## An illustration of duality

It is not possible to give a good analogy with wave-particle duality in the 'household world'. Certainly we can observe different properties of the same thing, depending on what we look for. A person may be at the same time a doctor, a parent, an athlete and a democrat, each aspect independent of the others. A certain machine can be a word processor, a computer, an electronic-mail communicator and a game station, all at the same time. These analogies are not very good, because being an athlete and being a democrat are not mutually exclusive, whereas in the household world particles never look like waves, or vice versa!

We can try another illustration, an optical illusion in which the appearance of an object depends on the observer's point of view. We reconstruct a concrete object in our mind when we interpret a picture. What that object is may differ from time to time quite dramatically. The illustration below is entirely symbolic and certainly should be taken as such. It has no direct connection with light, with photons, or with quantum theory.

The picture is an example of pictographic ambiguity, where more than one 'image' is contained in a single drawing. A similar picture was published in 1915 by the cartoonist W.E. Hill and is called 'My wife and my mother-in-law'. At first glance one sees immediately one image, but not the other. What is the chin of the young woman from one perspective becomes the nose of the old lady from another point of view.*

Again, the analogy with wave-particle duality is not close. The object which one sees is an abstraction in the imagination of the beholder. The physical reality is the material of the canvas, the painting oil, the frame of the picture, without ambiguity! It is not surprising that it is not possible to find a good illustration of wave-particle duality in the classical world. It is a quantum phenomenon in 'the world of the very small'.

Two images in one.

1.6 The birth of quantum mechanics

### 1.6.1 Particles have wave properties

In 1924, a dramatic idea was advanced which put a new slant on our view of waves and particles. In his doctoral thesis, submitted to the University of Paris, Louis de Broglie (1892-1987) proposed that not only light but all matter has properties of both particles and waves. The examiners were not convinced. The idea seemed quite absurd, and de Broglie had no experimental evidence to support his conjecture. To confirm their view they consulted Einstein, who, probably to everyone's surprise, recommended acceptance of the thesis. Specifically, de Broglie proposed that the relation between p, the momentum of a particle, and its associated wavelength, X, involves Planck's constant,

* An older version of the picture appears in an advertisement for the Ohio Buggy Company, captioned 'Here is my wife, but where is my mother-in law?'.

and is the same as that between the momentum and the wavelength of a photon, namely:

At the time de Broglie was not aware that there was already some experimental evidence to support his assertion. Within a year came what is now recognised as the official confirmation, in a paper by C.J. Davidson and L. Germer. When the two scientists sent a beam of electrons through a crystal, the electrons were scattered to form a pattern exactly like the diffraction pattern of light waves.

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