In the late 1920's when physicists were puzzling over the evidence that subatomic particles sometimes behaved like waves Niels Bohr proposed that such particles and such behavior were evidence of some complementary structure that included both particleness and waveness.

In the 1950's mathematicians discovered the solutions to some nonlinear partial differential equations had that property. As a solution to a wave equation they were in the nature of a wave but when two such solutions were collided they emerged from the collision in their original form. The were given the name solitons. There were other solutions which emerged from a collision not in their original form but in some related form. They were called solitary waves. Solitons and solitary waves satisfied Bohr's notion of complementary structures.

But Bohr did not have to look so far afield for something of a complementary nature. A modified version of a charged particle like an electron satisfies that notion as well. The classical notion of an electron is of a particle which generates a field that pervades all space. The modern notion has the effect of the charged electron being carried by photons. Photons are taken to be the force-carrying particle for the electromagnetic field. This has led to the idea that for any field there is a force-carrying particle. So if there is the so-called nuclear strong force between nucleons then there must be the force-carrying particle called the gluon. But such hypothetical structures are not necessary to have Bohr's complementarity.

If an electron is taken to be intrinsically a particle and its field together then the movement of an electron involves the movement of its core particle and its field but the field movement involves waves.

Consider the famous double-slit experiment. Physicists have interpreted the result as evidence that the particle electrons misteriously go through both slits simultaneously. That leads to notions of the particle electrons being wave-like structures. But that interpretation is not the only interpretation compatible with the experimental evidence. When the electron and part of it field is going through one slit another part of its field is going through the other slit. The passage of the field through both slits would generate waves which could produce the interference pattern of the experiment.

(To be continued.)