Wave-particle duality aka the central pillar of quantum mechanics

In two of my last posts on quantum mechanics, I introduced the concept of the wave-particle duality.

I have discussed that light (or actually waves) can exhibit the behavior of a particle (see here) and that inversely, a wave could be associated with a particle like an electron (see here).

Since this is a central pillar in quantum mechanics, I would like to dedicate a full blog post to it, in particular to emphasize the differences between the classical physics case (where the world is not quantized), and the quantum case.

Classical physics (or in other words, non-quantum physics), is based in two distinct concepts: particles and waves. The important word here is ‘distinct’. Particles and waves have nothing to do with each other.

This is not of course not the case anymore for quantum mechanics. With this respect, the works of Einstein, Planck and de Broglie were really a revolution in our understanding of how the world works.

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CLASSICAL PARTICLES

Let us start with a classical particle, like the blue ball from the picture of the right that rolls towards the top of a hill and that will go down after reaching the summit.

What is going on there results from some action that happened in the past. For instance, someone may have kicked that ball out strongly enough so that it can go up to the top of the hill.

In classical physics, this ‘ball-particle’ is assimilated to a material point of a given mass. The action of the environment (our initial kick) is assimilated to forces, and the fundamental principle of dynamics allows us to calculate the trajectory of the particle and what is happening to it.

The very important point is that the particle always occupy a well determined position in space at any well determined moment.

Futhermore, This simplistic picture can be generalized to many particles interacting with each other, as well as to solid and fluids.

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CLASSICAL WAVES

In classical physics, the notion of waves appears when one tries to model continuous phenomena, like ripples on water or sound in the air.

A synonym to a wave is the notion of a classical field. Two well-known examples of fields acting in our everyday lives are the gravitational and the electromagnetical fields.

The key property of the fields (or waves, as these are the same things) is that they are known to propagate both in space and in time.

To explain this better, we can study the location of one of the crests of the ripples shown on the picture on the left.

A crest moves in space from the center to the outside, and this is nothing but the propagation of the wave in space.

Similarly, the location of a crest at a given moment does not stay the location of a crest forever. After a short moment, there is no crest anymore there, and after a longer moment, the crest is back there. This consists of propagation in time.

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UNIFICATION WITH QUANTUM MECHANICS

In quantum mechanics, the concepts of waves and particles are unified. What we usually call a ‘particle’ is actually both a particle in the sense of the classical ball, as well as a wave in the sense of the ripple.

In order to understand that better, it is good to restart from the double-slit experiment of the previous post.

To sum up what is going on in there, particles are sent through the two slits, as shown on the picture.

Considering these particles as classical objects, they should pass either through the first slit of through the second one and one should thus detect two well-localized spots on the second screen E2.

This is however not what we get, and we observe on the screen E2 an interference pattern typical from a wave.

There are two questions we can ask here.

How is it possible to conciliate an wavy interference pattern with the fact that we throw particles one by one through the slits, and by which slit a given particle goes through.

To answer to the first question, one must keep in mind that particles arrive on by one on the E2 screen and it is only when many particles have been sent that the interference pattern shows up.

To clarify it, we can check the picture on the left.

When the first particle arrives to the screen (upper panel), one gets a well-defined spot on the screen.

After 10 particles (central panel), one gets 10 well-defined spots. And so on…

However, after a larger number of particles (lower panel), we observe zones with a maximum of hits and zones with almost no hit at all.

Here is our interference pattern. It is a point-like way to see a wave.

Concerning the second question of the slit through which a given particle passes, it is trickier. If we remove one of the slits, one only gets a single spot on the screen and there is no more interference.

There is solely one possible conclusion to this: the particles are going through both slits at the same time, and the probability to get a hit here or there is then linked to the properties of the wave associated with our particles.

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DISCUSSION AND REFERENCES

With this post, I wanted to come back a little bit to one of the greatest pillars of quantum mechanics: the wave-particle duality.

I started this blog post with some basics about classical physics, where waves and particles are different concepts that are not talking with each other.

In quantum mechanics, the story is different. Both concepts are unified: a wave is associated with each particle and a particle is associated with each wave.

And actually, one interesting point is that we do not care whether the particle is massive or massless. Which is good as one cannot in principle measure precisely that a particle is massless (one can only establish that the mass of a particle is smaller than some threshold). We indeed do not want to have sharp transitions in the predictions when we take the limit of masses going to zero. But this is another story!

For more information (and references), one can check either this book, or the wave-particle duality Wikipedia page that contains plenty of details.

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Table of contents of this series of posts

I. Introduction
1. Concepts and fundations
2. Interactions and conservation laws
3. Systems of particles

II. The origins of quantum mechanics
1. Fundamental physics at the beginning of the 20th century
2. The mysteries of the atomic spectra
3. The mysteries of the black bodies
4. Quantization of the electromagnetic radiation and the birth of the photons
5. The Compton effect
6. The planetary model of the atom
7. The Bohr model of the atom
8. Matter waves
9. More on the wave-particle duality (this post)

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