The Photon Hoop Model for light:
A new model to aid analysis and computation of light reflection and refraction phenomena,
and towards a resolution of the dichotomy between wave models and particle models for light

David Noel
<davidn@aoi.com.au>
Ben Franklin Centre for Theoretical Research
PO Box 27, Subiaco, WA 6008, Australia.



Background: Is light a wave phenomenon or a particle phenomenon?
Starting around 1664, the great English scientist Isaac Newton made fundamental studies into the nature of light. He published the results in his seminal 1704 book 'Opticks'. Newton regarded light as made up of particles.

Even back then, others, such as Robert Hooke and Christiaan Huygens, had developed theories suggesting light was a wave phenomenon. During and after 1672, Newton and Hooke were involved in acrimonious controversy over the matter. Huygens published his 'Treatise on Light' in 1690, while Newton held back on 'Opticks' until Hooke died in 1703.

Since the early days, most experiments have led to the interpretation that light behaves as waves, while for some investigations, the particle model explains results better. The currently accepted view is that light has both wave aspects and particle aspects simultaneously, and in any analysis, either the wave model or the particle model may be used, even though each of these models would seem to exclude the other.

The Photon Hoop Model
Here is proposed a new model for light, the Photon Hoop Model (PHM), which appears to unify both wave and particle aspects into a single model. Moreover, the new model may open up many aspects of light behaviour to mathematical analysis, which has been fairly inaccessible until now.

The model applies over the whole electromagnetic spectrum, so when 'light' is mentioned, everything from x-rays to radio waves is implied.

Figure PHM1 shows a Photon Hoop. This is a segment of light in the form of a 2-dimensional hoop, the arrow along the axis shows the the direction in which the light is travelling. The plane in which the hoop lies is the plane of polarization of the light.


Figure PHM1. Representation of a Photon Hoop

[Animations may be paused or restarted
by control-click (Macintosh) or right click (Windows)]

As the hoop travels, the two sides contract in towards the axis until the hoop is flattened into a line, then the sides expand out again to the shape of the original hoop. The length of the axis is half the wavelength of the light, and the contraction/expansion process occurs at twice the frequency of the light, so the hoop can be thought of as a single half-wavelength segment.


Figure PHM2. Flexing of a Photon Hoop


Interaction of Photon Hoops with matter
We now look at how these photon hoops interact as they come into contact with a solid surface, where changes such as reflection, transmission and refraction take place. The laws governing these things are well known, and brief summaries of them are to be found in [1] and [2].


Figure PHM3. Reflection of light at a mirror. From [1]



Figure PHM4. Snell's Law for refraction at a boundary. From [2]


Figure PHM5 is a representation of photon hoops striking the outer surface of a simple crystal surface. Only one slice through the grid of atoms is shown, and these are arranged in one of the simplest ways, at the corners of cubes. In the modern interpretation, each atom consists of a dense central nucleus surrounded by an electron cloud.


Figure PHM5. Photon Hoops striking a crystal lattice


This electron cloud is somewhat like the Earth's atmosphere, densest close to the solid surface or nucleus and thinning out and tailing off away from the centre, although with real atoms the 'solid' nucleus is very tiny compared to the cloud.

In the Photon Hoop model, an atom can be thought of as having a hard centre coated with a very thick skin of elastic foam, with few foam bubbles near the centre but more and more bubbles towards the outside, so the 'outside' of the atom is more bubble than foam.

What happens to a hoop striking this array of atoms will depend on the size, shape, and orientation of the hoop and the position and angle at which it strikes the array of atoms. In simple terms, the hoop may bounce off an elastic electron cloud, or may pass through between atoms and penetrate into the solid.

In Figure PHM5, the stream of photon hoops on the left, shown in pink, is able to pass through between the atoms, while the stream on the right, coloured green, is in a position to reflect off the electron clouds. These hoops are both polarized in the plane of the image, and are shown fully swollen.

The central stream, shown in yellow, is shown flexing down to a line. It does this twice per cycle. It will be apparent that for certain sizes and layouts of atoms, the hoops may be well aligned to slip through an array because they have shrunk down whenever they are close to an atom, one they would impact with if swollen.

Clearly this picture is hugely simplified, actual outcomes depend on all the particular characteristics of the hoops and atoms, and in real life everything is taking place in three dimensions, not two.

Hoops polarized at right angles to those shown will look just like thin lines at all times, and may be able to slip through the atoms shown with little restraint.

Smaller hoops (of shorter wavelength) may also slip through, while larger atoms, or ones more tightly packed in the available space, may restrict flow. Calculation of the percentages of hoops reflected, transmitted, or absorbed in any particular case may be possible, but would demand a detailed three-dimensional picture of the crystal lattice structure and knowledge of the extents of the electron clouds involved.

In theory, the electron clouds round atoms tail off towards nothing away from the nuclei, and at present we don't know how well hoops could pass through very thin clouds.

While it may be useful to think of the hoops as 'bouncing off' electron clouds, it's really a case of a two-dimensional field interacting with a three-dimensional one.

Low-angle reflection
When a beam of light strikes a dense crystal surface at a low angle of only a few degrees, usually none of it passes into the solid, instead all is reflected off. This situation is shown in Figure PHM6.


Figure PHM6. Photon Hoops striking a crystal lattice at a low angle


This low-angle reflection happens even with very short wavelengths (very small hoops), such as in x-rays. X-rays can be corralled into a long twisting tunnel at low angles, though they would normally pass straight through most wall materials. The figure shows how everything hitting the surface at a low angle is likely to bounce off, rather than penetrate.

Electron Clouds
In real materials, the electron clouds are more complicated than that in the simple Fig. PHM5 picture. The electron clouds spread out and mingle with those of adjacent atoms. In fact, it is this mingling of electron clouds which forms the chemical bonds in a molecule.

Quite pretty electron-density 'contour maps' can be derived for a cross-section across a molecule with many atoms. Heavier atoms, such as lead or gold, have denser electron clouds (a chemist would say these atoms contain more electrons) and they show up as higher 'hills' on the cross-section map.


Figure PHM7. An electron-density map of a protein. From [4]


The Photon Hoop and the Wave models of light
So far we have looked at photon hoops as single entities, as particles, albeit two-dimensional particles. In reality, the hoops making up a light beam will normally be strung in a continuous line, as in Figure PHM8. All the hoops will have the same polarization, that is, will lie in the same plane.


Figure PHM8. A string of Photon Hoops approximating a sinusoidal light waveform


It will be immediately obvious that the string of hoops much resembles the conventional depiction of light as a sinusoidal wave. However, this wave is mirrored in its axis. In conventional wave optics, one wavelength, one complete cycle, is the distance over which the wave rises from its zero mid-value, peaks, falls back through the mid-point to a trough, and rises again to the midpoint. The frequency of the light is the number of times this cycle is completed in one second.

The Photon Hoop Model uses the same general picture, but the length of each hoop is half a wavelength, and the number of hoops passing per second is twice the frequency.

About models
In scientific parlance, models are an aid to understanding, and perhaps making calculations on or inferences about, a physical situation. The Particle Model of light, the Wave Model of light, and now the Photon Hoop Model of light are none of them right or wrong. Instead, each may be more useful or less useful, more applicable or less applicable, to a particular situation.

What can be gained in this way from PHM? It may be useful in giving accessible routes to calculation. Properties of photon hoops may be derived experimentally. Computer simulations of the electron-density cloud layout in particular solids may allow calculation of such things as the minimum low-angle for complete reflection.

In particular, more may be learned about refractive behaviour and refractive indexes. At present, refractive indexes, and their dispersion (variation with wavelength) can be measured very accurately. But we do not have good tools for calculating refractive indexes from the known structures of crystals and glasses.

We know that the presence of heavy atoms, such as lead, in glasses gives them higher refractive indexes. In solids, light travels more slowly than it does in a gas or vacuum, and in fact Snell's Law, illustrated in Figure PHM4, directly links refractive index changes across a boundary with change in the speed of light as it crosses the boundary.

It may be possible to calculate refractive indexes directly, from consideration of the behaviour of photon hoops as they pass through the gravitational fields of individual atoms in a structure. On a vastly larger scale, we can calculate the effects of 'gravitational lensing', when a star image appears displaced as its light travels to Earth and just grazes the edge of a massive body such as the Sun. We may be able to so something similar with individual atoms in a crystal structure.

Also on an astronomical scale, we know that the frequency of light is shifted towards the red as it passes through gravitational fields. There may be similar effects at the atomic level.

The confirmation of such phenomena during an early solar eclipse marked an important milestone in scientific progress. Closer examination of the implications of the Photon Hoop Model could mark a similar milestone.

Animations
The animations on this site were constructed by Andras Kovacs, bandibacsi2@gmail.com.

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References and Links
1. Reflection (physics). http://en.wikipedia.org/wiki/Reflection_(physics)
2. Refraction. http://en.wikipedia.org/wiki/Refraction
3. The Packing of Atoms. http://www.geo.arizona.edu/xtal/geos596a/spring06-01.htm
4. Molecular Origami. http://www.stolaf.edu/people/hansonr/mo/x-ray.html.





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Draft Version 1.0, 2010 Mar 18
First version 1.1 on Web 2010 Mar 20. v. 1.1.1, minor corrections, 2010 Apr 27
Version 1.5, with animations, on Web 2010 May 12