An illustration of the gravity waves — ripples in space-time — caused by the merger of black holes, such as the event detected by LIGO on 26 December 2015. Gravity waves are one of the most astounding predictions of Einstein’s theory of general relativity. Each spectacularly successful in its own domain, quantum physics and general relativity remain mutually incompatible, despite much effort to unify them into one theory of nature. [Image credit:Image: LIGO / T Pyle]
In the words of Carl Sagan:
The cosmos is full beyond measure of elegant truths; of exquisite interrelationships; of the awesome machinery of nature.
As I’ve tried to illustrate over the last few posts, this awesome machinery of nature operates according to the rules of the quantum world, rules that challenge our intuition about how things work and our notions of reality itself.The quantum revolution that got underway around 100 years ago has been the means by which we have unlocked many of the secrets of the universe and revealed many exquisite and unexpected interrelationships.
Since quantum mechanics has been our most successful theory of nature that we have ever come up with, you might wonder: is that it? Has quantum physics done its job? Is the quantum revolution coming to an end?Have we found what we were looking for?
The answer I am convinced is no.Here’s three reasons why
First. Quantum physics, and Einstein’s theory of general relativity are the two pillars of modern physics.Between them we can describe nature to unprecedented precision at the very large and the very small scales.Yet these theories are built mutually incompatible frameworks, despite much effort to unify them into one theory of nature.And many of the unanswered questions in cosmology and fundamental physics point to the regimes where we need both of these to work in tandem.
Starting with Einstein, efforts along this direction have been underway for 90 years.String theory is regarded by many to be a promising contender for a unified theory, but it brings it own headaches for theorists and remains tantalisingly out of reach of experimental testing.I’ll let the music explain….
The Machinery of Nature
The second reason. The equations in which the quantum rules are written reveal enormous complexity.For a long time, this astounding complexity has been an intractable problem.But now we are learning how to harness this complexity to our own advantage, for the purposes of ultra-precise measurement, of secure communication, of massively efficient computation.
It maybe that the second quantum revolution is about to begin, a revolution which will see the machines we encounter in everyday life operating on the same quantum rules as the fundamental machinery of nature.
Still Looking
Experimental results from the Large Hadron Collider (LHC). Smashing together two protons – the building blocks of the nucleus – unleashes a tangle of even smaller particles that momentarily pop into and out of existence. Such high-energy collisions are the tool we have used to force the universe to give up it secrets buried deep down at this miniscule scale. The ultimate theory of nature may still await us, but will we ever have the theoretical and experimental tools to grasp it? [Image credit: CERN]
Finally, quantum physics breaks our grip on reality, or at least our grasp of how we think things really are. It forces us to jettison some of our intuitive notions about things like objectivity, existence, connectivity and so forth.But it doesn’t really specify which notions have to go; it just says that the obvious pieces don’t seem to fit together into a coherent picture in the way we thought they should.
Quantum physics points out the problems, but does it offer a solution? Does it provide a satisfactory framework for rebuilding a coherent picture of reality? Certainly the emerging image is strange: fuzzy, intangible, strangely connected. Is this a reflection of how nature operates fundamentally, or is there a deeper theory behind it, waiting to be found?
We are still looking.Meanwhile there is lot of scope for vigorous debate on how to interpret the strange picture that quantum physics paints, and I invite you to join the conversation.
For the next three pieces we consider the cosmic connection.What insights do the heavens provide into the nature of quantum physics?And what does quantum physics tell us about the workings of the cosmos?
Inner Harmony of the Atom
Experimental determination of an electron wave function of Hydrogen. Unlike planets orbiting the sun, which could in principle orbit at any radius, electrons surrounding a nucleus are permitted in ‘orbitals’ of only certain energies. As the atom gains or loses energy, the electron must make quantum jumps between these orbitals. In Hydrogen, the simplest of all atoms, the characteristic radii of these orbitals follow a very simple pattern. [Image Credit: A. S. Stodolna, et al]
Human beings like to find order in the chaos. It was Johannes Kepler that first attempted to fit the observed orbits of the known planets into a simple geometrical pattern.In particular we wanted to find a simple mathematical ratio for the different distances from the sun to each planets: a proof of cosmic harmony. He found that the the data seemed to fit the distances you’d get by fitting various shapes – such as cube, sphere and triangular prisms – into one another.It seemed too beautiful and elegant not to be true.Unfortunately, more precise data dashed Kepler’s dream, and we now understand that the particular positions of the planets are to a certain extent an arbitrary accident of cosmic history.
However this vision of planetary harmony lives in on the atom.The solar system provided inspiration for early models of the atom, electrons orbiting the heavy nucleus.For sure, quantum physics tells us that electrons aren’t like planets, and that we need to envisage a fuzzy electron cloud rather than point particles on precisely defined orbits.But these fuzzy electron clouds do fit mathematically defined patterns, which arise from trying fit the probability waves in a closed path.Only particular shapes will match the conditions, and each shape, or orbital, corresponds to a precisely defined energy.It is characteristic of quantum mechanics that only certain energies are permitted.
The picture above shows an experimental determination of an electron wave function of Hydrogen, corresponding to one particular energy. As the atom gains or loses energy, the electron must make quantum jumps between these orbitals.In Hydrogen,the simplest of all atoms, the characteristic radii of these orbitals follow a very simple pattern. In this sense, the idea of cosmic harmony is restored in the microworld.
Quantum Secrets in Colour
The Gabriela Mistral nebula. The colours of a luminous gas provide a quantum fingerprint that uniquely identifies the kinds of atoms that make it up. From a quantum perspective, light must be thought of as particles – photons – which can only be emitted or absorbed if their energy matches exactly to that of an electron quantum jump inside an atom. The energy of a photon determines its frequency and hence colour. [Image Credit: Ben Marks.]
Go out of the city on a cloudless, moonless night and look up. An amazing vision greets your eyes: “The dome of heaven like a great hill and myriads with beating hearts of fire, heaven full of stars” (to quote the song we are about to hear).Look closely and you’ll see stars of different colours.Use a telescope, with some spectral filters, a digital camera and a bit of image processing, and an amazing world of colour greets your eyes: the colourful world of nebulae
The picture above shows an image of the Gabriela Mistral nebula. I’m sure you’ve seen similar spectacular images of nebulae: glowing clouds of gas in deep space. Although these colours are not what you’d see with the naked eye, they do provide a visual map of the actual frequencies of light being emitted.
Luminous gases only emit light of certain specific frequencies. What determines these frequencies, these colours? It turns out that colour is a little window into the quantum world of the atom.
From a quantum perspective, light must be thought of as particles – photons – whose frequency and hence colour is a measure of photon energy. Now a photon can only be emitted or absorbedby an atom if its energy matches exactly to that of an electron quantum jump inside an atom.So the colour of the photons tell us about the strange inner harmonies of the atom.And each atom has its own idiosyncratic set of harmonics.
Thus the colours of a nebula constitute a quantum fingerprint that uniquely identifies the kinds of atoms that make it up.
The world of quantum physics is a world full of colour.
Quantum on the Cosmic Stage
Before there were solar systems, stars, atoms, protons, or even quarks, there were the primordial quantum fields, whose fluctuations gave birth to the forms of matter we see today. [Image credit: CERN]
Twinkle, twinkle little star, how I wonder what you are.
Human beings wonder.We marvel.We are curious. We are inspired to investigate, to seek explanations and uncover patterns.These universal human urges are part of the story of science.
Our wonder of the stars has opened our eyes to an amazing universe; a universe that is amazingly big, and a universe that has a history, a history with many surprising turns.
One of those surprising turns is how quantum physics has played a role in this cosmic history.This is surprising, because quantum physics – normally dominant only on the smallest scale – has had a hand in shaping the large-scale structures of the universe.
To see this, have a look the diagram above: it shows the broad features of cosmic history as we understand it today in our expanding universe.The present time is on the right, and as you go left, you go back in time through successively earlier stages of cosmic evolution.Now there are certainly details to be worked out (things are particularly fuzzy right over of the left), but the overall shape is confirmed by multiple lines of evidence.
Here’s one way that quantum physics enters the story: it explains why we are lumpy.We are lumps of matter on a larger lump of matter (the earth) surrounded by mostly empty space.On a larger scale, galaxies are also lumps of matter surrounded by space that is even more empty.Given that the universe is mostly empty space, why is the little bit of matter in it clumped together in lumps rather than thinly spread out uniformly?You might answer: the reason is gravity.
Gravity – a universal attractive force – pulls matter together to form lumps: galaxies, stars planets and so forth.That’s true, but gravity had to have something to start from.If the universe were initially entirely uniform, the pull of gravity in one direction would be the same as another.For gravity to start forming lumps, it needed to be seeded with wrinkles in the overall distribution of matter.And this is where quantum physics comes in.
Before there were galaxies, solar systems, stars, atoms, protons, or even quarks, there were the primordial quantum fields.I’ve already talked about how quantum fields are never quiescent, they are constantly vibrating, seething foam of quantum fluctuations.These fluctuations mean the energy is distributed across them in a wrinkly way.Of course these wrinkles are tiny. But notice on the left of the picture – early on there was a period where the universe expanded more rapidly.Now this diagram is not to scale.We have several reasons to believe that there was a period of astonishingly rapid and enormous expansion in the very early stages: the inflationary epoch.One side effect of this rapid inflation was what it did to the quantum fluctuations. It froze them into place, and at the same time expanded them out to galactic size.
It was from these massively expanded quantum wrinkles that gravity could begin its work.In other words, quantum fluctuations provided the blue print for the structure of the universe.
Quantum fields are the true building blocks of nature, unifying the complementary pictures of wave and particle. Any particular electron you may encounter is merely an excitation of the electron field that pervades all of space. Even when there are no particles, the underlying fields are still present, forming a bubbling vacuum of quantum fluctuations. [Image credit: Stanford Online.]
If you think the idea of wave-particle duality is rather vague idea, or that having to simultaneously juggle incompatible models is rather unsatisfactory, you are in good company.This dissatisfaction led physicists to search for and articulate a deeper description of reality.Underlying these surface-level descriptions of wave and particle is the concept of quantum fields.
Fields originally arose as a way to describe how one object can affect another.For example, a charged particle creates an electromagnetic field, which mediates the electric and magnetic forces it applies on other charged particles. These fields can be made to vibrate – that’s the wave aspect – and when we apply the rules of quantum physics to fields, we find a certain lumpiness in these vibrations – that’s the particle aspect (photons).
Far more radically still, quantum physics tells us fields don’t just mediate interactions between matter, but that matter itself consists of fields.Particles of matter are themselves just the localised excitations of underlying quantum fields.Quantum fields therefore are the true building blocks of nature.
For example, any particular electron you may encounter is merely an excitation of the one electron field that pervades all of space.You and I and the rocks of the earth are just a bunch of quantized vibrations of the universal quantum fields that pervade all of space.
Now you can think of quantum fields as fields that obey Heisenberg’s uncertainty principle.Remember that, for particles, the uncertainty principle says that the more you know where the particle is, the less certain you can be about how fast it is going.For fields it is similar: the more precisely you pinpoint the value of the field at one particular point and time, the less you can be certain about how fast it is changing, and thus the less certain you can be about the value at a later time. The more you know now, the more quickly that knowledge becomes irrelevant! Trying to pinpoint a quantum field is like trying to grasp a hand full of foaming bubbles: the tighter your grip, the faster they slip away.
One implication of this is that even when there are no particles, the underlying fields are still present and active – they can never be set to zero –forming a bubbling vacuum of quantum fluctuations.
Quantum History
In the ‘path-integral’ formulation of quantum physics, we calculate the probability of a particle moving from one space-time coordinate to another by adding together the effects of all possible paths between the two. In a certain sense, all possible histories contribute to the present moment. [Image credit: Markus Pössel.]
What is time?We experience time as a kind of movement or transition from the past to the future.What distinguishes past and future?For one thing, the future is unknown to us, whereas the past is what has already been revealed.Even if our memory of the past is patchy, we feel that, in principle, we could sift through the evidence and work out the path that history took to bring us to the present moment.
But in the quantum world this is impossible.The past remains uncertain even when the present is known.This uncertainty is not just ignorance: quantum superposition tells us that many alternate histories in a sense coexist and intermingle to produce the configurations we see in the present.
The idea of many histories is made explicit in what we call the ‘path-integral’ formulation of quantum physics.To calculate the probability of a particle moving from one space-time coordinate to another, we add together the effects of all possible paths between the two.
When they think no-one is watching, human beings can be a bit devious and perhaps try to get away with things they shouldn’t. In the quantum world, it’s not just the case that you could get away with anything, but rather you do get away with everything.In the quantum world, if no one is watching, anything can and does happen.All unobserved paths contribute to the present moment.
What are some of the strange features from the quantum rule book?I’ll try to explain three: wave-particle duality, Heisenberg’s uncertainty principle, and quantum entanglement.
Wave-Particle Duality
A beam of light when split and then recombined can form an interference pattern, a classic manifestation of wave physics. But in quantum physics, a stream of particles can also form interference patterns, requiring each particle to be effectively in two places at once. Here a stream of complex dye molecules forms an interference pattern. [Image Credit: Quantum Nanophysics Group, Universität Wien]
First: ‘wave-particle duality’.Particles I have already spoken about, and as a classical model they are characterised by having well-defined locations and trajectories.
Waves, in contrast do not have well-defined locations or trajectories.A wave is a disturbance in some medium, like air, water or the electromagnetic field;a disturbance that moves through space, carrying energy and information.Waves at any point in time cover a certain region of space, and tend to spread out even more as they propagate.
So: waves and particles seem like very different models that have contrasting, even contradictory features.But in the quantum world all particles have wave characteristics and all waves have particle characteristics.
For example, we know for sure that light is electromagnetic radiation, i.e.,a disturbance in the electromagnetic field.Yet quantum physics says the energy that this wave carries comes in indivisible packets, called photons.
Even more strangely, quantum physics says that any chunk of matter – whether it be an electron, an atom, a molecule or a cricket ball –that we would normally think of as particles, can be made to do things that only waves can do.Associated with every particle is a probability wave, called a wave function, that tells us the likelihood of finding that particle at any particular place.
But this is really evidence of another wave characteristic, called interference. At some points, the peak of one wave overlaps with the peak of the other, forming a double-sized peak.At other points, a peak from one falls on a trough from the other, and they cancel each other out.The resultant pattern we call an interference pattern.
A beam of light, when split and then recombined, can form an interference pattern, which is very simple to understand in terms of waves. But in quantum physics,a stream of particles can also form an interference pattern.Now you might be tempted to think that half the particles go on one path and the other choose the other path, and that when the beam recombines, the two sets of particles interact with each other to form the pattern.However, we can turn the intensity down so that the photons go through one at a time (a photographic plate, for example, could be used, to record the arrive positions). We find that, over time, an interference pattern forms.We can do the same with electrons and even larger particles like molecules (as in the picture above).
Each particle can only have gone along one path, but the fact that there are two potential paths to take changes the outcome: If we block off one of the paths, the interference pattern disappears. It is as if two mutually exclusive realities – particle going left and particle going right – simultaneously exist, and that they somehow interact or interfere to determine the final outcome.
Uncertainty
In quantum physics, particle properties are governed by waves of probability, which makes them intrinsically uncertain. This imprecision is precisely stated in Heisenberg’s uncertainty principle: the more precisely we can predict the value of one variable – such as position – the less certain we can be about the complementary property (momentum in this case). [Image Credit: OpenStax]
We’ve seen how, in quantum physics, particle properties are governed by waves of probability.This makes the properties intrinsically uncertain.This imprecision is precisely stated in Heisenberg’s uncertainty principle: the more precisely we can predict the value of one variable – such as position – the less certain we can be about the complementary property (momentum in this case).
(It’s somewhat fitting perhaps that Heisenberg was uncertain what to call this strange new principle he had uncovered: he tried “ungenauigkeit” – inexactness, “unbestimmtheit” – indeterminacy, before finally settling on “unsicherheit”– uncertainty.)
Now I said before that the wavefunction of a particle tells us the probability of finding it any point in space.Therefore if the wave function of a particle is spread out over a large area, the uncertainty in the position of the particle is large.If the wave function is concentrated into a small area, the uncertainty in particle position is correspondingly small.
But position is only one property.To fully specify the state of a simple particle we need to know how fast it is going, essentially its momentum.It turns out that the momentum of a particle is determined from the wavelength or frequency of its wave function.The frequency of a wave is how quickly it oscillates up and down.A wave with an exactly known frequency is one that replicates itself over and over for ever, extending through all of space.For quantum particles this means that if the momentum is exactly known, the position is completely unknown: it could be anywhere in space.
How do we construct waves that are more localised? We’ve got to take waves with a range of different frequencies and add them together (see picture above).Imagine taking all of these waves and lining them up so that at one point in space they each have a peak: at this point they will all add together to produce a large-amplitude wave.As you move away from this point, they will get out of phase (because of the different frequencies) and will tend to cancel each other out.The result is a wave packet that corresponds to a more well-defined position, but only at the expense of having a range of frequencies.For a quantum particle this means position can be more certain, but only at the expense of increasing the uncertainty in momentum, and vice versa.
I’ve just spoken about position vs momentum.But the uncertainty principle is more general than this: it applies to all pairs of complementary properties, properties which, in a classical picture, you would need to specify to fully describe a system.
Now quantum physics is the most spectacularly precise and well-confirmed theory about nature that we have ever come up with.It might seem ironic that this most precise of all theories has imprecision and uncertainty built into it. But perhaps not.Perhaps it’s not so surprising that when we want to probe nature to such a level of detail, nature pushes back a little and is reluctant to give up all its secrets – at least not simultaneously.
Existence (or, Entanglement)
In Schrödinger’s famous thought experiment, the fate of a cat (a representative macroscopic object) is inextricably linked (“entangled”) with the quantum state of an atom and therefore in a superposition of mutually exclusive realities. Schrödinger’s aim was to point out the conceptual issues raised by quantum mechanics. Is the cat really in an indefinite state? Does the act of observation collapse the superposition onto one definite reality? Or does opening the box entangle the rest of the universe with the cat in its indefinite state? [Image credit: OpenStax]
So far we have seen how the ‘probability wave’ or ‘wave function’ that quantum physics associates with every particle leads to uncertainty, and we’ve seen how different parts of the probability wave that correspond to different possibilities can interfere with each other.Until you actually observe the location of a particle, not only is its position uncertain, but it is in a sense in more than one place at once. We call this feature – being in more than one state at once –‘superposition’ and it is an intrinsic feature of quantum physics.
Now not everyone involved in the early years of the quantum revolution liked how the emerging theory was shaping up.Einstein was one, Schrödinger another.They didn’t like that it was intrinsically probabilistic, or that it seemed to deny definite, objective reality to microscopic properties.Schrödinger in particular thought that it was ridiculous that physicists took the idea of superposition as a literal description of reality – that somehow before you observed the particle it really was objectively in more than one place at once. To illustrate his point, he came up with his famous cat in the box thought experiment(see picture above).
The idea is that you take something like a lump of radioactive stuff and put it in the box, along with a humane cat-killing device that is triggered by radiative decay (e.g., a Geiger counter, a hammer and a vial of poison).Finally you put in the cat and close the box.
Closing the box is important, because everyone agreed that the quantum rules only seemed to apply to microscopic system in isolation. As soon as you observe the system, you collapse the wavefunction, forcing it to take a definite measurement outcome.So if the box is closed, everything in it should evolve according to the quantum rules of probability waves, without interruption from the classical world.
Now radioactive decay is a quantum process, and a radioactive atom in isolation exists in a superposition of decayed and not decayed.But the ingenious cat-killing device links the fate of the cat with that of the radioactive atom.The quantum state of the cat is thereby ‘entangled’ with that of the atom, and should exist in a superposition of two different outcomes.But, surely, said Schrödinger, you don’t literally believe that, before you open the box and have a look, the cat is simultaneously both alive and dead.
Despite Schrödinger’s misgivings, the idea of superposition has endured.And, somewhat ironically, the concept of entanglement (“Verschränkung” – Schrödinger’s term) is now regarded as key distinguishing feature – perhapsthe most radical thing – about quantum physics.
I think most physicists accept the idea of the cat being in an indefinite state before the box is opened.Experimental progress has moved towards creating superpositions involving larger and larger objects . The record I think is a tiny tuning fork (10 trillion atoms) in a superposition of vibrating and not vibrating.
Nevertheless Schrödinger’s example highlights conceptual issues that are still debated today.
Just what happens when the box is opened? Does the act of observation “collapse” the superposition onto one definite reality?It’s been a popular idea, though not amongst physicists perhaps, that the crucial element is observation by a conscious observer – that somehow is the mind that shapes the reality that emerges from quantum physics. Personally I don’t think, in the grand scheme of things, that human consciousness is so fundamentally different from cat consciousness.Most physicists would I think accept that it is what we call decoherence that collapses the wave function: the quantum state being scrambled amongst all the degrees of freedom in the surrounding world.
Still, some fundamental issues of interpretation remain.If you believe that quantum physics applies to everything, you could take a step back and speculate about happens to the quantum state of the entire universe when the box is opened.Does universe evolve into a superposition of two realities: one in which the cat is seen to be alive and another in which the cat is seen to be dead?Does every microscopic quantum interaction cause the universe to split into multiple copies, each subtly different from the other?If this idea appeals to you, you fall into the many worlds camp in the interpretation of quantum mechanics.
An alternative class of interpretations which have been nicknamed zero worlds is just as radical.These interpretations deny that we can describe ‘objective reality’ with our physics theories: the quantum state is rather just a state of knowledge, and that ultimately it is information that constitutes the fabric of the cosmos.
In October 2019, I collaborated with Fusion Vocal Ensemble, directed by Dr Debra Shearer-Dirié, to present “Quantum: a choral exploration of the universe”. The singers of Fusion had the difficult job of presenting some challenging and diverse repertoire; I just had to explain how it all connected with quantum physics!
Below and in the next few blog posts, I’ll upload my script with the accompanying images and (where available) youtube clips of the music.
The links between the music and physics range from the literal to the somewhat metaphorical and tangential – I’ll leave it as a challenge to readers to work out the connections. If you think you’ve worked it out, please leave a comment!
A Quantum World
We live in a quantum world.The certainty, tangibility, and objectively reality of the everyday world we perceive around us is an illusion.The detailed machinery of the universe operates according to a quantum rule book, whose pages reveal the themes of uncertainty, duality, superposition and entanglement.
The strange world encoded in the quantum rule book is not apparent to our senses, and therefore does not inform our intuition.To grasp the quantum we have to set aside our intuition — or, rather, to be willing to reform our intuition — and to follow where the data and the mathematics lead us.
In this concert we will explore some of these themes in a duality of words and sound, a superposition of explanation and song, an entanglement of science and music.
A Dance of Particles
The proton — building block of the nucleus, the core of the atom — is a perpetual dance of three quarks, interacting via a swarm of massless gluons [Image Credit: D Dominguez/CERN]
The solidity and continuity of matter is an illusion.If you dig down deep enough you will find that what seems solid and continuous is actually a teaming swarm of bustling, interacting particles.
Richard Feynman once asked the question “If, in some cataclysm, all of scientific knowledge were to be destroyed, and only one sentence passed on to the next generation of creatures, what statement would contain the most information in the fewest words?”His answer: “all things are made of atoms — little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another. In that one sentence, you will see, there is an enormous amount of information about the world, if just a little imagination and thinking are applied.”
By the end of the 19th century, the existence of atoms was a sure bet: using atoms you could explain so much of the physical and chemical properties of matter.Taking these together with the laws of motion, of energy, and electromagnetism developed over the previous few centuries — what we call classical physics — physicists seemed to have a comprehensive grasp of how nature worked.
However, in the early years of the 20th century various experiments demonstrated that atoms had an internal structure, and in trying to explain this structure, classical physics became unstuck in spectacular ways.For example, it became clear that an atom was mostly empty space, with most of the mass concentrated in a positively charged core — the nucleus — surrounded by a scattering of ephemeral electrons.Knowing that like charges repel and opposite charges attract, classical physics could not explain why the nucleus did not blow itself apart through electrostatic repulsion, nor how an electron could exist in an orbit without spiralling in and crashing into the nucleus.Atoms seemed fundamentally unstable. Other mysteries and catastrophic failures emerged when trying to explain how atoms interacted with light.
If the atom was the means of fracturing classical physics, it was also the anvil on which quantum physics was forged. The only way to make sense of the atom was to accept the bizarre rules of the quantum world.
But the rules of the quantum world do not stop with the atom.As you dig deeper and deeper, you find particles within particles.What seems to be point particle at one scale, turns out to be a configuration of more fundamental particles, whose interactions and movements are governed by the quantum rule book.
So:Matter is an astonishing interplay of jiggling atoms.Each atom is an elegant, but rather fuzzy, procession of electrons around a nucleus.Inside a nucleus, a tight configuration of protons and neutrons, and each proton or neutron a perpetual dance of 3 quarks attended by a host of gluons, photons and other bosons.
In a couple of weeks, I will take over the teaching of a course on “Thermodynamics and Condensed Matter Physics”. The approach we adopt is one of strictly classical thermodynamics (i.e. no atoms please). For one thing, this counterbalances the reductionist tendencies implicit in just about all other physics courses that students take. In this regard, teaching it has also been good for me, since most of my research is focused on simulations done ‘at the quantum level’ (and I don’t think I really appreciated thermodynamics myself as an undergraduate).
Another excellent thing about classical thermodynamics is that it encourages healthy reasoning and problem-solving practices. The crutch of merely plugging numbers into equations to come up with an answer is of little use. (There are any number of formulas that relate P, V and T – to know what to use in a particular situation, it is crucial to be able to identify the appropriate approximations and relevant constraints.) Furthermore , if followed through consistently, thermodynamic reasoning leads to robust conclusions that are independent of the details of microscopic models. It is for these kinds of reasons that thermodynamics gets a strong recommendation from Einstein:
A theory is the more impressive the greater the simplicity of its premises, the more different kinds of things it relates, and the more extended its area of applicability. Therefore the deep impression that classical thermodynamics made upon me. It is the only physical theory of universal content which I am convinced will never be overthrown, within the framework of applicability of its basic concepts.
Usually I teach the first half of the course that covers the fundamentals – energy, temperature, entropy and the three (or is it four?) laws of thermodynamics. This year, however, I’ll be doing the condensed matter part of the course. Here is what I would like to cover, in just 12 lectures:
Gibbs free energy
First-order phase transitions
Thermodynamics of mixing
Chemical equilibrium
Continuous phase transitions and critical phenomena
That list covers a whole host of phenomena – from superconductors to why they put salt on icy roads. But hopefully the common threads will be clear to students. In fact it can probably be boiled down to two recurring ideas:
free energy (that it should be minimised)
entropy of mixing (that it reduces the free energy)
and even then the second is just an application of the first.
I like to get students to read ahead of the lectures (in fact I quiz them to make sure they do so!). For most of these topics I’ll use Schroeder’s excellent book – for its clear and engaging style, focus on the essentials, and well-designed physics problems, even if it mixes in some statistical mechanics and is now over 10 years old. For continuous phase transitions, it was a little harder to find a suitable book (for second year students), but I think I’ve settled on the opening chapter of an advanced text by Binney et al, “Theory of Critical Phenomena”, mainly because of its excellent motivation; it would be perfect if only its diagrams were a little clearer.
Any good suggestions on what topics to cover and which text to use will most gratefully be considered!
You may be wondering what the title means. I offer you the following explanations:
Quantata is a reference to physics as the quantitative science par excellence. As good Popperians, we all know that good science is about prediction in addition to mere explanation. Hence common pastimes for physicists include predicting the umpteenth digit in the fine structure constant, or searching for minute inaccuracies in Newton’s theory of gravity. Sometimes this passion for precision even has practical use.
A quantata is a musical celebration of all things quantum. Bach’s well-known “Coffee Cantata” BWV211 is a somewhat tongue-in-cheek celebration of that divine drink. Just as a quantum bit has become known as a qubit, a quantum cantata, should someone write one, would no doubt become known as a quantata (because qucantata is just too silly).
Quantata is the plural form of quantum field, as in “Quantum control, quantum computing, and various other quantata promise to usher in a new revolution in technology.”
Quantata is what I made up somewhat in desperation since all the other obvious blog names seemed to have already been taken. (I have since discovered that I wasn’t the first to make up that word.)
A quantata is a (partially) coherent superposition of all of the above.
All things are made of atoms. That is the key hypothesis
It was Richard Feynman who contended that the most valuable scientific idea was that everything was made of atoms [1]. Knowing that there are different kinds of atoms that can be put together in different ways forms the basis of chemistry, materials science and our understanding of the processes of life itself. In the other direction, probing the internal structure of atoms has revolutionised our view of the physical world (through the discovery of quantum mechanics) and has enabled the technology that underpins our civilization – from lasers and electronics to atomic clocks and nuclear energy [2].
But for all the different kinds of atoms that populate the period table, when it comes to the ultracold world [3], there are only two types of atom that matter: bosons and fermions. You won’t find these listed on the periodic table; but they form the fundamental dichotomy into which all particles can be classified.
(The dichotomy has to do with what happens to the many-body wavefunction when you swap two particles. If nothings changes, you have bosons. If the wavefunction changes sign, you have fermions.)
Normal chemistry (at room temperature and one atmosphere of pressure) doesn’t really care whether its particles are fermions or bosons. But at absolute zero, this is the key distinction that sets the rules of the game, and the periodic table becomes largely irrelevant [4]. Bosons, for example, are gregarious by nature and tend to collect in the same state, forming the matter equivalent of coherent laser light. Fermions, on the other hand, are rather protective of their personal space, with no two occupying the same state. What fermions lack in easy-going coherence, they make up for in the propensity to form stable, highly correlated configurations [5].
What determines whether an atom is a boson vs fermion? It comes down to a simple counting game. If the number of protons + electrons + neutrons that make up the atom is even, you have a boson, if it is odd, you have a fermion. Since, for neutral atoms, the number of electrons equals the number of protons, the determining factor is the number of neutrons.
Now here is a thing that I find very strange. Despite the fact that one extra neutron will radically alter the personality of the atom, the neutrons themselves are locked away within the nucleus, quite inaccessible at ultracold energy scales. Thus a collection of Lithium-6 atoms behaves entirely differently at ultracold temperatures to a collection of Lithium-7 atoms, despite the two isotopes having almost identical physical and chemical properties [6]. It underlines the point, I suppose, that the ultracold dichotomy of bosons-fermions, and the “chemistry” that derives from it, has nothing to do with interactions between atoms, as in the case of ordinary chemistry, but is a purely quantum statistical effect.
Now on this blog I will try to avoid gratuitously provoking my colleagues by making overreaching claims for the field of ultracold atoms. But I will say this: The field of optics (or at least the quantum version of it) is preoccupied with photons, which are bosons; the vast field of condensed matter physics arises primarily from the rich physics of electrons, which are fermions. With ultracold atoms, you can choose which personality you want to deal with, which makes for an interesting playground.
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[1] R. P. Feynman, “Six easy pieces”
[2] Less controversial forms of power generation – eg solar – also depend on knowledge of the internal structure of an atom
[3] where the temperature is measured in nanokelvin, i.e. in thousandths of a degree above absolute zero.
[4] OK, there are some technical reasons to do with cooling and trapping that mean only some candidates from the periodic table are feasible for getting to nanoKelvin temperatures. Furthermore, the choice of atomic species has consequences for the strength and nature of the interatomic interaction, but these are things that can be controlled by other means (eg external magnetic or electric fields) and are thus not intrinsic to particular kinds of atom.
[5] I hope you’ll forgive the silly anthropomorphism.
[6] Their mass will be slightly different, naturally, but this is just another incidental property.
I recently was asked to speak to a group of potential PhD students about why they would want to do a PhD in physics. Here are the reasons I came up with:
Curiosity. You’ve just spent the last 4+ years learning about how the universe works based on what others have discovered. Now it’s your turn to discover something new. If you’re not fundamentally driven by curiosity about the subject matter, a PhD is going to be a long and difficult road!
Contribution. You can enjoy that warm fuzzy feeling, knowing that you’re contributing to the sum of human knowledge. The technologies of the future are based on the discoveries of today, including, perhaps, your own.
Skills. Problem solving, critical thinking, independent investigation, writing: there’s a lot more to a physics PhD than just the maths and the physics.
A job. A PhD is the minimum requirement for a research or academic career. You won’t ever find someone who tells you that such a career is easy, but plenty will tell you how rewarding it is. But you don’t have to stick to physics research: there are plenty of other options that would make use of the high level skills you will hone and develop. Make money working for a bank, or perhaps become prime minister. (The world’s most powerful women has a PhD in physics!)
Travel and meet interesting people. Somehow physicists arrange to have many of their conferences in very nice locations. And physicists are interesting, aren’t they?
The title. If this is one of your main reason for wanting to do a PhD, you should think again! I admit, however, that it is nice to get the recognition for the hard work, and you might need every scrap of motivation to pull you through those final months of intense thesis-writing.
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