A Grand Unified Fractal Theory

Atoms as flat fractal loops

The object of this paper is twofold:

  1. To provide evidence that the atom is a member of a cosmic hierarchy of spirals/loops.
  2. To postulate that Schrödinger’s wave equation applies to all of these objects.

Heisenberg warned that research into the atom has its pitfalls. Further, his uncertainty principle showed that the avoidance of artefact is impossible when using direct observation. So the trick is to use indirect, non-invasive techniques.

It worked for Mendeleyev with stunning success: he and other chemists evolved the periodic table of the elements. In doing so they not only established the quantum nature of chemistry, they effectively integrated it with physics in the process. What they did was to resort to an oblique route by assessing the patterns of behaviour of all the elements and to draw the resultant inferences. Atomic physics, lacking this subtlety, has been left well behind.

We may be pretty sure that the presently accepted picture of atomic structure, based as it is on the spectra of ions, is a distortion. The tool used to produce them is intrusive, precluding by its very nature any untainted observation.

To what extent scientists have been deceived hitherto, is perhaps not knowable but, as already mentioned, improvement is possible via fractal geometry i.e. by following Mendeleyev in the use of the non-intrusive method of pattern-spotting. With the universe proposed in the e-book “Electrofractal Universe” this is a lot easier than might first be thought.

The strategy is based on its hypothesis that the universe follows a pattern: that it is populated by a hierarchy of similarly-shaped, electrically powered, spirals/loops such as galaxy clusters, galaxies. nebulae, stars, and smaller. Their shared features, all carrying tell-tale information, are on-record and available for interpretation. Initially six were found, promisingly pertinent to atoms:

  • They are long-lived.
  • They have angular momentum.
  • They have torroidal magnetic fields.
  • They are alternators/oscillators.
  • They emit electromagnetic energy.
  • They are flat.

Signs of atomic fractality, including a positive feedback (oscillatory) mechanism, akin to the one found for celestial objects, are already apparent in atomic spectra:

The wide-spectrum emissions of ions, the so-called “fine structure”, are a sure sign of such feedback in an over-driven oscillator, well-known to electronic engineers. The chaotic nature of the radiated frequencies is characteristic of fractals in that it is bifurcated.



As the graph shows any oscillator is able to produce a single pure waveform or a complex and unpredictable mixture, or anywhere between, depending on the energy input. This multiplication, from the simple to the chaotic, in fractal parlance, is the “butterfly effect”. At the lowest energy level the one frequency, that of the Bose-Einstein condensate, equips the structure for lasing. Further evidence for the inclusion of atoms in this family of flat, looped objects is the recent announcement, at the University of Rome, of the calculation (from WMAP data) of the fractal dimension of 2.1 for the universe.

This coincides with the hypothesised deployment of matter: that the habitual morphology of the universe is essentially two-dimensional and that everything in it has its origins in just one formative process.

Certainly there are deviations, sometimes huge, from the postulated flat format in stars, supernovae, Seyfert galaxies and the like, but they are fleeting, requiring a great expenditure of energy.

It is interesting to note that even today’s physics textbooks find it necessary, to depict paramagnetic substances as being composed of rotating, looped, electromagnets, not Schrödinger’s three dimensional models. The reality is probably somewhere between.

Typical text book cross section

Typical text book cross section

So, being from the same proposed stable, atoms are ripe for research by comparison with their bigger relatives. It is argued that in spite of a great disparity in size, there are striking similarities. In the early twentieth century, atoms were seen as resembling the Solar system and galaxies, and as early as Lord Kelvin’s time, it was suspected that their stability stems from their shape and their dynamics: that they are active “vortices”.

To be sure, what quantum mechanics has to tell us about atoms is extremely useful, but it is limited. Probing the fractal aspects offers a new, surer route to discovery.

For instance the forth quantum number, magnetic spin, was a mathematical device to account for the mysterious splitting of spectral lines. (the Zeeman effect). Later this was ascribed, quite arbitrarily, to “magnetic spin” but no other empirical corroboration was found.

The recommended study of fractal similarities, as will be explained, has the potential to correct this undoubtedly astute, but misleading assumption.

Zeeman’s experiment of 1896 showed that the spectral lines of atoms, constrained by strong magnetic fields, are simplified into doublets or triplets. So even the flawed information from the spectra of atoms had shed some light; it filled a gap in the maths, albeit arbitrarily.

The famously widely-separated Sodium Doublet

The famously widely-separated Sodium Doublet

Its merit is that it introduces two extra states for each energy level and hence the necessary doubling, but this ad-hoc labelling has obscured certain fundamentals; something important had been missed.

There was an underlying hint of some two-fold feature in the structure of the atom, capable of making the doublets. It has remained undetected until now.

De Broglie laid down the quantum nature of the universe when he conceived that, like all oscillators, the resonances of atoms are quantised: confined to integral.

Divisions of wavelengths

Divisions of wavelengths

This finding, together with the split spectral lines and the half-integer quantum number, rang a bell, and again the comparison tool provided the new insight. This time, it arose from a combination of two observations: that the looped arms of many structures in space are paired and that the polarity of the Sun’s magnetic field is reversed every eleven year half cycle, i.e. every 180 degrees.

Cygnus Nova and Galaxy Cluster MS0735

Cygnus Nova and Galaxy Cluster MS0735

Together, these evoke the notion that the two values of electron spin (positive and negative) apply not merely to the polarities of the two electrons but to a phase change which engenders them! Pairs of electrons occupying paired half-orbits, diametrically opposed across the nucleus, would, on rotation, produce both alternating current, and alternating magnetic polarity. The viability of such a machine is generally disputed by physicists as being contrary to theory. But experiment shows otherwise, and until they put theory second to observation they will continue to flounder.

Galaxy Model Alternator

Galaxy Model Alternator

More about the photo above

Hence Pauli’s exclusion principle appears to apply, not to a single orbit, but to two half orbits, each with an electron out of phase, by 180 degrees, with the other.

The application of external magnetic fields is invasive and artificially divides their one common frequency into two slightly different values. The energy of the one electron is increased, being in parallel with the new field, and the other, being anti-parallel is reduced. Removal of the intrusion restores the single line.

There are more amazing correspondences, between the macro and the microcosmic. Certain planetary nebulae and certain Schrödinger atomic models are alike in all but size.

The picture shows planetary nebula eta Carinae at right and the Schrödinger model at left of an atom, of quantum numbers 4f m=0. Once more the patterns reveal a wealth of information.

Eta Carinae and the Schrödinger model of an atom

Eta Carinae and the Schrödinger model of an atom

Clearly there is a common process at work. So many similarities between bodies of such discrepant sizes can not be accidental. The message here is that the promotion of valency electrons to higher energy levels in atoms and the ejection of plasma in high energy nebulae and galaxies are related actions.

The overall indications are that atoms fit into a fractal picture of the universe. The “uncertainty” of quantum mechanics looks no different to fractal unpredictability and the two concepts of “complexity out of simplicity” and “the persistence of islands of order within chaos” appear to apply at both the atomic and cosmic levels.

A sound theory has the ability to prompt predictions and this one has a good number. It fractally hints, for example, that atoms at the lowest energy level, that is, in the ground state, must be at very low temperatures and that they have electrons, not with identical properties, but closely matched, and occupying orbits with similar electrical characteristics. Driving all of them would be a tiny version of the simple alternator already described, flattish and orderly. Their less than perfectly-matched natural frequencies of oscillation would not prevail. Resonance would automatically lock them to just one!

All this would result in very unusual behaviour, but such a description vividly brings to mind recently-confirmed Bose-Einstein condensates, even to the so-called “indistinguishability” of electrons (which is a mathematicians dream, impossible in an imperfect, fractal universe).

These highly-ordered, self-tuning and presumably self-aligning assemblages of atoms might be thought somewhat featureless but they have remarkable properties, displaying, amongst others, both superconductivity and superfluidity. Their atoms act in concert; not surprising in an orchestra (!!!!!) with only one type of instrument, playing only one note. This is ideally suited to lasing, see above.

Questions Arising.

There are many, but for starters:

  • Are protons, neutrons and photons etc hierarchs?
  • Do Bose-Einstein condensates occur in space?
  • Is there a lower limit to the number of subatomic particles?

There are many more.


This hypothesis is no less than a Unified Fractal Theory, a “GUFT”, if you will.

The implications for science in general and particle physics in particular, are far-reaching, indeed fundamental.

It means that Schrödinger’s wave equation describes a very simple process which by iteration is creating our highly complex universe.

Two dimensional bodies briefly eject matter in two or three dimensions, to grow and propagate themselves. Metaphysics?

Only one formative process makes them all, using only one type of engine, and differing only in size from one to the next.

A vastly different approach is needed to pursue the recommended path. It is necessary to accept that “mathematical rigour” is engendered by sound, and necessarily subjective initial assumptions, and not otherwise. Hence imagination, as always is at a premium.