claims regarding quantization of velocities and red shifts by variations in physical constants. The author seems unaware of the entire literature concerning observational constraints on varying constants. In this respect I would draw attention to the very strong astronomical limits that come from quasar spectra on possible variations of constants between us and the location of the quasar in space and time. See for example Varshalovich et al, Astronomy Letters 22, 6 and Space Science Reviews 74, 259 and Cowie and Songalla, 'Astrophysical limits on the Evolution of Physical Constants over Cosmological Time', Ap. J. Nov 10th (1995). Other limits include T. Damour and F. Dyson, The Klo Bound and the Time Variation of the Fine Structure Constant, Nucl. Phys. B 1996. These investigations place upper limits on the time variation that are at least ten thousand times slower than the Hubble expansion rate. I recommend that this paper be rejected on the grounds that its methods are unfounded and it fails to account for the existing literature.
Now, it was clear to me from this referee's comments that he (or she) had not read my paper properly. Nowhere in my paper is there any suggestion that the physical constants mentioned were changing over time. I was simply saying that in far off galactic regions where energy concentrations are more intense than they are in our local galactic territory there was reason from my theory to see cause for a very small range of difference in the fine-structure constant. My theory had explained the precise value of the zero-energy threshold of the fine structure constant and I could see that the same theory indicated the slightly different quantum-stepped values for that constant that were actually being observed! To talk about changes over Hubble time is complete nonsense. The whole structure of my theory demands a constant structural form in space and allows only slight quantum-stepped perturbations of the energy thresholds that affect physical constants.

I have had many rejections of my papers over the years and, though unfair rejections are the norm, I can remember only one previous occasion where I decided to challenge the Editor's decision. That previous case warrants a Lecture of its own in these Web pages and it will be added soon. As to this subject situation I protested and requested Professor Holland to ask another referee to take a look at my paper.

I received another formal rejection as a reply dated February 5, 1997 which included a report by the second referee to be consulted. It reads:

Changes in N cause changes in alpha, the fine structure constant. That in turn would cause changes in the spacing of spectral lines. This is never observed in spectra of galaxies or even very high red shift quasars.

The integer changes in N which yield the 72.4 km/sec red shift periodicity, however, are very interesting. (And I think the observed accuracy of that number is +/- 0.1) but there is no way I, or anyone else, I believe, can tell what N is from what is written in this paper or the referenced Phys. Lett. A paper. If it is meaningful I believe it is possible to explain it simply. Does N have any connection with the proton/electron mass ratio of 1836?

Because of the above mentioned restriction on changing alpha I would investigate whether something like the magnetic moment of the electron in the atom (connected with alpha) were projected at different quantized states. I was also interested in the suggestion that fod was a universal constant.

But there are a number of papers now appearing on this subject which the author should read, ponder and reference in an attempt to clear up, instead of deepening, the confusion. One of these is Astron. Astrophys., 315, L9, 1996. In that paper, regardless whether Nottale gets it almost right about the planets, he makes the same mistake that most people make with regard to the galaxy red shift quantization. Those favoured galaxy red shifts cannot represent velocities because differently projected peculiar or orbital velocities would wipe out the quantization!

Another paper Aspden should read and discuss is the Tifft paper in Ap. J. 468, 491, 1996. Tifft believes that time is three dimensional and that periodicities are given by ninth roots of the speed of light. I have not met anyone who understands this theory but I note that Aspden also has periodicities coming out of ninth roots. I don't believe anyone will pay any attention to a paper unless they (a) understand physically what the mechanism is and (b) how it is related to the observations. I urge Aspden to read the new material (including Apeiron, vol. 2, No. 2, p. 43, April 95) and not try to publish until he can bring some measure of clarification to the problem.

So here was something more normal from a referee. He (or she) had read my paper, understood its gist, but did not know how I derived N, even though the earlier Physics Letters paper (which had involved analysis by two scientists at the Australian National Measurement Laboratory) had been accepted by reference to the derivation of N in my book 'Physics without Einstein'. You see, if a referee is not already familiar with the background state of the art that is referenced he or she presumes that what is proposed has no foundation.

The first paragraph of the referee's letter is puzzling. Is it just a statement that there is no dispersion evident in red shift observation? That has no relevance to my paper, because all the lines in the frequency spectrum of a radiating atom are shifted in the same proportion if the fine structure constant changes. That is implicit in expression (1) in my paper. The question of dispersion is important in interpreting the physical processes which account for the cosmological red shift but that is something my theory has dealt with elsewhere. See reference [1984a] in these Web pages.

The penultimate paragraph is a criticism of a paper published by someone else. It may be useful to open a paper by criticism of work of others, to show that one is familiar with the literature, but that reference poses no obstacle to what is suggested in my paper. The km/s measure is notional and is just a convenient way of expressing a red shift value. If the fine structure constant changes, red shift changes without any doppler factor coming into play.

Concerning the remainder of the referee's opinion it expresses interest in what I say and aims to be encouraging but the end result is that you, the world at large, will not now see my paper to Physics Letters amongst the many millions of scientific papers that adorn university library shelves. The fact that the Tifft findings confirm the method of derivation of the fine structure constant of my aether theory is therefore something that you can learn about only from these Web pages.

As to the formula I derived from my theory I cannot expect anyone to understand what that integer N means unless there is a willingness to study the basics of my theory as explained in my books and now in these Tutorial Notes. Hopefully, if you have followed this course of tutorials to this point you will by now understand how the formula involving N is derived and will know that it is a step function involving energy thresholds governing particle creation processes prevailing in the aether.

In conclusion I am tempted to say again that there is little point in scientists wasting time and government money trying to probe the secrets of 'Big Bang' creation, 'Black Holes' and the presumed expansion of the universe, when they still do not understand the true nature of gravitation and the photon as seated in aether activity. They look at spectral images without regard to how energy creating those images is deployed as between aether and matter. For my part the Tifft observations tell me that jitter radius r of the aether deserves our attention because it determines the store of energy that we can visit when we go shopping for that commodity.

As and when I progress on that technological excursion I will aim to report my findings in these Web pages. This concludes the last of these ten Tutorials.

H. Aspden
June 28, 1997

Footnote added in August 1997: There has been a development on the subject of this Tutorial No. 10 as you will see if you follow this link to:
Lecture No. 6