Wave Particle Duality

Wave particle duality tells us that light and matter exhibit properties of both waves and particles. Thanks to the work of Christiaan Huygens, Isaac Newton, Albert Einstein and Louis De Broglie it was established that all objects have both wave and particle nature. However, this phenomenon, exist as it may, is only detectable on small scales such as within atoms. The explanation of a few simple experiments can show this phenomenon. These experiments also show directly that the atomic world is different form our world.

To illustrate the first experiment, think of a wall at the heart of the experiment with two slits in the middle. To the right of the wall there is a screen and a detector and to the left there is a device which shoots out bullets.

For simplicity we assume that nothing bounces off the walls-  that is, when the bullets are fired they only go through the slits. If we cover up one slit and fire the bullets, we can observe one bright fringe on the screen where the bullets are hitting the screen. The fringe is near the centre of the slit. If we now cover up the other slit and shoot bullets through the first slit we covered up then the same thing can be observed with respect to the slit that's open.
 
We can try the same thing with water waves. If we move the whole experiment into a ripple tank and instead of the bullet device we use a vibrator to generate water waves. On the other side of the wall we place a detector that measures the amplitude of the wave that passes. The amplitude of the wave is the maximum height of the wave from the equilibrium point. Once again if we close up one slit we would observe a pattern similar to that of the bullets with one slit. The water wave goes through the slit and diffracts once it leaves the slit. With the other slit closed the result is the same. With both slits open we observe a wave pattern. In the centre there is a wave with greater amplitude than the wave which was observed using one slit. Next to it there is a wave with much smaller amplitude.

Furthermore the pattern repeats. This can be explained by considering interference of the waves. Where the wave appeared larger, constructive interference occurred to reinforce the wave. In other places destructive interference occurred to cancel the wave. The difference between this experiment and the bullet experiment is explained by saying that while the bullets went through only one slit, the waves each went through both slits at the same time and interfered with themselves to make a wave pattern.

We now try the experiment with tiny negatively charged particles that make up the outer layer of an atom, namely electrons. If we had to choose which pattern the electrons would be similar to, surely we would choose the bullet pattern as, like the bullets, they can only go through one slit at a time. If we now place an electron gun at one side of the wall and an electron detector at the other side we can perform the same experiment again. If we close up one slit at a time the results are just like the results of the bullet experiment, as expected. However, if both slits are opened up, the results on the screen are similar to the water wave experiment with both slits open! If the electron gun is slowed down, so that only one electron is going through the slits at any one time, there is a gradual interference pattern which builds up on the screen. A build up of electrons hitting the screen shows a pattern of several light and dark fringes. This experiment suggests that a single electron simultaneously goes through both slits and hits the screen as a single particle.

The act of trying to observe the electron will cause the wave nature of the electron to collapse so that it behaves just as the bullets. This leads us to one of the most fundamental lessons in quantum physics - an observation is only valid in the context of the experiment in which it is performed. So in order to say that something behaves in a certain way or even exists one must specify the context of this behaviour or existence. This is because in another context it may behave differently or not exist at all. It can not simply be stated that an electron is a particle since we have come across proof that this is not always the case. We can however say that when we observe an electron in a two slit experiment it behaves as a particle.

Niels Bohr presented what is known as the Copenhagen Interpretation of Quantum Theory, which declares the particle is what you measure it to be. It is meaningless to ascribe any properties or even existence to anything that has not been measured. Bohr is suggesting that nothing is real unless it is observed.

The Uncertainty Principle

If we were able to determine the position and the momentum of the electron as it leaves the electron gun then we would have a fighting chance of determining where exactly the electron goes. However as mentioned above the act of observing the electron alone causes wave function collapse so determining the position and the momentum is not as easy at it first sounds. In 1925, Werner Heisenberg said that "it is physically impossible to measure the position and momentum of an electron simultaneously." This is now known as Heisenberg's uncertainty principle. Einstein was not convinced at first (he famously said "god does not play dice.")

Einstein spent many years trying to find a contradiction in quantum theory. He suggested a crucial test of the theory called the EPR experiment but when in 1982, Alain Aspect, carried out the EPR experiment it agreed with Heisenberg. The Heisenberg Uncertainty Principle has held its ground and is accepted in modern day physics.

Schrödinger's Cat

Schrödinger was able to come up with a thought experiment which demonstrated just how incomplete the physical view of the world given by quantum physics is. He proposed one could place a cat in a box with a radioactive source, a bottle of cyanide and a Geiger counter. There is a fifty-fifty chance that the radioactive material will decay in some period of time. If it does decay the Geiger counter detects the particle and crushes the bottle of cyanide killing the cat. Since there is a fifty-fifty chance of decay, if the material does not decay the cat will stay alive. To any observer outside the box, the time of detection is when the box is actually opened and it is revealed whether the cat is dead or alive. Until then, the cat is both dead and alive! However, one might think that the presence of a cat might cause wave function collapse? If this is so then would the presence of a hamster do the same? If the cat is replaced with a human presumably this would cause the wave function to collapse. From this thought experiment we can see that there remains confusion in quantum theory as to what constitutes a measurement.

Many Worlds

Many worlds is an interpretation of Schrödinger's Cat first presented by Hugh Everett in 1957. It is also known as the branching universe interpretation. In this interpretation,  whenever a measurement takes place, the entire universe divides as many times as there are possible outcomes of the measurement. For example, if you throw a quantum dice, the universe divides into 6 so that in each universe there is one possible outcome of the dice. All universes are identical except for the outcome of that measurement. It is not possible for any of these universes to interact with each other. This interpretation solves the Schrödinger's Cat problem as in one universe the cat is dead and in the other the cat is alive.
 
For anyone who wishes to read further please read In Search of Schrödinger's Cat By John Gribbin

or to visualise what has been stated in this website please visit

https://mail.phys.soton.ac.uk/Redirect/video.google.com/videoplay?docid=-4237751840526284618