In the previous section, we saw that the old premises of classical physics, most notably that the energy of an oscillator (or indeed any other object) can take on any value, are not sufficient to explain all phenomena, even such everyday observations such as the glowing of a heated iron bar.  In this section, we will examine another conundrum that arises when dealing with very small objects, which is often referred to as "wave particle duality".

First though, we need to be clear about what we mean by "waves" and "particles".  Consulting a textbook on physics tells me that:

A particle is an object with mass that occupies a single point in space.

A wave is an oscillation that transfers energy from one point to another.

So, in our everyday world, particles and waves are quite distinct entities.  Just as apples and dogs are distinct entities (did you ever see something that was half apple and half dog?), so are particles and waves.  Billiard balls, bowling balls and apples are examples of particles.  Visible light, microwaves, sound waves and ripples on a pond are all examples of waves.

Let us once again go back to the start of the 20th century and consider two experiments that cast some doubt about this distinction in the quantum world.  The details of these experiments can be found in various textbooks and on various websites, so I will not describe them in great detail, here we are only interested in the outcome of the experiments.

The first such experiment is the "photoelectric effect".  Consider the figure below.

In this experiment, light is shone on a piece of metal, and if you do this under carefully controlled conditions and detect very carefully, you will find that electrons are emitted from the metal.  Further, if you increase the frequency of the light that is shone on the metal, the energy of the electrons emitted increases proportionately.

Without going into details, this phenomenon is very difficult to explain if we use the physics that assumes that light is a wave!  Instead, it is necessary to assume that incident light wave has particle properties, and if you assume that the light is indeed a stream of particles, then the explanation of the photoelectric effect is relatively straightforward.  Nowadays we call these particles of light "photons".

Conversely, we can do another experiment that relates to the diffraction of electrons.  Diffraction is a phenomenon that is normally associated with waves, and is explained briefly in the diagram below.  Diffraction is a phenomenon common to all of us, even if we are not aware of it.  For example, it explains why we can hear the voice of someone even though they're round the corner from us, or why we do not need to be in direct line with a transmitter to get a radio signal.

Without going into details (which basically involve firing electrons at a crystalline material and looking at the way in which the electrons are scattered from the crystal), it turns out that you can produce diffraction effects with a beam of electrons, which under the old physics we would think of as a beam of particles!

These two experiments, the photoelectric effect and electron diffraction, illustrate the fundamental issue makes quantum physics different from our every day world.  They show that, under some circumstances, things that we would normally consider to be a waves (e.g. light) can behave as though they were a stream of particles (photoelectric effect).  Similarly, entities that we would normally consider to be particles (e.g. electrons) can behave as though they have wave properties (e.g. showing diffraction effects).

To understand this further, consider the basic experiment shown in the figure below, which consists of a "source" of various things that we will consider shortly, a screen with two slits in it, and another screen on which we can see where things that pass through the screen land.  So, we fire things at the slits, they either pass through or miss the slits, and then hit the back screen if they make it through the slits.

Let us first of all consider firing bullets from a gun.  Assuming that the middle screen is bullet proof, then the bullets either pass through the slits and hit the screen at the back, or they miss the slits and bounce back off the middle screen.  If we fire enough bullets, then we would observe a pattern on the back screen that looks something like that shown below.

That is, the bullets make a pattern that matches the shape of the slits.  Evidently the bullets are behaving just like classical particles.  They go through the slits and produce a pattern that mirrors the shape and size of the slits.  This is hardly an unexpected conclusion, and shows that our bullets are good classical particles.

Now let's shine light on our double slits.  (Note that this experiment can be easily repeated in a laboratory but not at home, as you need carefully controlled conditions to get the effects I'm about to describe).  This time, the pattern on the back screen looks like this

That is, you get alternating bands of dark and light.  This is an extremely well-known and characteristic pattern that is made by waves, and if you apply the theory of waves to the light as it passes through the slits, it is very easy to explain why you get alternating bands of light.

In this instance, light is behaving like a wave, just as we would expect.  The bands of light arise from a phenomenon common to all waves, called "interference".  Basically, the slits act as two new sources of light when light is shone upon them, and the light waves from these two sources either add up to make a stronger wave, or they cancel each other out.

Now let's make things more interesting, and fire a beam of electrons at our slits, and see what comes out on the back screen.  The result is similar to that shown below.  (In fact the bands are not as "sharp" as I've shown here).

That is, we get an interference pattern, with "bands" of electrons, in a similar way to when we shone light upon the slits!  Our electrons are behaving as though they are waves, and exhibiting the wave phenomenon of interference!

Now, clever people can try to be smart, and they try to fool the electrons into behaving like particles, and thus make them give a pattern like the bullets did, i.e. characteristic of particles.  This is done by firing the electrons one at a time at the screen, rather like bullets, instead of as a stream of electrons.  So, what happens when they do this?  At first, they observe the electrons leaving a clear particle-like mark on the back screen, just as a bullet would.  However, as the total number of electrons fired increases, it becomes clear that the individual marks are in fact starting to form an interference pattern, as shown in the figure above!  So, even though we are trying to make our electrons behave like particles, and they are doing so in isolation, put them all together and they are behaving like waves and giving us an interference pattern!

The wave-like nature of particles can be expressed through the "de-Broglie wavelength" of the particle, which is defined as

λ = h / p

where h is Planck's constant and p is the momentum of the electron.  The de-Broglie wavelength expresses the extent to which the electron behaves like a wave.  The larger the value of the de-Broglie wavelength, the greater the extent to which a particle behaves like a wave.

Note that for a bowling ball, p is a very big number compared with values encountered in the quantum world, and the de-Broglie wavelength is found to be incredibly small, far too small for the ball to have wave-like properties.  Electrons, on the other hand, have much smaller momenta, and as a result the de-Broglie wavelength is much larger.

So there you have it, in the quantum world, the distinction between particles and waves is not at all clear cut.  It seems that quantum objects behave like waves when they need to, and they can also behave like particles when they need to.  This is what is meant when people talk about "wave-particle duality".

Should we be at all worried about this?  Should we lose sleep worrying about why things are like this in the quantum world, and so different from our every day experiences?  Personally I think not.  I agree with James Trefil, who in his EXCELLENT book, Cassells Laws of Nature, states that philosophers have made far too much of wave-particle duality.  As he further points out, where is it stated on tablets of stone that quantum objects should behave like classical ones? 

Perhaps it's easier if we just accept that this is how things are in the quantum world.  Different from how things are in our classical world.

If the above was a mystery to you, then the key message is as follows:

In the quantum world, quantum objects can take on, to a greater or lesser degree, the properties of both particles and waves.  This interpretation is completely at odds with our conventional notion that particles and waves are distinct entities, and that an object is either one or the other.  The wave-like nature of particles can be expressed through the de-Broglie wavelength.

On to the Heisenberg Uncertainty Principle