In this quantum physics introduction for beginners we will explain quantum physics, also called quantum mechanics, in simple terms. Quantum physics is possibly the most fascinating part of physics there is. It is the amazing physics that becomes relevant for small particles, where the so-called classical physics is no longer valid. Where classical mechanics describes the movement of sufficiently big particles, and everything is deterministic, we can only determine probabilities for the movement of very small particles, and we call the corresponding theory quantum mechanics.

You may have heard Einsteins saying “Der Alte würfelt nicht” which translated to English roughly means “God does not roll dice”. Well, even geniuses can be wrong. Again, quantum mechanics is not deterministic, but we can in general only determine probabilities. Since we are used to fairly big objects in our everyday life, quantum mechanics and its laws may at first seem strange and quantum theory is often considered to be complex. But for example electrons and photons are sufficiently small that quantum physics is needed, and on this website we will show you that understanding the basics of quantum physics is easy and fun.

In the following paragraph we will describe a thought experiment that we perform at two different length scales: With bullets as known from pistols (the large scale) and with electrons (the very small scale). While the experiment is essentially the same but for the size, we will show you how the result is very different. This will be your first lecture in quantum mechanics.

## Classical Bullets vs Electrons in a Two-Slit Experiment

### a) Classical bullets

Consider first a machine gun that fires bullets to a wall. Between the wall and the machine gun there is another wall that has two parallel slits that are big enough to easily allow a bullet to pass through them. To make the experiment interesting, we take a “bad” machine gun that has a lot of spread. This means it sometimes shoots through the first slit and sometimes through the second, and sometimes it hits the intermediate wall.

If we block the second slit, all bullets that reach the outer wall will have come through the first slit. If we count the number of bullets as a function of the distance from the center of the outer wall, we will find a curve distribution that could be similar to a Gaussian curve. We can call this probability curve P1.

If we block the first slit, all bullets that reach the outer wall will have come through the second slit. The probability curve will be mirrored around the center, and we call it P2.

If we open both slits, all bullets at the outer wall will have come through either slit 1 or 2. What is typical for classical mechanics in this situation is that then the total probability distribution P can be determined as the sum of the previously-mentioned probability distributions, P = P1 + P2.

### b) Electrons – Quantum Mechanics

Now consider the same experiment on a much smaller scale. Instead of bullets from a machine gun we consider electrons that for example can stem from a heated wire that is parallel to the two slits in an intermediate wall. The electron direction will have a natural spread. The slits are also much smaller than before but quite a bit broader than a single electron.

#### The electron experiment results

Consider again the case that the second slit is blocked. For proper sizes of the slits and distance between the wire and the walls, the probability distribution P1 will be similar to before. Similarly, if we block the slit 1, we will for proper distances find a probability distribution P2 similar to before.

What do you expect will happen if we do not block any slit? Will we find a probability distribution P = P1 + P2 as before? Well, after all we said you may guess that this is not the case. Indeed, we will instead find a probability distribution that has various minima and maxima. That is, for x = 0 there would be the strongest peak of electrons, for a certain +-Delta x there wouldn’t be any electrons at all, but for +-2 Delta x there would be another peak of electrons, and so on.

#### Explanation of the electron experiment results

How can we explain these results? Well, the explanation is rather straight forward if we assume that electrons in this specific case do not behave as particles, but as waves. “Waves?” you may ask. Well, consider a plain of water, and the same wall as before and the same intermediate wall with a double slit as before. At the place where the machine gun or the wire where, consider a pencil punching periodically downwards into the water. If you do this, you will get concentric waves around the point where you punch the water, until the intermediate plain with the two slits.

Behind each slit, there will be a half circle of concentric waves, up to the point where the new waves from the two slits cross each other. There, the waves from the two slits can add up or eliminate each other. As a function of the periodic punching you will find points where the height of the wave is always the same. There will be other places where the wave is sometimes very high and sometimes very low. At the outer wall, these two phases will be repeatedly following one another. The places where there is a lot of variation correspond to the places where there are the most electrons. The places with no variation correspond to the places where there are no electrons on the wall at all.

So, why do electrons in this case behave like waves and not like particles? Well, this is the thing where you will not find a satisfying answer. You just need to accept it.

### c) Photons (light particles)

What if you do not believe this? Well, the thought experiment with the electrons is rather difficult to perform with the proper scale of all elements of the experiment. But there is another very similar experiment that you can do at home. Instead of the electrons you use the photons (light particles) from a laser which you can buy for a few bucks. You let the laser shine through a double slit, darken the room, and look at the outer wall. And boom! What you see is not just two light lines on the outer wall, but a pattern of light line, dark line, light line, dark line, and so on. The intensity of the lighter region becomes less far away from the center. It corresponds exactly to the result of our thought experiments with electrons.

Why does the laser experiment give the same result as the thought experiment with electrons? It is quite easy: Light particles, called photons, are also very small and therefore behave quantum mechanically. And like electrons, they behave like waves in this specific situation. As a side remark, research has shown that light behaves like particles in another respect: If one reduces the intensity a lot, one will find single light spots from single photons on the wall. This means the light behaves like particles as well. One therefore talks about the **particle-wave duality** of photons or electrons.

What do you wait for? Do the experiment, and you will become a believer of quantum mechanics, or more generally phrased, of quantum physics.

## Advanced Remarks

### Don’t watch!

The pattern with maxima and minima is called an interference pattern, since it comes about by the interference of the waves through slit 1 and slit 2. It has been found that you only get this interference pattern if you do not by other means (some additional measurement instrument) watch through which of the two slits the electrons or photons pass. If you do measure which of the two ways the particles pass by any other means, the interference pattern goes away. You will then find the sum distribution P = P1 + P2 as in the classical experiment.

### Uncertainty principle

A measurement device for electrons would typically disturb the electrons. More precisely, their momentum p would typically change due to a measurement device, while the place x of its path would become known more precisely. In general, there will be some uncertainty left in the momentum and in the place of the electron. It was postulated by Heisenberg that the product of these uncertainties can never be lower than a specific constant h: Delta x times Delta p >= h. Noone ever managed to disproof this relation, which is at the heart of quantum mechanics. Essentially it says, we cannot measure both momentum and place with arbitrary precision at the same time.

### Single slit experiments

We said that for proper distributions you will find a similar result P1 and P2 as in the classical case. However, for other sizes one can achieve an interference pattern even for the single slits. This is the case when the slit is so broad that one can achieve an interference of the wave stemming from one side of the slit with the wave stemming from the other side of the slit.

### How Small Is Small?

We said above that quantum physics becomes relevant for small particles — whereby we mean that *naturally*, quantum effects are only seen for small particles. However, the theory itself is thought to provide correct results for large particles as well. Why is it then, that quantum effects (which cannot be explained with classical theory) become increasingly difficult to observe for larger particles? Larger compound particles in general experience more interaction both within themselves and with their surroundings. These interactions typically lead to an effect physicists call “decoherence” — which simply put means that quantum effects get lost. In this case (for sufficiently large matter), quantum physics and classical physics yield the same result.

Now you may wonder: “At which size does this happen?”. While one doesn’t naturally observe quantum effects in large particles, ingenious people have managed to specifically prepare test environments which showed quantum effects for an ever growing size of particles. Already 1999 an experiment showed a quantum superposition in particles as large as C_{60} molecules (original article). A 2013 article already claims to observe quantum superpositions in molecules that weigh more than 10000 atomic mass units. The question of where the achievable limit lies, and whether one can be sure that experiments really demonstrate quantum behavior, is still of interest. That these questions are not finally concluded is also reflected in a more recent article on the American Physical Society site. In principle, if one would be able to somehow get rid of decoherence effects in specifically prepared systems, the theory itself imposes no upper size limits on where quantum effects could be shown.

### Quantum Effects To a Satellite And Back

The aspect of the length scale for quantum physics that we just discussed was the particle size – which typically is on the microscopic scale. A completely different matter is the length scale of how far you can move or separate such particles after an initial interaction, without loosing quantum effects. You can view the two-slit experiment as showing an interaction between particles at the slit. If you tried out the experiment yourself, you probably realized, that the distance between the slit and the wall were you observe interference patterns can easily be some meters – not microscopic at all!

Other experiments prepare two particles in a special quantum superposition called entanglement — which, by the way, lies at the heart of quantum computation — and then separate these particles. In some experiments, it was possible to show interactions between these particles despite a separation over many miles. Essentially, if one measures the state of one such particle, one can thereafter predict the state of the other particle (within errors), despite the large separation between the particles. A recent experiment demonstrated this entanglement effect over extreme distances. Particles were sent to a satellite and back to earth – a fairly large scale distance compared to the size of a human.

## Summary of this Quantum Physics Introduction

In this quantum physics introduction we told you that both photons and electrons behave as both particles and waves. This particle-wave duality is not understandable with classical mechanics. It results in us only being able to predict probabilities, while one classically can make deterministic predictions. You can easily test these results at home by performing the two-slits experiment with a laser pointer. Have fun! We hope you enjoyed this quantum physics introduction for beginners. If you haven’t read it yet, you should continue with our article What Everyone should Know about Quantum Physics. And if you want to learn even more, why not have a look at our article Best Quantum Physics Books for Beginners?

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