What actually are these quanta?

A quantum of happiness, a quantum leap in technology, Firefox Quantum.

Quanta seem to be a thing nowadays, they have entered common speech, the newspapers are frequently reporting about quantum computers. Yet hardly anyone outside physics knows what quanta actually are. And what do you do if you have a question? You look it up on Wikipedia:

In physics, a quantum (plural quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a physical property can be “quantized” is referred to as “the hypothesis of quantization”. This means that the magnitude of the physical property can take on only discrete values consisting of integer multiples of one quantum.
On a normal meadow one can choose any path.

Crystal clear. Thanks Wikipedia! All right, let’s start again from the beginning: imagine you are walking across a meadow covered in leaves. Let’s also assume that you don’t like to walk over leaves, so you have to clear away the leaves on your path. But you are not allowed to throw the leaves on other parts of the meadow, burn them, or anything like that – let’s call it the law of leaf conservation. You can choose any path and depending on how long it is, you will end up with more or fewer leaves. Conversely, you can control the number of leaves by choosing your path. We say that the amount of leaves is continuous.

On a meadow in the quantum field, one may only move from one field to the next.

Now let’s look at another meadow, which is not in our classical, but in the quantum world. Here the rules are a little different: the meadow is built like a chessboard and, like the king, you are only allowed to move from one square to another. In addition, you always have to clear away all the leaves of a whole field – let’s say you collect them in a bucket of the right size. Since there are the same amount of leaves on each field, all the buckets you fill are the same size and full to the brim. At the end of your path, you will have filled as many buckets as you have covered fields and you will never have a half-full bucket (or a half-empty one, for the pessimists among us). So you can no longer accumulate as many leaves as you like – it is impossible to accumulate the leaves from one and a half or 9¾ buckets. The amount of leaves is divided into discrete packages – leaf quanta.

With the help of this story, we can now translate and understand the above definition. The checkerboard meadow is a system with discrete values and when we move on it, we change our “state” – we are then standing somewhere else. A (leaf) quantum is now the object that is created when we move. Of course, we do not “create” leaves in the literal sense, but it was previously part of the meadow. We separate it from the meadow and reshape it.

Now, this all sounds very adventurous but in fact, this is exactly how it works in the quantum world. Not with leaves, of course, but with energy, for example. The prime example of this is electromagnetic radiation, or, in other words, light. If you could zoom in close enough, you would see that light consists of small packets of energy, so-called photons. It works the same way in the meadow: while the foliage looks very continuous to you as a human, every single leaf counts to a mouse. In the same way, when Ant-Man shrinks himself to subatomic size, he can see individual energy packets in quantum space.

Well, actually not. In theory, it’s a nice idea, but in practice, it’s complete nonsense. For the sake of completeness: it is impossible to shrink oneself to quantum size. So back to real physics.

One of the tasks of quantum physicists is to study the structure of the checkerboard. The size of the squares can vary, resulting in different sized buckets. To get from one side of the meadow to the other, you have to have the right buckets. As already mentioned, the buckets represent light quanta. But what is the meadow? There are many possibilities, but one of the simplest is atoms – the building blocks of matter. Everything around us is made of atoms: air, water, coffee cups, and even ourselves.

The leaves on the meadow correspond to the energy that can be stored in an atom. Just as we removed leaves from the meadow in buckets, we physicists can remove energy from the atom in packets. Conversely, we can also give energy packets to an atom. The important thing here is that the energy of the quanta matches the atom. For example, if I have a bucket that is too big, the leaves in it will not fit in a field of the meadow. I can’t just put the necessary amount of leaves on a field and take the rest bak home again – bucket and field have to fit together exactly. In quantum physics, there is only: all or nothing!

Atom absorbing a photon
An atom can absorb a photon if it fits it exactly (left). But if the photon has more energy than the atom needs, the atom cannot absorb it (right).

How far would I have to zoom in to see not the leaves, but the quantum meadow – the atoms – in the first place? Atoms are the smallest building blocks of our world. And they are very small. The smallest atoms have a radius of about 0.1nm (nanometres), a ten-millionth of a millimetre. That is 250,000 times smaller than the thickness of a hair. A hair, therefore, relates to an atom roughly like the earth (12,742 km) to a sports swimming pool (50m). Atoms, however, are not indivisible (as it was long assumed), but consist of a positively charged nucleus and negatively charged electrons flying around the nucleus. The atomic nucleus has a size of about 1fm (femtometre), which is another 100,000 times smaller than the atom. So that would be about a grain of salt (0.5mm) in a swimming pool. So an atom is not only very small but also incredibly empty. If you were to compress the entire mass of the earth and the empty space between the atoms and within the atoms, the resulting sphere would have a diameter of barely 2 cm – the size of a cherry.

Structure of an atom
An atom consists of negative electrons (blue) and a nucleus, which in turn consists of protons (red) and neutrons (grey). Gluons (green) provide the binding of the atomic nucleus.

The structure of atoms – a “grain of salt in a swimming pool” – is anything but intuitive and indeed it took a very long time to decipher it. The basic idea that matter is made of atoms, however, goes back to ancient history. Around 400 BC, Democritus claimed that all of nature consisted of small, indivisible particles. In fact, the word “atom” also comes from ancient Greek and means non-divisible. Although the ancient Greeks got this point a little wrong, their foresight is impressive.

The image of the atom has evolved a little bit more over the last 2400 years. Let’s jump straight to 1909 and Ernest Rutherford. At that time, it was already known that the atom consists of electrons and protons – positively charged particles. However, they did not yet know in what form. There were two competing models: on the one hand, Rutherford’s, in which the electrons orbit around the compact atomic nucleus, which consists of protons. On the other side was Joseph Thomson‘s model of the atom with the wonderful name “plum pudding model”. He assumed that an atom consisted of a positively charged mass in which the electrons were distributed – like plums in a pudding. However, Rutherford was able to support his theory with an experiment that was historic for physics and won the race. For the moment at least, because his model was replaced by Bohr’s atomic model just four years later.

Niels Bohr‘s model of the atom is the first to incorporate quantum physics, which was still in its infancy at the time. The problem with Rutherford’s model was that it could not explain why the atom was stable in the first place. A principle of electrodynamics is that equal charges repel each other, while different charges attract. Why doesn’t the negatively charged electron fall into the positively charged nucleus? Bohr tried to solve this problem by setting up postulates. What is a “postulate”? A bold assertion without justification. Yes, you can do that in physics, and it’s not that rare. First, something is asserted, and later someone else may bother to prove why it is true. Or smash it, as Rutherford did with Thomson.

So, Bohr claimed the following:

  1. An electron may only move on certain orbits.
  2. An electron can jump from one orbit to another. In doing so, however, it must absorb or release exactly the right amount of energy. This is called a quantum leap.

Aha, the quanta are back! The second postulate states what we already know: The number of leaves in the bucket must exactly match the number of leaves on the chessboard. Another point also becomes clear: a quantum leap is something very small. It is the smallest change that an atom, the building block of matter, can make. So when you hear the phrase “researchers underwent a quantum leap in technology” in the media, you can now safely throw your hands up in horror! Complete nonsense! However, you can talk your way out of this with a little linguistics. In technical language, this is called a Janus word, or auto-antonym: a word with two opposite meanings. In technology, a quantum leap is something big, significant. In physics, a quantum leap is tiny. Another example would be the verb to dust: “First, I dusted the cake with powdered sugar and then I had to dust the house.” Unless you are a witch, you don’t want to dust your house (with powdered sugar).

Bohr’s model was very successful and even today atoms are symbolically drawn as nuclei with electron orbits around them (guilty as charged). The fact is, however, that Bohr’s postulates contradicted the rules of physics at the time and could not be explained. It took 10 years until this atomic model was replaced by one that is still used today. This model is based on the results of quantum physics and is therefore in accordance with the rules of physics. Thank God!

At school, by the way, I went through all these atomic models chronologically. Around the 7th grade, I learned that there are atoms and that they are small spheres. Later, I learned about electrons orbiting the atomic nucleus. When I heard in my advanced physics course that Rutherford’s model was wrong and that electrons fly around the nucleus on very specific paths (Bohr’s model), I began to doubt what we were actually taught at school. Why do we learn one wrong model after the next? How many models are still to come and what does the atom really look like? Or are atoms just an invention of the education system??

Atomic models
The atomic models of Democritus, Thomson, Rutherford and Bohr.

But I digress. Atoms really do exist and for now, Bohr’s atomic model is good enough for us. It explains (with daring claims) why the atom is stable and the electron does not crash into the nucleus. But it does not explain why the nucleus itself is stable. Remember: Equals repel each other. Shouldn’t the protons in the nucleus just fly apart? In the meantime, neutrons had been discovered – particles without charge that form the nucleus together with the protons – but they could not solve the problem either. Again, physicists went to great lengths and postulated a solution. Around 1970, they thought that there must be a very strong force that glues the protons and neutrons together. This force was later found and named the “strong interaction“. The particle (and the second quantum that we are privileged to know) that imparts this force was called a “gluon“. As you can see, there were some very creative minds at work.

This whole story shows nicely that many discoveries in physics are the result of clever guessing. In science, this is called postulating – it sounds better. Of course, hard work and mathematical skills are also useful. But in particular, quantum physics is a story of smart guessing, sharp looking, wild speculation and a quantum of luck.

(Sorry Thomson)

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