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This is an article about non-relativistic Quantum Mechanics. For more modern versions of Quantum Mechanics, see Quantum Field Theory.

This is a very short introduction to Quantum Mechanics. For a longer, more detailed explanation, see the article in Wikipedia.

Quantum Mechanics (QM) is a physical theory which was developed in the early 20th century by a number of physicists including Bohr, Schroedinger, Planck, Heisenberg and others. Quantum Mechanics describes the behavior of elementary particles but, even though it is sometimes described as such, it doesn’t only deal with the microscopic world: since the whole Universe is made of elementary particles, Quantum Mechanics gives us a description of any system, microscopic or not. The behavior of macroscopic systems, such as computers, is unexplainable without its aid. Most of our current technology is based, directly or indirectly, on Quantum Mechanics.

QM has several features which make it counter-intuitive or just plain bizarre for some people. As John Wheeler put it, “if you are not completely confused by Quantum Mechanics, you do not understand it.”

One of the most striking features of Quantum Mechanics is the fact that it does not predict definite experiment outcomes, but only their probabilities. This is related to the fact that particles in the theory behave both as waves and particles, depending on the kind of experiment performed on them. This has been called the wave-particle duality.

In order to get a glimpse of what the theory says and how it works, it is a good idea to look at some specific experiments involving it and to try to understand their outcome. One of the clearest examples is the double-slit experiment.

Let’s first imagine the following setup: we have a gun, a wall with two slits on it, and a screen at the end. Now let’s suppose someone takes the gun and starts shooting at random. Most bullets will end up at the wall, while some will make it to screen. After some time, we will have something like the picture shown below.

Now let’s change the setup: instead of a gun, we have the two walls immersed in water; what we have now is waves emerging from the gun’s former position, splitting at the slits and then hitting the last wall.

In this case, the waves will produce a phenomenon called “interference”. At any point in the second wall, there will be two colliding waves, one coming from each of the slits. Now, when waves collide they can reinforce each other or cancel each other out, as can be easily seen from the picture below.

Two peaks at the same place will double the strength; a peak and a valley will cancel each other out. That’s the reason behind the pattern seen at the screen, in the first picture.

The situation becomes more interesting if we repeat the experiment, but now with an electron gun. This gun fires electrons at random, one by one, just like in the first case. And the question we ask ourselves is what will happen this time. Below one can see different stages of the experiment, where the white dots signal places where an electron has landed.

It is easy to see that, after enough repetitions, the pattern ends up resembling the wave experiment, not the particle one.

Now it’s time to look for explanations. Firstly, the fact that each electron leaves a point-like impression on the screen tells us electrons must be particles. However, the final pattern is that of a wave. Therefore, something wave-like must be happening at some point. A possible explanation is that electrons interfere with each other before hitting the screen. That, however, is not plausible, since electrons are fired one by one. The next explanation one comes up with is that the electron may somehow split up, interfere with itself and then hit the screen.

If the electron does split up, it should be possible to detect it while passing through both wholes at the same time. In order to do so, we could place an electron detector at each of the slits and see what happens. If one does that, one gets an unexpected outcome: the detectors show that electrons go through either of the slits, not the two at the same time. However, the pattern we get at the screen changes: electrons stop behaving like waves and start behaving like bullets.

In order to explain this apparent bizarreness, physicists had to be extremely creative. The puzzle wasn’t completely solved until Schroedinger suggested his famous equation, governing the behavior of something called “the wave function”. The basic idea is like this: every particle has an associated wave, which behaves according to the wave equation. The behavior of the wave, at the same time, determines the behavior of the particle. Thus, if we fire an electron from an electron gun, the associated wave will go through both slits and form an interference pattern, just as observed in the first experiment.

However, things get complicated when we perform a measurement. When we do so, the wave function is said to “collapse”. That is, if the wave is spread through space, when we measure the electron’s position we only get one answer, not many. The electron will be somewhere amongst the wave’s positions in space. Where exactly? We don’t know. We cannot know. All QM tells us is how the wave will behave; however, the wave does not tell us where its particle will be. It tells us where it may be. And, luckily, it gives us something else: the probability of finding the particle at that position. This probability is given by the square of the wave’s amplitude (the amplitude of a sea wave would be its height, for example). Therefore, QM allows us to predict the distribution of measurements over many particles, but it does not allow us to know the outcome of one single experiment, only its probability. This baffled and appalled many physicists at the time, Einstein being one of them, and it lead him to his famous quote “God doesn’t play dice with the Universe”. However, all evidence points to the contrary: apparently, God is a consummate gambler.

For different interpretations of Quantum Mechanics, see Interpretations of Quantum Mechanics.

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