The Map of Quantum Physics

I’ve been fascinated with quantum physics for a  very long time so much so I did a PhD in it and I wanted to share the subject with you so I made  this map of quantum physics to lay out the ideas within the subject, to set some bounds on it so  you know its not endless and to introduce you to lots of concepts that if you are interested in  them you can dig deeper. When you are approaching a subject like this that’s so complicated  it can be quite challenging because you don’t know where to start and you don’t know  how all the concepts relate to each other so hopefully this will put everything in context. Okay first lets just look at the geography of this map to the north west we have the foundations  of quantum physics, and then travelling further south we go through quantum phenomena to quantum  technology.

And in the south and east we have the academic disciplines of quantum physics. In the  centre, quantum theory, and in the north and east the theoretical future of quantum physics,  beyond what we already know. That is your quantum forecast for this video.

I’ve also made a  poster of this available so if that’s of interest, check it out in the description below. And  without further ado, let’s get into it. The theory of quantum mechanics developed from a  set of mysteries in the late 1800s and early 1900s where reality didn’t quite match  the models of physics at the time.

We now call these older theories of physics,  classical physics. There were several clues that pointed to some deeper model of reality. When light shines through a gas, the gas absorbs and emits specific frequencies of light which we  call atomic spectra.

This was a mystery there was no known classical explanation for this. And there was a lot of confusion about how atoms could be stable. In classical physics  the electrons should continually radiate their energy and collapse into the nucleus.

The source of radioactivity was unknown. When you look at a hot body like the Sun,  it emits electromagnetic radiation in many different frequencies and this distribution  of light is called blackbody radiation. Now the distribution we observe  from black bodies didn’t match the predictions of classical physics.

And when you shine light on certain metals, you can make electrons fly off, this is  called the photoelectric effect. This experiment showed that light didn’t behave like  a wave, but like a stream of particles and was the first indication of particle wave duality. All of these mysteries can only be explained with the laws of quantum mechanics.

Let’s take a look at the foundations of quantum mechanics. A cornerstone experiment in quantum mechanics is the double slit experiment where  electrons are fired through two thin slits and make an interference pattern on a detector behind.  This interference pattern is something you only see with waves and this is more experimental  evidence for particle wave-duality.

In actual fact, in the mathematics of quantum  mechanics all particles are described as waves by a thing called a wavefunction, and the way this  wave evolves over time is described by the famous Shrodinger equation. But we can never see these  quantum waves as all we ever detect are particles, but from the wave function we can predict  where the particles are likely to turn up but we have to do a bit of maths  on them first called the Born rule which derives a probability distribution of where  the particle might be from the wavefunction. So quantum mechanics tells us that the universe is  fundamentally probabilistic, we don’t know exactly where the particle will turn up the best we have  is a probability of where it will be.

This brings us to the Heisenberg uncertainty principle  which says that quantum objects don’t have definite values for certain pairs of properties,  for example, position and momentum. You can get a flavour of this from these pictures. The first  is a snapshot where the particle had a definite position, but we have no information about its  momentum, as in: the direction it was going and how fast it was travelling.

The second picture has  a motion blur which tells us about its momentum, but now we have got an uncertainty about where  the particle was when we took the picture. Another important equation is the Dirac  equation which extends the Schrodinger equation to include special relativity and describe  particles with high kinetic energy. And another important foundational concept is Bell’s theorem  which proved that the uncertainty in quantum mechanics is not caused by our lack of knowledge  about hidden variables, but is a fundamental part of the universe, and also led to the concept of  non-locality which we’ll meet a little later.

Finally we get to energy quantization  which is where objects like electrons can only have certain definite energies when  they are in atoms. This is where the quantum in quantum mechanics comes from. And this  quantization is because their wave functions can only vibrate in certain specific ways.

You can see this if I reduce the atom to one dimension. The energy field of the proton in  the atom is represented by this bucket shape, you can think of the electron as being attracted  to the proton and so it wants to fall into the bottom of the bucket. But because the electron  is a wave it can only exist in certain modes shown here which are just like the vibrational  modes of a guitar string, with higher frequency modes having a higher energy.

This also means that the quantum objects always have a minimum amount of  energy known as the zero-point energy, and this applies not only to electrons in atoms,  but to everything, even to empty space itself. Now I understand that this is all quite  a lot to take in if you are new to this. But don’t worry if all these terms are  confusing, the point of this video is to expose you to a lot of the concepts in quantum  physics just so that you know they exist.

I can’t delve into every one otherwise we’d be  here forever. But if you want to dig deeper into any of these concepts I’ve made a playlist  of other videos that covers a lot of them. There however are a lot of gaps though, and  I’m planning on filling them in in the future, so if you want to make sure you don’t miss  out consider subscribing to this channel for more details in the future.

Okay let's carry on and take a look at the interesting properties we see in  quantum systems with quantum phenomena. Particles in quantum mechanics have  many properties. I’ve already mentioned position and momentum, but there are  others which I’ve listed here.

Spin is a very important property and all  particles are split into one of two categories, bosons which have got an integer spin  and can all have the same quantum state, and fermions, which have half integer spin and  can’t have the same quantum state as each other, which is called the Pauli exclusion principle. Superposition is a property when a particle has a probability of being in many different states, for  example, two different places at the same time. This simply means that it’s wavefunction  has values in two different places, although when you measure it it will turn up  in just one place.

Being in multiple places at once is confusing if we think of particles, but  is completely natural when we think of waves, for example any point on the surface of the ocean  is a superposition of thousands of waves. You may have heard of Schrodinger's Cat is a  popular description of superposition, although not a very helpful one as it was originally designed  to show how absurd quantum mechanics seems as cat’s can’t be alive and dead at the same time.  Which is true, but not because superposition is not real, we now know large things like cats loose  their quantum behaviour because of decoherence.

Decoherence happens when a quantum object  interacts with an environment and its quantum behaviour is lost to that environment. Decoherence  is what takes us from the quantum realm to the world that we inhabit, and you break the coherence  of quantum objects when you make a measurement. Entanglement is where the wavefunction of  the two or more particles interact and mix causing them to become a single quantum object. 

This means that the properties of the different particles will be correlated even if they  are separated a large distance. This concept, where the wavefunction that describes a particle  is spread far away from the particle is known as non-locality, and is another thing that doesn’t  happen in the world that we experience. There are several other interesting phenomena  which only happen in quantum systems which include: quantum tunnelling - the ability for  particles to cross narrow barriers because their wavefunction penetrates through.

Superconductivity  - the ability for electrons to move with zero resistance at low temperatures, and superfluidity  - allowing fluids to flow with zero viscosity. There’s also the quantum hall effect which is  the quantisation of conductance in 2D materials, and the casimir effect which is an  attractive force at short distances caused by cutting out large quantum waves  between two plates. An important concept when looking at the quantum behaviour of  large systems are phase transitions from one collective behaviour to another.

These are  analogous to the different phases of matter, solid, liquid and gas but in quantum phase  transitions it is not only temperature and pressure that plays an important role it  can also be applied magnetic field. Whenever we discover new interesting  behaviours in physics, one of the first questions is can we use this to develop  some new interesting technology? And there is a lot of technology that we use  every day which takes advantage of the amazing properties of quantum systems.

Lasers use a  process called stimulated emission to create beams of light with many photons which  all have the same frequency and phase. Atomic clocks keep incredibly accurate time  by using the frequency of light from a very specific hyperfine transition in caesium atoms and  are the basis of our global positioning system. The band theory of solids describes the energy  levels of electrons in different solid materials and is the basis of the semiconductor industry  which has yielded many different technologies solid state transistors, so basically the  building block of every computer in the world, LEDs which you are probably using to watch  this, CCD’s used in every digital camera and solar panels turning the energy  in sunlight into electricity.

Electron microscopes, scanning tunneling  microscopes and atomic force microscopes allow us to see objects we can’t see with  optical microscopes because they can see smaller than the wavelength of visible light  to resolve objects like viruses or atoms. And magnetic resonance imaging techniques are  used in biology and chemistry, for example to look inside our bodies, and these use giant  superconducting magnets to create large magnetic fields, and the most sensitive magnetic sensors  in the world called superconducting quantum interference devices (SQUIDs) whose core  components are a loop of superconducting wire which contain an insulating gap  called a Josephson junction. New technologies are being built and  improved in the world of quantum information.

Quantum cryptography takes advantage of  entanglement to make communication which is extremely secure and forms the basis of the  quantum internet. And quantum teleportation is the ability to perfectly copy the quantum state  of an object from one location to another. Quantum bits or qubits are the building blocks  of quantum computers which use superposition and entanglement to create states that are practically  impossible to simulate on a classical computer.

The challenge is to engineer large groups of  qubits that can stay coherent for long enough to perform their computations which is not an easy  task. But the potential is huge because their combined superposition means they can explore an  exponential number of states at the same time. This puts them in a different complexity class  to the classical computers we use every day.

There are many exciting applications of quantum  computers but my favourite is quantum simulation: the ability to simulate a quantum system  which would be amazing for things like discovering new materials with entirely new  properties or for solving computationally expensive tasks like protein folding. Now let's move on to the fields of quantum physics research. These include condensed matter  physics, quantum biology, cold atom physics, quantum chemistry, nuclear physics,  particle physics and theoretical physics.

Condensed matter physics is the study of large  systems of many atoms in solid or liquid form, and seeking to understand their collective  behaviour on a quantum level. I've placed this here because condensed matter  physics covers a lot of these other fields and condensed matter theory describes the  quantum behaviour of collections of electrons in solids which explains collective  behaviours like superconductivity, and the energy bands of semiconductors. There are many unsolved problems in condensed matter physics, for example, we still don't  have a theoretical model that explains how high-temperature superconductivity works. 

In a way the frontier of condensed matter physics is complexity. Because the subject  studies complex combinations of many atoms which make many different materials with  different physical and electronic properties, the potential avenues for study are basically  endless because the combinations are endless. Quantum biology studies the role that quantum  mechanics has in biological systems.

There are many processes in biology that are difficult  to explain without quantum mechanics being involved, like the efficiency of energy transport  in photosynthesis, to magneto-reception in birds, how our sense of smell and sight work, and  how enzymes speed up chemical reactions. Cold atom physics evolved from condensed matter  physics and studies gasses which are controlled in magnetic or optical traps and cooled to  ultra-low temperatures using laser cooling and other cooling techniques. Cold atom physics studies many exotic phases of matter like Bose-Einstein Condensates  and Rydberg matter, and looks at their behaviour like quantum phase transitions, quantum spin  systems and many more.

Cold atom experiments can also be used as quantum simulators and  quantum sensors like gravity sensors. Because quantum mechanics describes the behaviour  of electrons in atoms, it also describes the basic rules of chemistry. The Schrodinger equation is  used to describe electronic structure of atoms and how molecules are bonded and move called  molecular dynamics.

Solving the quantum mechanics of molecules is a very computationally intensive  task and so computational techniques are very important to quantum chemistry a popular approach  is a method called quantum monte carlo. Nuclear physics is the study of the nucleus  of the atom and the ways nuclei can join in nuclear fusion or split apart in nuclear  fission, and the particles and energy involved in these nuclear reactions. Applications of nuclear physics include nuclear power, nuclear weapons, nuclear  medicine, and techniques such as MRI, ion implantation and radiocarbon dating.

Particle physics evolved from nuclear physics and is focused on understanding what the  fundamental particles of the universe are and how they interact. Experiments in particle  physics are performed in large particle accelerators where high energy particles  are smashed together to make new particles out of the collision energy. This is why this  field is also known as high energy physics.

The standard model of particle physics describes  all of the fundamental particles we know of, which we’ve discovered over many decades,  the last of which was the Higgs boson. A useful tool for visualising particle  interactions are Feynman diagrams which show what happens when particles collide and they simplify the equations of quantum  field theory into much simpler pictures. The theories of the standard model include  quantum electrodynamics which describes the electromagnetic force.

Electroweak  interactions which include the weak force, and quantum chromodynamics which  also describes the strong force. In the standard model, these are all quantum  field theories where particles are understood to be excitations of quantum fields which also  govern how they interact with each other. There may be other particles out there that we  haven’t discovered yet.

People have proposed that dark matter might be made of particles  called weakly interacting massive particles, and the large discrepancy between the weak force  and gravity known as the hierarchy problem may be solved by supersymmetric particles. So the frontier of particle physics is to try and work out new ways to explore the landscape  of potential particles at very high energies. Now onto the field of quantum theory  which, although I’ve put it in this box, it really covers this whole map with specific  implementations in each of the fields.

Here are some specific aspects of  quantum theory worth knowing about. The core of quantum physics are the postulates of  quantum mechanics that set the ground rules. The path integral formulation of quantum  mechanics is a very elegant way of calculating the motion of particles by integrating over every  possible path that the particle can take.

And Hilbert spaces are a useful tool to describe  all of the possible states of a quantum system, in a giant multidimensional space. The symmetries of quantum mechanics are an important part of the theory to tell us the  conservation rules which are basically the rules of particle interactions: what should come out of  a particle interaction based on what goes in. This is where we hit the limits of our current  knowledge of quantum physics.

But there are two main areas of theoretical work looking beyond  the existing models. Firstly the interpretations of quantum mechanics are attempts to resolve the  counterintuitive implications of the wavefunction, and quantum gravity aims to reconcile quantum  field theory with general relativity to make a grand theory of everything. The core of the interpretations of quantum mechanics is the measurement problem. 

When we make a measurement on a quantum object it’s wavefunction suddenly changes when we  detect the particle. And the laws of quantum mechanics don’t contain any explanation of what  is actually happening to the wavefunction at the instant of measurement. We also don’t know  if the wavefunction is actually real or not.

And these conceptual problems in quantum  mechanics are what the interpretations of quantum mechanics attempt to explain. For many years the default approach was the Copenhagen interpretation, but other  popular interpretations include pilot wave theory, the many worlds interpretation and quantum  bayesianism and many others. It is too much to get into all of them, but I’ve made  another video which covers this ground.

They are called interpretations because  we don’t yet have any experiments to tell which ones are real and which are not, so  really they are a collection of interesting ideas rather than proper physical theories. Quantum field theory is the most comprehensive description of reality we have, combining  quantum mechanics with special relativity. But we know it is not a complete description as it  doesn’t include general relativity and gravity.

There are many attempts to merge quantum  mechanics and general relativity into a grand unified theory everything and the two  main candidates are string theory and loop quantum gravity. String theory is also known  as M-theory which is a theory that unites all different consistent versions of string theory. It is very difficult to test the theories of quantum gravity because you need to go  to such high energies, you would need to build a particle accelerator like the large  hadron collider, but the diameter of the solar system with detectors the size of jupiter.

So currently, the best hope we have of signatures of quantum gravity are from observing high energy  processes in the universe: signatures from the big bang or black holes might give us some clues  and this is an active area of research. So that’s it, that’s all of quantum physics.  Congratulations you’ve got to the end.

Obviously this is a lot to take in so don’t worry  if you didn’t get it all at a first pass. But you can always watch it again or grab this  image for a reference in the future. This part of the video was sponsored by Brilliant,  and if this video has made you want to learn more about quantum physics or get better at maths  and science in general Brilliant is a fantastic resource.

It is a website with many courses  where you learn and solve problems at your own pace. They have a whole section dedicated to  quantum physics and actively learning by solving problems means that you learn the material a lot  more thoroughly than just watching videos because nothing challenges your understanding than  a good question. As I have found many times.

So this is a simple, fun way to keep learning  more. If that sounds interesting go to brilliant dot org slash dos or click on the link in the  description below which helps me out as they know you’ve come from here, and the first 200 people  to do so will get 20% off the annual subscription which unlocks all of their premium content. Also as I mentioned at the beginning of the video, I’m selling this map as a poster  which you can find on my DFTBA store and a big shoutout to everyone who gave  me feedback on twitter, and a special thanks to @physgal and @chriferrie for their input.

And if you’d like to support my work I have a patreon page as well. In any case I’ll be  here making more videos aiming to make science easier to understand. Sp thanks again  for watching and I’ll see you soon!