The ancients had rainbows and mirrors to puzzle over, but they didn't speculate on the nature of light. It wasn't until Isaac Newton around 1700 split white light into the colors of the rainbow with a prism and recombined them back again into white light that there was a basis for a speculation on the nature of light. Newton concluded that light was composed of colored particles.

Around 1800 physicists began collecting evidence that light was in the nature of waves. In 1875 James Clerk Maxwell established that light is in the nature of an undulatory perturbation in the electric and magnetic fields of space.

About 1900 Max Planck concuded that light is made up of packets of energy which he called quanta. Albert Einstein found that the energy of those packets is proprortional to the frequency of the light. Thus the wave phenomenon of light also has a particle aspect. The light particles came to be called photons

Then in 1924 Louis de Broglie (dee broyee) proposed that subatomic particles have a wave character. Niels Bohr in the 1920's began to look for a structure that was simultaneously a wave and a particle.

In the 1950's when mathematicians got access to computers they started getting numerical solutions to onlinear partial differential equations. In numerical experiments with the solutions to some such equations they found that some solutions had the property that when two such solutions collided they emerged from the collision unchanged. They thus had the property of being particles as well as being waves. They were given the name solitons. It appeared that subatomic particles might be solitons and that particles of radiation, photons, might also be solitons. That explained parts of the wave-particle duality, but there remained the problem of how collections of photons collections of photons could appear as a wave.

What is shown below is a two dimensional illustration of how this can occur.

Conclusions