We have seen how links that pull unified the forces, predicted new forms of matter, and could explain other mysteries.  After revealing how a single photon always goes through only one of two slits and it is the “paraphotons” which exhibit the interference, it had to happen.  People then asked, “can links also explain the two-slit experiment using single particles of matter instead”?  You bet. 

It is often said that “particles have a wave nature” but that carries the incorrect implication that particles have an inherent ability to also behave as waves.  Separate and distinct waves can nevertheless be associated with real particles of matter.  This relationship had been demonstrated in the second quarter of the 20^th century by the crystal diffraction of electrons. 

It was not until the 1950s however that those electrons were used in a set-up functionally similar to Young’s two-slit experiment for light.

Because of the wavelengths involved it was a real challenge to build a plate in which the slits were narrow enough and close enough.  Gottfried Möllenstedt and co-workers at the University of Tübingen devised an ingenious solution.  (Figure 1).

A very thin conducting wire was made by gold plating a fibre from a spider’s web.   When placed in the electron beam, this wire acted as an electron biprism, splitting the beam into two components.  A film placed behind the biprism recorded the successful passage of electrons.  Again, a wave interference pattern was observed on the film. 

In 1989, Akira Tonomura and co-workers at Hitachi succeeded in allowing only one electron at a time through a similar set-up.  Even more amazing than for light, the pattern still built up after many individual electrons had passed.

I could never believe that an electron is anything but a solid particle of matter and find any assumption that it splits and takes both paths, ridiculous.  How can an electron interfere with itself?  There has been a lot of hand waving and muttering about quantum weirdness again but this experiment has never been successfully explained.

These observations unfortunately led to the erroneous assumption that the electrons could act either as particles or as waves.

The fact is of course, that both are present, in both cases.  Electrons are particles of matter that can not be destroyed nor changed into waves of any kind. 

When the interference pattern is formed, particles still impact the film; it is only their distribution that is influenced by the waves in attached links. 

In the case of a ballistic pattern behind a single slit, waves are also present, but have no effect on distribution.  To put it another way; it's not that particles have a “dual nature” but simply that conditions of the experiment do or do not allow attendant waves to influence distribution of the particles.

To understand what is going on, consider an electron heading for the biprism wire and film.  This is where it gets interesting because the electron can now go to the left of the wire, hit the wire, or go to the right of the wire.  In addition, waves that were not noticed before now make their presence known.  Duke Louis Victor de Broglie called them “pilot waves” in 1923.  He is famous for recognizing the relationship between the electron’s momentum to associated wavelength in his equation, p=h/l. Unfortunately, his other legacy is his stated notion that “waves are particles and particles are waves”.

While on its way, the electron gets slightly buffeted as it brushes past intervening links and some of its own are sheared and replaced. 

Depending on the mass of the particle and its speed (momentum), a resonance can develop similar to what one might experience when driving on a washboard road.  Vibrations of the electron thus set up non-propagating standing waves.  These are real, continuous waves in links attached to the ‘front’ of an electron and have nothing to do with electro-magnetic or gravitational radiation in the usual sense.

We now have two possible paths of links from the film to an approaching electron.  Both paths will always be found because there are so many links from nuclei in the film.  Waves from the electron cannot be absorbed by relatively immobile nuclei in the film and are therefore reflected back toward the electron.

If the two paths originate from nuclei in the film that are in light-band areas of the pattern, then the reflected waves will arrive back at the electron in-phase.  This is because path lengths are the same, or differ by even multiples of ½ wavelengths.  As the electron moves toward the wire, a tug-of-war develops as links try to pull the electron to both sides of the wire at once.  This condition obviously cannot last long.  In-phase waves on the attached links only exacerbate the problem.  The electron gets a very bumpy ride and one path or the other must fail.   Links in the ‘winning’ path then pull the electron past the wire to the film, registering a hit in a light-band area.

If the two paths originate from nuclei in the film that are in dark-band areas, then the reflected waves will arrive back at the electron out-of-phase.  This is because path lengths differ by odd multiples of ½ wavelengths.  The electron has a smoother ride because the reflected waves cancel and do not reinforce the original. Links from both paths thus survive longer.  By the time one path or the other finally does break, it is too late.  The electron is now too close and its inertia prevails.  The electron impacts the wire and is conducted away, leaving a dark spot on the film.

In summary, nuclei in dark areas of the pattern succeed in maintaining links on both sides of the wire for too long, and lose their quarry in the end.

Only a nucleus in a light band of the film can succeed in pulling in the electron and registering a hit.  Its position does not allow links via both paths to survive as long, and can therefore win the ‘tug of war’.

Variations of this experiment have since been performed on everything from single atoms to Buckyballs.  The same principles always apply however.

We have again confirmed that particles of matter are the solid ‘stuff’ and in this case, waves are in the attached links.  Particles and waves are related to be sure, but are not one and the same.

The Duke really confused the whole issue of particles vs. waves.  It must be reiterated therefore that electromagnetic waves consist of many individual photons (transverse pulses in bundles of energy links).

Such a pulse of energy while minute, acts like the tip of a whip travelling at light speed.  In the case of light it is such a sharp pulse that it should not be surprising it can act like a solid particle and eject an electron from metal.

Seeing this photoelectric effect, Einstein at one point thought the photon actually was a particle.

The wave property of light manifests itself in two ways.  The wavelength of an individual pulse is related to its momentum.  The wave property is also seen in the distribution of individual photon pulses.  An analogy is waves (rows) of individual soldiers advancing toward the enemy.  In this view, the “wave” is really a wave of probability for where photons might be.