3.1 Quantum waves

This is where the quantum world gets weird. Contrary to the previous examples of waves, quantum waves do not appear to represent a physical quantity, but instead describe something like a probability. A quantum wave describing an electron in a hydrogen atom, say, will tell you how likely it is to find the electron in a particular region. Note that this already mixes up both the particle and the wave point of view.

Even weirder, the most popular interpretation (called the Copenhagen interpretation, largely devised between 1925 to 1927 by Niels Bohr and Werner Heisenberg) asserts that physical systems generally do not have definite properties prior to being measured. Quantum theory can predict the probability of a given measurement’s results, but it is the actual act of measurement which affects the system, causing the measured quantity to assume a definite value.

What happens if we send a beam of electrons (rather than light) through a double-slit setup, like the one seen in Figure 8 earlier? The electrons can pass through either slit. If they were just particles, you would presumably get two shadows (maybe a bit diffuse at their borders) of the two slits. However, if they behave as waves, they will interfere in the manner of classical waves, with the bright and dark stripes corresponding to regions with high and low probability of finding an electron, respectively. Indeed, that is what is observed. Even if you do the experiment with electrons very slowly, so you can register the point where electrons arrive one-by-one, you still find that this eventually builds up the expected interference pattern.

However, if you try to set up the experiment in a way that allows you to find out which slit the electron passed through, you will find that the interaction required to detect the electron’s path destroys the interference pattern. The same thing happens if you close one slit while keeping the other open, and it doesn’t matter how often you switch this round. The electron, while having to pass through one of the slits (when seen as a particle), somehow ‘knows’ about the presence of both slits.

It may not come as a surprise that the probabilistic nature of the information provided by quantum theory has troubled many scientists, including some of the most famous minds of the time, like Albert Einstein. Discussions about the interpretation of quantum theory are continuing to this day. Regardless, quantum theory is an incredibly successful step forward in describing the microscopic world. There are many applications for it – the rest of this week will introduce a few examples of scientific processes, theories and thought experiments.