### Quantum for dummies – Part 1 – The Basics

In Part 1, we visit the basic concepts, starting with what quantum actually represents, and then discussing the major attributes of quantum, including its lumpiness, its behaviour as both particle and wave, the uncertainty principle and entanglement.

I must admit, covering these topics in few short paragraphs, and without any maths, is challenging, but here goes.

#### Definitions

What do we mean when we talk about ‘the quantum world’?

Let’s start with the world we experience on a day to day basis. We are surrounded by objects we can see, feel, taste, hear, and smell. This is the macroscopic world – which consists of big stuff.

This big stuff is generally well-behaved, too. Things move in predictable ways – they fall at a predictable acceleration and move in straight lines unless they are pushed sideways, and planets move in nice elliptical orbits. All this is known as Newtonian mechanics, after Sir Isaac Newton. It is also known as classical mechanics.

Newtonian mechanics has served us well for around 3 centuries, but going into the 20th century it became clear that those same principles did not apply in the microscopic world – the world of atoms and their constituent parts. At one time, it was thought that atoms were like mini solar systems, with a big lump in the middle, and little spheres orbiting. While we still teach using this imagery, we now know that it does not represent the reality at all. The reality is much weirder and harder to swallow – but more on that later. We discovered that at the microscopic level we needed a new set of laws or rules to describe the behaviour of the particles, since Newton’s principles wouldn’t work.

And so, in the early 20th century, the subject of quantum mechanics was born, thanks to Max Planck. (Incidentally, it was around the same time when Einstein was developing his Special and General theories of Relativity – oh boy, what a stimulating period that must have been if you were involved in physics).

In the quantum world, we learn that some quantities can only change in ‘lumps’ or ‘quanta’, hence the name. In the classical world, things seem to be able to take an infinite range of values – resulting, for example, in the smooth movement of a ball through the air, or a planet on its orbit. In contrast, in the quantum world, the energy of an atom can only take on certain values.

So, that’s the deal with the quantum. What’s really interesting is the behaviour of particles in the quantum world, and some of the practical outcomes, so we’ll cover some of these in the next sections.

#### Lumpy Energy

One of the things this finding explains is the nature of the interchangeability of matter and energy. Even the most science-shy person will have heard of Einstein’s famous formula: E=mc^{2}. This describes the relationship between energy E, and matter of mass m. But it turns out that E cannot take any value – it is subject to quantisation. In an atomic bomb for example, as each atom splits to release energy, the energy released can only be a multiple of a ‘quantum’ of energy. That energy quantum is based on the frequency of the energy, and related by a constant known as Planck’s constant, thanks to Maxxy.

Now that we know roughly what is meant by a ‘quantum’, we can look at two major attributes of the quantum world – Wave-particle duality, and, the Uncertainty Principle. Once we discuss these, you’ll come away with a bit more jargon to throw around at parties, and more than enough to start your own brand of pseudo-science.

#### Wobbly bits

In the last para, I slipped in the phrase ‘frequency of the energy’ – if you’re still awake, you’re asking – how can a particle have a frequency? Isn’t frequency a property of something that wobbles – like sound waves or waves on a pond? Great question! I’m glad you asked.

This is the next unexpected thing which separates the quantum world from the classical world. In the classical, macroscopic world, a billiard ball is just mass – it doesn’t wobble, and certainly doesn’t have a frequency (ok, if you give it a spin it does – stop making trouble for me, imagine it’s just sitting there). But, in the quantum world a particle (let’s take a photon for example, the fundamental unit of light), is both a particle AND a wave, depending on how you look at it. Yes, I said ‘particle AND a wave’, your eyes do not deceive you. This is imaginatively called the ‘wave-particle duality’, and tells us that sub-atomic particles have properties of both particles and waves. Now you may think this is just semantics, or some mathematical trick, but this duality is observable in experiments, and we have been doing these experiments for decades. For example, there is the famous ‘dual slit’ experiment, which goes as follows. If you fire a beam of light at a single narrow slit in a piece of material, we get a blob of light on the wall on the other side of the material. So far so good. But what if we put a second slit next to the first? What do we get? If you said a second blob of light, you’d be wrong. What we get is a lovely ‘interference pattern’, which is similar to the ripples on pond if you dropped two stones at different points.

So, with one slit, the photons behave like lumps, and just add up to a bigger lump, but when we add a slit, the photons suddenly behave like waves. But how do they know to change their behaviour? Yes, it’s quantum weirdness at work.

But here is the reason that quantum mechanics is so important. Classical mechanics could never explain why energy is quantised, or why particles can behave in two different ways, depending on how you observe them. But quantum mechanics can. Very cool.

As a result, we have developed extensive mathematics to describe the real world very accurately as sub-atomic levels, and this complements the great work done over centuries in the macroscopic world.

#### Some Uncertainty

The second major attribute is the Uncertainty Principle, formulated by Werner Heisenberg. In a nutshell, it seems that there is a fundamental limit to the accuracy with which we can measure properties of things at the quantum level. The typical example is the pair of properties of position and momentum (momentum being mass times speed). We can’t know both of these exactly for a quantum particle. If we measure one accurately, the other one is less certain. In fact, the product of the uncertainties of the two is constant! This means that the less uncertain one becomes, the more uncertain the other becomes. And what is that constant? If you said Planck’s constant, you were right. Go to the head of the class.

#### It takes two to tangle

We are now ready to wind up the weird-o-meter, and talk about a thing which even Einstein dubbed ‘spooky’ – the notion of quantum entanglement.

Imagine two quantum particles in the same region which interact to achieve the same quantum ‘state’. The so-called state is the collection of properties at the time which describe each particle. One of these is known as ‘spin’ (it’s not actually spin as we know it, but it’s ok to visualise it as two balls spinning). So, because they interact, they are both spinning in the same direction. The particles are now said to be entangled. But remember, we can’t be certain of the spin of either until we measure the spin of one of them, so we go ahead and measure one, and find it is spinning clockwise. Excellent you say. Closely followed by ‘so what?’. Well, as soon as we measure one, we know the spin of the other, because we know they were entangled. Big deal, you say. There are two interesting things here. Firstly, we know a property of the second particle, even though we haven’t measured it. Secondly, and more remarkably, this is true even if the two particles have been separated by long distances. Very long distances. In principle, it could work over any distance. The implication is that we can send one particle to another galaxy for argument’s sake, and by examining our local particle, determine the properties of the distant particle – instantly. While this sounds fanciful, and frankly useless, it has spawned the discipline of quantum cryptography (amongst other things) which enables us to use quantum-based coding for high-security communications. This ‘action at a distance’ was also not very popular initially because it seemingly bypassed our magical light speed limit – by sending a signal at faster-than-light speed. However, the conventional wisdom is that as no information is actually moving between the two points, and therefore no laws are being broken.

So, all clear?

Your homework for the week – derive Schroedinger’s non-linear, time-invariant wave equation from first principles, and shoot me any questions you have.

Next week we’ll look at what it all means. There are a number of interpretations of what is actually going on in quantum systems, and we’ll discuss the nature of reality, cats and parallel worlds. Sounds fun, right?

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