Condensed matter physics is about how order emerges from disorder

 The order of things

Life and the world around us sometimes appears chaotic and random. We may feel this way about traffic, weather, economics, social change, politics, or our personal relationships. Perhaps that is why many yearn for regularity, predictability, order, and stability. Science is a search for patterns and order in the natural world. Condensed matter physics is about how order emerges from disorder.

This chapter explores how different states of matter are associated with different types of ordering of the atoms in the material. The symmetry of the state reflects the type of ordering, i.e., the patterns associated with the state. There is also a rigidity associated with the ordering and the rigidity determines the nature of the deviations from perfect ordering and results in entities such as vortices that are central to the physical properties of the state of matter.

The association of a state of matter with a specific type of ordering is illustrated in Figure 15 by an analogue with the dodgem bumper cars at an amusement park. A quiet day at the park is not much fun as collisions between cars are rare. In other words, there is little correlation between the relative locations and speeds of the cars. In comparison, on a busy day at the park the spatial separation of the cars is small, and their positions and speeds are more correlated with one another than on a quiet day. But, in both cases, there is no ordered arrangement of the cars. In contrast, after the park closes the cars are parked and arranged in an orderly manner. There is a rigidity associated with their spatial arrangement. One car cannot be moved without moving others. These three states of the dodgem cars are an analogue of three states of matter: gas, liquid, and crystal. 

Figure 15. A dodgem car analogue for the three states of matter: crystal, liquid, and gas. The only ordered arrangement is for the crystal (car park after hours) and this is associated with a specific symmetry and rigidity. The liquid and gas (busy and quiet day) only differ in density and the amount of correlation between the positions of the different atoms (dodgem cars).

In the dodgem car analogue, there are other possible types of ordering. In some amusement parks there is a track, and the cars are meant to all go in the same direction. The symmetry between clockwise and anti-clockwise of the track is then broken.  In the car park, Figure 15 shows cars that are symmetrical with respect to front and back. However, real cars have a front and back, and so can be parked either front first or back first. Hence, several types of ordering are possible: all cars park back first, all cars park front first, cars are front first or back first at random, alternating patterns of front first and back first as one goes along a row, alternating rows of front first and back first, and so on. These different types of ordering in the car park all have analogues in different solid states of matter.

Liquid crystals involve unique types of ordering. These materials are composed of elongated organic molecules, such as those shown in Figure 16. At high temperatures the material is in a liquid state and the orientations and positions of the molecules are random. The liquid has both continuous translational and rotational symmetry. At low temperatures the molecules form a solid crystal without the continuous translational and rotational symmetry of the liquid state. As the crystal is heated the temperature increases and there is a phase transition to the liquid crystal state, in which all the molecules point in the same direction, but their positions are random. Hence, the liquid crystal state has the continuous translational symmetry of the liquid, but not its continuous rotational symmetry, like the crystal. As the temperature increases further there is a transition to the liquid state (Figure 16). In terms of the dodgem car analogue the liquid crystal state is similar to when cars park in a field all pointing in the same direction but there are no grid lines, and their positions are then random.

The existence of a state in between a liquid and crystal was first proposed in 1888 by botanist and chemist Friedrich Reinitzer who was doing research on cholesterol at the Institute for Plant Physiology in Prague. He performed a heating experiment similar to that described in Figure 4. Instead of one melting transition he observed transitions at two distinct temperatures. 

Figure 16. Liquid crystals. (a) An example of the type of elongate organic molecule found in these materials. Each molecule can be represented by an oval shape. (b) In the nematic liquid crystal state, the molecules tend to point in the same direction, but their positions are random. 

There are multiple alternative orderings for liquid crystals with names such as nematic, smectic, chiral nematic, discotic, and chlorestic. In the smectic phase molecules form layers of oriented molecules. The character of the liquid crystal state can be detected by shining polarised light on the material. Liquid crystal displays (LCDs) in electronic devices use the property that an electric field can orient the molecules, and this changes the interaction of the material with polarised light.

For solid crystals the nature of the ordering and the symmetry associated with a specific crystal structure is clear once the spatial arrangements of the atoms in the crystal are determined, such as by X-ray diffraction. For other states of matter, such as superconductors, superfluids, and antiferromagnets, the nature of the ordering and the symmetry is often not apparent and has only been determined with significant scientific insight. 

An extract from "The order of things," chapter 4 in Condensed Matter Physics: A Very Short Introduction.

Symmetry matters in condensed matter physics

 Snowflakes form incredibly diverse structures, seen when they condense onto a plate of glass. Every snowflake is different. On the other hand, every snowflake is the same. They are all composed of ice, a solid state of water. Every snowflake is composed of units that have a six-fold symmetry (Figure 8). Every snowflake is composed solely of water molecules. This paradox of the particular and the universal is at the heart of condensed matter physics. Although diversity prevails anything is not possible. No snowflake has five-fold symmetry. Snowflakes have enchanted scientists for a long time. The astronomer Johannes Kepler studied them and in 1611 wrote a small book about them as a gift for his patron. Kepler suggested snowflakes provided clues to deeper questions about the composition of matter. Today, Kenneth Libbrecht, a physicist at Caltech, has spent most of his career studying snowflakes and has produced beautiful volumes of photographs of them.

Figure 8. A snowflake shows a six-fold symmetry, just like a hexagon. The snowflake appears identical when it is rotated by an angle of sixty degrees about an axis passing through its centre and perpendicular to the page.

Condensed matter physicists ask several questions about snowflakes. What is the reason for the six-fold symmetry of the snowflake? What is the connection between the macroscopic properties of snowflakes and the properties of the underlying microscopic constituents, molecules of H2O? How is the diversity of snowflake shapes possible? Is there a phase diagram that defines the external conditions under which the different shapes form?

There is a long history in art, architecture, philosophy, and science, of associating symmetry with beauty and perfection. The ancient Greek philosopher Plato was a proponent of this view. He studied a particular class of solid shapes: cube, tetrahedron, octahedron, icosahedron, and dodecahedron. Plato identified the first four shapes with the four “elements”: earth, wind, fire, and water, respectively, and the fifth with the heavens. Each of these solid shapes is highly symmetric. Every face of a Platonic solid is the same shape (square, triangle, pentagon,...) and each of those shapes has edges of equal length. 

Like Plato, Kepler believed that “God is a geometer” and that God’s creation should reflect the perfection of God. These convictions led Kepler to propose in 1597 that the orbits of the planets around the Sun were circular and that the Platonic solids determined the relative size of the orbits. Later this model for the solar system was shown not to be true. In fact, Kepler himself became famous because he showed that the planets moved in elliptical, not circular orbits. Nevertheless, Kepler’s model was the beginning of a long history of successfully relating physical laws to symmetry and geometry.

A key discovery in physics from the past century is that symmetry is central to understanding a wide range of physical phenomena, whether colliding billiard balls, the allowed energies of an atom, the fundamental forces of nature, or different states of matter. Symmetries determine what is physically possible. For example, that energy cannot be created or destroyed is a consequence of the fact that physical laws do not change with time.

In this Chapter I explore three key ideas. First, transitions between different states of matter are associated with changes in symmetry. Thus, symmetry provides a criterion for specifying the qualitative difference between distinct states of matter. Second, for a specific state of matter the relevant symmetry constrains what is physically possible. Third, symmetry is central to making connections between the macroscopic and microscopic properties of a state of matter. The next chapter will explore how symmetry is associated with the type of ordering that occurs in a state of matter.

An extract from Chapter 3, Condensed Matter Physics: A Very Short Introduction

A mystery about science is that humans can do it

We are surrounded by scientific knowledge and have become so used to it that we often take science for granted. We may rarely reflect on the amazing revelations of science—and so miss the opportunity to recognize the awesome nature of the universe. Things that we know, learn, and do today in science would have been inconceivable decades, let alone centuries, ago. 

Einstein said, “The most incomprehensible thing about the universe is that it is comprehensible.”  For Einstein, the success of science was a wonderful mystery. As he wrote to his friend Maurice Solovine: 

. . . I consider the comprehensibility of the world (to the extent that we are authorized to speak of such a comprehensibility) as a miracle or as an eternal mystery. Well, a priori, one should expect a chaotic world, which cannot be grasped by the mind in any way . . . the kind of order created by Newton’s theory of gravitation, for example, is wholly different.  

There are several dimensions to the comprehensibility of the universe being mysterious. Einstein highlighted the first mystery, which is that there is order in the world, as reflected in scientific laws, such as Newton’s theory of gravity, and that this order can be succinctly stated in the language of mathematics. To the best of our knowledge, these laws hold for all time and everywhere in the universe. The existence of the orderly behaviour encoded in scientific laws is necessary for science to work, which leads to the second mystery. Why have we been able to discover these laws?

A second dimension that makes science possible is the intellectual abilities of humans. Humans not only have the rational ability to do science—to reason, to understand, to communicate—but also the ability to design instruments, such as telescopes and microscopes. There seems to be a connection between the rationality of the universe and human rationality. The idea that there may be harmony between the structures of the universe and those of the human mind has a long history.  In the Renaissance, it was encapsulated in the metaphor of the “music of the spheres”. In his book, Harmonies of the World (1619), Johannes Kepler connected music and his explanations of planetary orbits. Einstein said that “Mozart’s music is so pure and beautiful that I see it as a reflection of the inner beauty of the universe.” 

Humans might have been different. Suppose that the average human intelligence was lower than it is today, and the variation of human intelligence was smaller. Then, there might have been no Galileo, Isaac Newton, Robert Boyle, Charles Darwin, Albert Einstein, Richard Feynman, Phil Anderson, or Linus Pauling. Without these brilliant figures in scientific history, scientific progress would have been slow. 

The third dimension is that human language enables scientists to formulate, represent, and communicate ideas, theories, and the results of scientific experiments. This language sometimes involves mathematics, graphs, or tables of data. Scientists can understand one another. Even though there can be misunderstandings, these can be resolved. There is a scientific culture that transcends the diversity of cultures associated with different countries, linguistic groups, and ethnicities.

The fourth dimension is the physical dexterity of humans. I am a theoretical physicist not an experimental physicist. I am “all thumbs” and not particularly good in the lab. Consequently, I have done no laboratory work since I was a Ph.D. student. In contrast, some gifted scientists have an ability to do things in a laboratory that most people cannot. Their manual dexterity allows them to fabricate precision instruments, grow pure crystals, blow exquisite glassware, see faint images, and fine-tune electronic instruments in extraordinary ways. If some humans did not have such amazing abilities, scientific progress would have been much slower—or possibly non-existent.

A fifth dimension that makes science possible is the availability and processability of materials that have been central to scientific progress. Making instruments requires specific materials, such as metals, glass, rubber, insulators, plastics, and semiconductors. If we lived in a world where some of these materials were very rare or could not be processed to the purity or malleability required for scientific instruments, we would not have supercomputers, electron microscopes, or the James Webb Space Telescope today. We might be struggling to make even the simple telescopes used by Galileo.

These five dimensions are all required for humans to be able to do science. There are several additional mysteries of science.  These can be divided into two classes: what science can do and what we can learn about the universe from science. Science allows us to know certain things about reality (epistemology) and also to understand the nature of that reality (ontology). In other words, science helps us make maps of physical reality. The terrain represented by those maps is amazing. And the fact that we can make the maps is amazing.

A multi-disciplinary perspective on mental illness

How is mental illness defined? What causes mental illness? How can a person be healed? Answering these questions will be influenced by our answer to the question of what a person is. Returning to the stratification of reality resulting from emergence, we see that there are social, psychological, neurological, physiological, and genetic dimensions to a person. To illustrate the complexity, I now take a brief tour of different university departments to get their unique perspective on mental health. Each represents a different tradition.

Biomedicine

The biomedical model for mental illness is based on the idea that brains are machines involving physical and chemical processes. Mental illness occurs when these processes do not function normally. Over the past few decades, brain imaging techniques have shown differences between the brains of healthy patients and those with mental illnesses such as depression, schizophrenia, and bipolar disorder. The best course of treatment is deemed to be drugs that target the parts of the brain or processes that are dysfunctional. Sometimes, physical interventions such as electrical shock therapies or surgeries are advocated. This biomedical model was embraced and promoted by most psychiatrists until relatively recently.  

Antidepressant drugs have been widely prescribed, and now there are many studies examining their effectiveness, side effects, and biochemical mechanisms. I mention three scientific problems. First, there is a large placebo effect. This is found in studies where two groups of patients are told they are receiving an antidepressant drug. One group receive the actual drug, and the second group receives a placebo, a pill that, unknown to them, does not contain the drug. The proportion of patients reporting a significant improvement in mental health was about 25% for taking the actual drug compared to 10% for those taking the placebo. In other words, it seems that believing one will get better can lead to significant improvements in mental health. 

Second, there is a large variation between patients concerning how effective the drugs are. Patients’ perceptions of change in their mental health range from getting slight worse to no change to large improvements. Third, the biochemical mechanism of the drugs has become controversial. When the class of drugs known as Selective Serotonin Reuptake Inhibitors (SSRIs) were introduced, psychiatrists were confident that they knew how they work. Depressed patients lacked serotonin. SSRIs blocked the reuptake of serotonin into neurons, increasing the levels of this neurotransmitter in the synaptic cleft. However, a recent meta-analysis concluded as follows. 

“The main areas of serotonin research provide no consistent evidence of there being an association between serotonin and depression, and no support for the hypothesis that depression is caused by lowered serotonin activity or concentrations. Some evidence was consistent with the possibility that long-term antidepressant use reduces serotonin concentration.”

In her book, Mind Fixers: Psychiatry's Troubled Search for the Biology of Mental Illness, Anne Harrington, a historian of science at Harvard, commented.  

“Today one is hard-pressed to find anyone knowledgeable who believes that the so-called biological revolution of the 1980’s made good on most or even any of its therapeutic and scientific promises. It is now increasingly clear to the general public that it overreached, overpromised, overdiagnosed, overmedicated and compromised its principles.”

Psychiatry is a tradition, for better or worse. Its proponents persist in their faith that the biomedical model has the best answers to mental illness, even though the evidence for this belief is ambiguous. Science can involve faith. 

The stakes are high. If a patient takes medication, they may get better, worse, or experience no change. If they don’t take medication, they risk missing out on healing.

Psychology 

Psychologists present a multitude of theories of and treatment plans for mental illnesses. The focus is not on biology but on mental processes. Some focus on the subconscious and others on thoughts we are aware of and can articulate. Some focus on current life experience and thinking patterns, whilst others delve into the past, including unresolved childhood conflict or trauma. Sigmund Freud, the founder of psychoanalysis, claimed that depression was due to aggression toward the self.  A century later, there is no empirical evidence to support his claim. Other psychologists claim depression is predominantly a loss of hope. Opinion is divided about the best method of psychotherapy, where a patient has regular sessions with a trained professional to address unhelpful thoughts, emotions, and behaviours. Names for different methods include Cognitive Behavioural Therapy (CBT), Dialectical Behaviour Therapy (DBT), Psychodynamic Therapy, Humanistic Therapy, and Acceptance and Commitment Therapy (ACT).  Central to CBT is the claim that "Irrational thinking is at the root of much emotional distress that people experience."

This diversity of perspectives and treatments highlights the level of scientific uncertainty about both causes and treatment.

I now mention three developments that are receiving increasing attention in psychology research and have a transcendent dimension.

Mindfulness practices. These involve training patients to focus their “attention on the present moment—thoughts, feelings, sensations, and environment—with an attitude of openness, curiosity, and non-judgment. It involves observing experiences directly, rather than overthinking or reacting impulsively. Key elements include breathing techniques, meditation, and bringing awareness to daily activities.”  (Google AI overview).

Forgiveness. The American Psychological Association offers a continuing education article that cites studies showing that practising forgiveness can improve mental health.  

Awe and wonder. Dacher Keltner has made extensive studies of the experience of awe and recounted them in a popular book.  In a recent article with Maria Monroy, they:  “review recent advances in the scientific study of awe, an emotion often considered ineffable and beyond measurement. Awe engages five processes—shifts in neurophysiology, a diminished focus on the self, increased prosocial relationality, greater social integration, and a heightened sense of meaning—that benefit well-being. We then apply this model to illuminate how experiences of awe that arise in nature, spirituality, music, collective movement, and psychedelics strengthen the mind and body.”

Integrated medicine

The past few decades have seen the rise of integrated medicine, which promotes the view that many diseases, both physical and mental, are best treated by a holistic approach that combines treatments from different specialists. For mental health, it proposes that treatments might include not just drug and talking therapies but also address lifestyle issues. This means considering the role of sleep, exercise, diet, stress reduction, connection to nature, and screen time. With regard to diet, this builds on recent research showing deep connections between what goes on in the gut and the brain. Perhaps this is not surprising because our brains are not disembodied. They are part of our bodies and are connected to our whole nervous system.

Sociology 

Sociologists have investigated how mental illness can arise from social isolation. Emile Durkheim (1858-1917) was one of the founders of sociology. His book, Suicide: A Study in Sociology was published in 1897 and pioneered the scientific study of social phenomena. He proposed that suicide comes in four types, being distinguished by the level of imbalance of two social forces: social integration and moral regulation. Based on a detailed analysis of statistical data, Durkheim concluded that suicide was more likely in men than women, for single people than those who are married, for people without children than people with children, among Protestants than Catholics and Jews, among soldiers than civilians, and in times of peace than in times of war.

Since Durkheim, many more sociological studies suggest that social isolation and a lack of meaningful relationships can be a major contributing factor to depression. Some of this research has been reviewed in a popular book, Lost Connections: Uncovering the Real Causes of Depression and the Unexpected Solutions by Johann Hari.  He was motivated by his own experience of being prescribed and taking antidepressants for many years without consideration of how his social isolation might be a contributing factor.

This short survey of the perspective on mental illness from a range of scientific disciplines illustrates the complexity of the issue, the multifaceted nature of reality, and scientific uncertainty.

Naturally, this survey of different scientific perspectives raises questions about my own experience. Why did the antidepressant drugs seem to work sometimes and not others? Did I experience a placebo effect? Why was mindfulness helpful to me two decades ago but not more recently? What was the role of stress, childhood experiences, social isolation, personal pride, or introversion in creating my mental illness? I simply don’t know the answers to these questions and don’t think I ever will. What does matter is that, somehow at different times, I did experience degrees of healing that allowed me to function, albeit sometimes at diminished levels. Regardless of which traditions you choose to guide your journey and whatever choices you make, trust (faith) is involved.

A forgotten physicist: Amelia Frank (1906-1937)

In honour of International Women's Day, I bring to your attention a fascinating recent piece in The Conversation, Who was Amelia Frank? The life of a forgotten physicist, by Peter Jacobson and Beck Wise.

Amelia Frank was a PhD student of John Van Vleck. Her work was cited by him in his 1977 Nobel Lecture. In the early days of quantum theory, she explained deviations of the magnetic moments of the rare earth ions Sm3+ and Eu3+ from Hund's rule predictions. Tragically, she died from cancer when she was only 31.

The legacy of 40 years of cuprate superconductivity

In February 1986, Bednorz and Müller made a stunning discovery: superconductivity at a temperature of 35 K in a doped copper oxide (cuprate). Arguably, this discovery changed condensed matter physics. In April 1986, they submitted their results to Z. Phys. B. Only nineteen months later, they were awarded the Nobel Prize in Physics, the shortest time ever between a discovery and the award. A nice and short review of the history is here.

One measure of my estimate of the influence of this discovery is that it received about 5 pages of coverage in my Condensed Matter Physics: A Very Short Introduction. (See Chapter 5, Adventures in Flatland).

How things have developed over the past forty years, for better and worse, may be representative of how science advances: discovery by serendipity, hype about applications, unexpected secondary benefits, foundational questions, new concepts, unification, and incremental advances.

Hype about technological applications

On March 20, 1987, The New York Times had a front-page article, DISCOVERIES BRING A 'WOODSTOCK' FOR PHYSICS, by James Gleick. This followed the 1987 APS March meeting. It began 

"Physicists from three continents converged on the New York Hilton for a hastily scheduled special conference on a string of discoveries that seem certain to produce a rapid cascade of commercial applications in electricity, magnetism and electronics.There are many things we know and understand that we did not when they were first discovered."

This has largely been unfulfilled. There are a few niche applications, but cuprates are not used in electricity distribution or even in the superconducting magnets in hospital MRI machines, which are probably the main commercial application of superconductors. One of the significant obstacles is that it is hard to make wires from these materials, as they are ceramics. This is an example of the common gap between research laboratory science and commercially viable technology.

After 40 years, do we have a successful theory?

It depends on who you ask. But I would say there is a lot we do understand.

We have a phenomenological theory for all the macroscopic phenomena associated with the superconducting state: Ginzburg-Landau theory!

Properties of the superconducting state are well-described by a BCS wavefunction with a d-wave order parameter and the associated Bogoliubov quasiparticles. [This is somewhat puzzling, as in the metallic state quasi-particles are not well defined].

Although not everyone agrees, I think it is fair to say that the essential physics is in a one-band Hubbard model, and the key physics is:

strong electronic correlations,

a doped antiferromagnetic Mott insulator,

d-wave pairing that is "mediated"/caused from some mixture/variant of antiferromagnetic spin fluctuations or RVB spin singlets,.....

We certainly don't understand the cuprates at the same level as elemental superconductors. But we do understand the essential physics.

What is harder to describe and understand are the states adjacent to the superconducting state in the phase diagram: the pseudogap state and the strange metal.

Strongly correlated electron materials became a large, vibrant and unified field

Before 1986, there were small, disconnected communities intermittently interested in transition metal oxides, rare earths, Kondo impurities, Mott metal-insulator transitions, organic superconductors, heavy fermions, and quantum antiferromagnets.

The discovery of the cuprates brought together these communities as they found common interests, challenges, questions, concepts, and techniques.

The discovery of superconductivity in strontium ruthenate, alkali fullerides, iron pnictides and chalcogenides, twisted bilayer graphene and more cuprates, organic charge-transfer salts, and heavy fermions has shown how rich these systems are. The challenge is to understand the similarities and differences between these chemically and structurally diverse systems. In many of them, superconductivity is proximate to a Mott insulating state.

The unity and excitement were probably stimulated and enhanced by the activities and ideas of high-profile theorists such as Anderson, Schrieffer, Scalapino, Pines, Rice, and Varma. On the other hand, their acrimonious disagreements probably did not help.

Secondary theoretical benefits

The things I list below were not new ideas when the cuprate discovery happened. However, interest in the cuprates led them to become major research themes and ideas.

Importance of phase diagrams, including as a function of interaction parameters in toy models

Highlighting the limitations of electronic structure methods based on Density Functional Theory with approximate Exchange-Correlation functionals (i.e., anything computational). In the presence of strong correlations, DFT methods have spectacular failures. For example, predicting a metallic state instead of the Mott insulator.

Low dimensionality leads to qualitatively different behaviour, including the possibility of new types of order and quasiparticles. This is most dramatic in one dimension, where one has Luttinger liquids and spin-charge separation.

Spin liquids. Landau was wrong. Spontaneous symmetry breaking does not always occur in antiferromagnets.

Non-Fermi liquids. Landau was wrong. Not all metals are Fermi liquids.

Quantum criticality. Although this is a robust concept for certain toy models, whether it is relevant to the cuprates remains contentious.

Systematic improvements in approximation schemes and numerical techniques - exact diagonalisation, DMRG, DMFT, quantum Monte Carlo,...

Emergence. Chemical complexity and strong interactions can lead to new states of matter.

Secondary experimental benefits

Better probes. The desire to characterise the cuprates helped drive significant improvements in the resolution of ARPES (Angle-Resolved PhotoEmission Spectroscopy), STM (Scanning Tunnelling Microscopy), and inelastic neutron scattering. These advances have born fruit in the study of a wide range of other materials, beyond the cuprates.

Growth of single crystals. The early days of the cuprates produced a lot of junk experimental results because of the poor quality of the samples produced by "shake and bake". However, the involvement of solid-state chemists has improved things. The techniques have also led to the production of single crystals for a wide range of strongly correlated materials.

Why is there so little research on cuprates today?

Today, there is little research directly on cuprates, both theoretically and experimentally. It is hard to get funding to work on them, even though there is a lot we don't understand really well.

This is because of the problem of fashion in science. The low-lying fruit has been picked. There is a continuous new stream of materials being discovered with exotic properties, the latest being twisted bilayer van der Waals compounds.

Maxwell's demon and the history of the second law of thermodynamics

I recently reread Warmth Disperses and Time Passes: The History of Heat by Hans Christian von Baeyer

As a popular book, it provides a beautiful and enthralling account of the discovery of the first and second laws of thermodynamics. The book is a great companion to teaching and learning thermodynamics and statistical mechanics. The narrative is unified by the puzzle of Maxwell's demon.

Aside: The book was first published in 1998 with the title Maxwell's Demon. My guess is that the publisher changed the title because most people have probably not heard of the demon, unlike Schrodinger's cat.

Baeyer captures both the wonder of the subject and the fascinating story of how the science of thermodynamics developed. He describes quirky personalities and illustrates how science proceeds with a mixture of brilliant insights, clever experiments, false leads, and forgotten discoveries. It is easy and compelling reading.

I appreciated that there is a lack of hype, in contrast to too many popular science books.

The book is enhanced by showing that the story is not over. Many reports of the demise of the demon have been premature. The penultimate chapter discusses Zurek's definition of entropy in terms of algorithmic randomness. The last chapter considers molecular motors, such as kinesin, which can be viewed as ratchets driven by thermal noise.

Physical insights

The first and second laws tell us something about the fundamental nature of the universe. Although they are macroscopic and may have some (debatable) microscopic justification,  they can be viewed as fundamental.

Central to the development of the first law was the notion of the mechanical equivalent of heat.

There are three rather different ways to formulate the second law: a Carnot cycle represents an engine of optimal efficiency, heat never passes from a cold to a hot body, and the arrow of time. It is profound that these formulations are equivalent and not something that was anticipated. We should marvel at this.

Entropy can be viewed as the absence of information. Consequently, the second law can be viewed as statistical.

Things I want to understand

A good book stimulates us to want to engage more with its subject. Some things I want to understand are the entropy of the initial state of the universe, Boltzmann's H theorem, Feynman's ratchet, Shannon's information theory, molecular motors, Zurek's definition of entropy, and Gerald Holton's book, Thematic origins of scientific thought.

A recent tutorial is A Friendly Guide to Exorcising Maxwell’s Demon, by A. de Oliveira Junior, Jonatan Bohr Brask, and Rafael Chaves

Beautiful things missed

As a popular book, I think the length and scope of topics are right. Nevertheless, in a longer book, here are some things I would enjoy reading about: the zeroth and third laws, the contributions of Gibbs, the ergodic hypothesis, Brownian motion and evidence for atoms, the role of thermodynamics (and statistical mechanics) in the development of quantum theory (blackbody radiation, Einstein solid, identical particle statistics, and the Sackur-Tetrode equation) and perhaps phase transitions.

Two quibbles

von Baeyer has a somewhat reductionist perspective that the true nature of thermodynamics was revealed by the microscopic descriptions of Maxwell and Boltzmann.

I will write separate posts on why I am not comfortable with the following two statements.

Temperature IS the average kinetic energy of molecules.

Entropy was mysterious until Boltzmann's definition S=k ln W. 

Why is the state of universities such an emotional issue for me?

It all about values!

Universities have changed dramatically over the course of my lifetime. Australian universities are receiving increasing media attention due to failures in management and governance. But there is a lot more to the story, particularly at the grassroots level, of the everyday experience of students and faculty. It is all about the four M's: management, marketing, metrics, and money. Learning, understanding, and discovering things for their own sake is alien and marginalised. I have stopped writing posts about this. So why come back to it?

I am often struck how emotional this issue is for me and how hard it is to sometimes talk about it, particularly with those with a different view from me. Writing blog posts (e.g. this one) about it has been a somewhat constructive outlet, rather than exploding in anger at an overpaid and unqualified "manager" or one of their many multiplying minions.

A few weeks ago, I listened to three public lectures by the Australian historian Peter Harrison. [He is my former UQ colleague. We are now both Emeritus. I benefited from excellent seminars he ran at UQ, some of which I blogged about].

The lectures helped me understand what has happened to universities and also why it is a sensitive subject for me. Briefly, it is all about values and virtues.

The lectures are nicely summarised by Peter in the short article, 

How our universities became disenchanted: Secularisation, bureaucracy and the erosion of value

Reading the article rather than this blog post is recommended. I won't try and summarise it, but rather highlight a few points and then make some peripheral commentary.

I agree with Peter's descriptions of the problems we see on the surface (bureaucracy, metrics, and management features significantly). His lectures are a much deeper analysis of underlying cultural changes and shifting worldviews that have occurred over centuries, leading universities to evolve into their current mangled form.

A few things to clarify to avoid potential misunderstanding of Peter's arguments.

Secularisation is defined broadly. It does not just refer to the decline in the public influence of Christianity in the Western world. It is also about Greek philosophy, particularly Aristotle, and the associated emphasis on virtues and transcendence. Peter states:

"The intrinsic motivations of teachers, researchers and scholars can be understood in terms of virtues or duties. According to virtue ethics, the “good” of an activity is related to the way it leads to a cultivation and expression of particular virtues. These, in turn, are related to a particular conception of natural human ends or goals. (Aristotle’s understanding of human nature, which informs virtue ethics, proposes that human beings are naturally oriented towards knowledge, and that they are fulfilled as persons to the extent that they pursue those goals and develop the requisite intellectual virtues.)"

The virtue ethics of Aristotle [and Alisdair MacIntyre] conflicts with competing ethical visions, including duty-oriented (deontological) ethics, consequentialist ethics, and particularly utilitarianism. This led to a shift away from intrinsic goods to what things are "good for", i.e., what practical outcomes they produce. For example, is scientific research "good" and have "value" because it cultivates curiousity, awe, and wonder, or because it will lead to technology that will stimulate economic growth?

Peter draws significantly on Max Weber's ideas about secularisation, institutions, and authority. Weber argued that a natural consequence of secularisation was disenchantment (the loss of magic in the world). This is not simply "people believe in science rather than magic". Disenchantment is a loss of a sense of awe, wonder, and mystery.

Now, a few peripheral responses to the lectures.

Is secularisation the dominant force that has created these problems for universities? In question time, Peter was asked whether capitalism was more important. i.e., universities are treated as businesses and students as customers? He agreed that capitalism is a factor but also pointed out how Weber emphasised that capitalism was connected to the secularising effects of the Protestant Reformation.

 I think that two other factors to consider are egalitarianism and opportunism. These flow from universities being "victims" of their own success. Similar issues may also be relevant to private schools, hospitals, and charities. They have often been founded by people of "charisma" [in the sense used by Weber] motivated by virtue ethics. Founders were not concerned with power, status, or money. What they were doing had intrinsic value to them and was "virtuous". In the early stages, these institutions attracted people with similar ideals. The associated energy, creativity, and common vision led to "success." Students learnt things, patients got healed, and poverty was alleviated. But, this success attracted attention and  the institution then had power, money, status, and influence.

The opportunists then move in. They are attracted to the potential to share in the power, money, status, and influence. The institution then takes on a life of its own, and the ideals and virtue ethics of the founders are squeezed out. In some sense, opportunism might be argued to be a consequence of secularisation. 

[Aside: two old posts considered a similar evolution, motivated by a classic article about the development of businesses.]

One indicator of the "success" of universities is how their graduates join the elite and hold significant influence in society. [Aside: ignoring the problem of distinguishing correlation and causality. Do universities actually train students well or just select those who will succeed anyway?]  Before (around) 1960, (mostly) only the children of the elite got to attend university. Demands arose that more people should have access to this privilege. This led to "massification" and an explosion in the number of students, courses, and institutions. This continues today, globally. Associated with this was more bureaucracy. Furthermore, the "iron triangle" of cost, access, and quality presents a challenge for this egalitarianism. If access increases, so does cost and quality decreases, unless you spend even more. It is wonderful that universities have become more diverse and accessible. On the other hand, I fear that for every underprivileged student admitted whose mind is expanded and life enriched, many more rich, lazy, and entitled students suck the life out of the system.

Metrics are pseudo-rational

Peter rightly discussed how the proliferation of the use of metrics to measure value is problematic, and reflects the "rationalisation" associated with bureaucracy (described by Weber). Even if one embraces the idea that "rational" and "objective" assessment is desirable, my observation is that in practice, metrics are invariably used in an irrational way. For example, managers look at the impact factor of journals, but are blissfully oblivious to the fact that the citation distribution for any journal is so broad and with a long tail that the mean number is meaningless. The underlying problem is that too many of the people doing assessments suffer from some mixture of busyness, intellectual laziness, and arrogance. Too many managers are power hungry and want to make the decisions themselves, and don't trust faculty who actually may understand the intellectual merits and weaknesses of the work being assessed.

The problems are just as great for the sciences as the humanities

On the surface, the humanities are doing worse than the sciences. For example, if you look at declining student numbers, threats of job cuts, political criticism, and status within the university. This is because science is associated with technology which is associated with jobs and economic growth. However, if you look at pure science that is driven by curiousity, awe, and wonder, then one should be concerned. There is an aversion to attacking difficult and risky problems, particularly those that require long-term investment or have been around for a while. The emphasis is on low-lying fruit and the latest fashion. Almost all physics and chemistry research is framed in terms of potential applications, not fundamental understanding. Sometimes I feel some of my colleagues are doing engineering not physics. In a similar vein, biochemists frame research in terms of biomedical applications, not the beauty and wonders of how biological systems work. 

Are universities destined for bureaucratic self-destruction?

Provocatively, Peter considered the potential implications of the arguments of historian and anthropologist Joseph Tainter concerning the collapse of complex societies. On the technical side, this reminded me of a famous result in ecology by Robert May, that as the complexity of a system (the number of components and interactions) increases, it can become unstable.

I don't think universities as institutions will collapse. They are too integrated into the fabric of modern capitalism. What may collapse is the production of well-educated (in the Renaissance sense) graduates and research that is beautiful, original, and awe-inspiring. This leads naturally into the following question.

Is the age of great discoveries over?

Peter briefly raised this issue. On the one hand, we are victims of our own success. It is amazing how much we now know and understand. Hence, it is harder to discover truly new and amazing things. On the other hand, because of emergence we should expect surprises.

There is hope on the margins

Peter did not just lament the current situation but made some concrete suggestions for addressing the problems, even though we are trapped in Weber's "iron cage" of bureaucracy.

• Re-balancing the structures of authority
• Finding a place for values discourse in the universities
• Develop ways of resolving differences with a sense of the rationality of Alisdair MacIntyre in mind

On the first, I note the encouraging work of the ANU Governance Project.

Peter also encouraged people to work on the margins. I also think that this is where the most significant scholarship and stimulus for reform will happen. A nice example is the story that Malcolm Gladwell tells in a podcast episode, The Obscure Virus Club.

One hundred years of Ising

In 1925, Ising published his paper on the solution of the model in one dimension. An English translation is here.https://www.hs-augsburg.de/~harsch/anglica/Chronology/20thC/Ising/isi_fm00.html

Coincidentally, next week I am giving a lecture on the Ising model to an undergraduate class in statistical mechanics. To flesh out the significance and relevance of the model, here are some of the interesting articles I have been looking at:

The Ising model celebrates a century of interdisciplinary contributions, Michael W. Macy, Boleslaw K. Szymanski and Janusz A. Hołyst

This mostly discusses the relevance of the model to understanding basic problems in sociology, including its relation to the classic Schelling model for social segregation.

The Ising model: highlights and perspectives, Christof Külske

This mostly discusses how the model is central to some work in mathematical physics and probability theory.

The Fate of Ernst Ising and the Fate of his Model, Thomas Ising, Reinhard Folk, Ralph Kennac, Bertrand Berche, Yurij Holovatche.

This includes some nice memories of Ising from his son, Thomas.

Aside: I wanted a plot of the specific heat for the one-dimensional model. According to Google AI "In a 1D Ising model with no external magnetic field, the specific heat is zero at all temperatures."

Confusing bottom-up and top-down approaches to emergence

Due to emergence, reality is stratified. This is reflected in the existence of semi-autonomous scientific disciplines and subdisciplines. A major goal is to understand the relationship between different strata. For example, how is chemistry related to physics? How is genetics related to cell biology?

Before describing two alternative approaches —top-down and bottom-up —I need to point out that in different fields, these terms are used in opposite senses. That can be confusing!

In the latest version of my review article on emergence, I employ the same terminology traditionally used in condensed matter physics, chemistry, and biology. It is also consistent with the use of the term “downward causation” in philosophy. 

Top-down means going from long-distance scales to short-distance scales, i.e., going down in the diagrams shown in the figure above. In contrast, in the quantum field theory of elementary particles and fields (high-energy physics), “top-down” means the opposite, i.e., going from short to long distance length scales. This is because practitioners in that field tend to draw diagrams with high energies at the top and low energies at the bottom.

Bottom-up approaches aim to answer the question: how do properties observed at the macroscale emerge from the microscopic properties of the system? 

History suggests that this question may often be best addressed by identifying the relevant mesoscale at which modularity is observed and connecting the micro- to the meso- and connecting the meso- to the macro. For example, high-energy degrees of freedom can be "integrated out" to give an effective theory for the low-energy degrees of freedom.

Top-down approaches try to surmise something about the microscopic from the macroscopic. This has a long and fruitful history, albeit probably with many false starts that we may not hear about, unless we live through them or read history books. Kepler's snowflakes are an early example. Before people were completely convinced of the existence of atoms, the study of crystal facets and of Brownian motion provided hints of the atomic structure of matter. Planck deduced the existence of the quantum from the thermodynamics of black-body radiation, i.e. from macroscopic properties. Arguably, the first definitive determination of Avogadro's number was from Perrin's experiments on Brownian motion, which involved mesoscopic measurements. Comparing classical statistical mechanics to bulk thermodynamic properties gave hints of an underlying quantum structure to reality. The Sackur-Tetrode equation for the entropy of an ideal gas hinted at the quantisation of phase space. The Gibbs paradox hinted that fundamental particles are indistinguishable. The third law of thermodynamics hints at quantum degeneracy. Pauling’s proposal for the structure of ice was based on macroscopic measurements of its residual entropy. Pasteur deduced the chirality of molecules from observations of the facets in crystals of tartaric acid. Sometimes a “top-down” approach means one that focuses on the meso-scale and ignores microscopic details.

The top-down and bottom-up approaches should not be seen as exclusive or competitive, but rather complementary. Their relative priority or feasibility depends on the system of interest and the amount of information and techniques available to an investigator. Coleman has discussed the interplay of emergence and reductionism in condensed matter. In biology, Mayr advocated a “dual level of analysis” for organisms. In social science, Schelling discussed the interplay of the behaviour of individuals and the properties of social aggregates. In a classic study of complex organisations in business, understanding this interplay was termed differentiation and integration.

I thank Jeremy Schmit for requesting clarification of this terminology.

Remembering the student protestors who died 36 years ago

Memorial plaque in the Great Court of the University of Queensland today.

An authoritarian government takes over universities: one case history

Adventures of a Bystander, by Peter Drucker, contains the following account. Drucker was a faculty member at Frankfurt University in 1933.

“[S]everal weeks after the Nazis had come to power, was the first Nazi-led faculty meeting at the University. Frankfurt was the first university the Nazis tackled, precisely because it was the most self-confidently liberal of major German universities, with a faculty that prided itself on its allegiance to scholarship, freedom of conscience, and democracy. The Nazis knew that control of Frankfurt University would mean control of German academia altogether. So did everyone at the University. 

Above all, Frankfurt had a science faculty distinguished both by its scholarship and by its liberal convictions; and outstanding among the Frankfurt scientists was a biochemist of Nobel Prize caliber and impeccable liberal credentials. When the appointment of a Nazi commissar for Frankfurt was announced around February 25 of that year and when not only every teacher but also every graduate assistant at the University was summoned to a faculty meeting to hear his new master, everybody knew that a trial of strength was at hand. … 

The new Nazi commissar wasted no time on the amenities…. [He] pointed his finger at one department chairman after another and said: ‘You either do what I tell you or we’ll put you into a concentration camp.’ 

There was dead silence when he finished; everybody waited for the distinguished biochemist. The great liberal got up, cleared his throat, and said: ‘Very interesting, Mr. Commissar, and in some respects very illuminating. But one point I didn’t get too clearly. Will there be more money for research in physiology?’ The meeting broke up shortly thereafter with the commissar assuring the scholars that indeed there would be plenty of money for ‘racially pure science’.”

I became aware of this chilling story through Peter Woit's blog who got it from a blog post by Adam Przeworski

Superconductivity: a poster child for emergence

Superconductivity beautifully illustrates the characteristics of emergent properties.

Novelty. 

Distinct properties of the superconducting state include zero resistivity, the Meissner effect, and the Josephson effect. The normal metallic state does not exhibit these properties.

At low temperatures, solid tin exhibits the property of superconductivity. However, a single atom of tin is not a superconductor. A small number of tin atoms has an energy gap due to pairing interactions, but not bulk superconductivity.

There is more than one superconducting state of matter. The order parameter may have the same symmetry as a non-trivial representation of the crystal symmetry and it can have spin singlet or triplet symmetry. Type II superconductors in a magnetic field have an Abrikosov vortex lattice, another distinct state of matter.

Unpredictability. 

Even though the underlying laws describing the interactions between electrons in a crystal have been known for one hundred years, the discovery of superconductivity in many specific materials was not predicted. Even after the BCS theory was worked out in 1957 the discovery of superconductivity in intermetallic compounds, cuprates, organic charge transfer salts, fullerenes, and heavy fermion compounds was not predicted.71

Order and structure. 

In the superconducting state, the electrons become ordered in a particular way. The motion of the electrons relative to one another is not independent but correlated. Long-range order is reflected in the generalised rigidity, which is responsible for the zero resistivity. Properties of individual atoms (e.g., NMR chemical shifts) are different in vacuum, metallic state, and superconducting state.

Universality. 

Properties of superconductivity such as zero electrical resistance, the expulsion of magnetic fields, quantisation of magnetic flux, and the Josephson effects are universal. The existence and description of these properties are independent of the chemical and structural details of the material in which the superconductivity is observed. This is why the Ginzburg-Landau theory works so well. In BCS theory, the temperature dependences of thermodynamic and transport properties are given by universal functions of T/Tc where Tc is the transition temperature. Experimental data is consistent with this for a wide range of superconducting materials, particularly elemental metals for which the electron-phonon coupling is weak.

Modularity at the mesoscale. 

Emergent entities include Cooper pairs and vortices. There are two associated emergent length scales, typically much larger than the microscopic scales defined by the interatomic spacing or the Fermi wavelength of electrons. The coherence length is associated with the energy cost of spatial variations in the order parameter. It defines the extent of the proximity effect where the surface of a non-superconducting metal can become superconducting when it is in electrical contact with a superconductor. The coherence length turns out to be of the order of the size of Cooper pairs in BCS theory.  The second length scale is the magnetic penetration depth (also known as the London length) which determines the extent that an external magnetic field can penetrate the surface of a superconductor. It is determined by the superfluid density. The relative size of the coherence length and the penetration depth determines whether  the formation of an Abrikosov vortex lattice is stable in a large enough magnetic field.

Quasiparticles. 

The elementary excitations are Bogoliubov quasiparticles that are qualitatively different to particle and hole excitations in a normal metal. They are a coherent superposition of a particle and hole excitation (relative to the Fermi sea), have zero charge and only exist above the energy gap. The mixed particle-hole character of the quasiparticles is reflected in the phenomenom of Andreev reflection.

Singularities. 

Superconductivity is a non-perturbative phenomenon. In BCS theory the transition temperature, Tc, and the excitation energy gap are a non-analytic function of the electron-phonon coupling constant lambda, Tc \sim exp(-1/lambda).

A singular structure is also evident in the properties of the current-current correlation function. Interchange of the limits of zero wavevector and zero frequency do not commute, this being intimately connected with the non-zero superfluid density.

Effective theories.

These are illustrated in the Figure below. The many-particle Schrodinger equation describes electrons and atomic nuclei interacting with one another. Many-body theory can be used to justify considering the electrons as a jellium liquid of non-interacting fermions interacting with phonons. Bardeen, Pines, and Frohlich showed that for that system there is an effective interaction between fermions that is attractive. The BCS theory includes a truncated version of this attractive interaction. Gorkov showed that Ginzburg-Landau theory could be derived from BCS theory. The London equations can be derived from Ginzburg-Landau theory. The Josephson equations only include the phase of order parameter to describe a pair of coupled superconductors.

The historical of the development of theories mostly went downwards. London preceded Ginzburg-Landau which preceded BCS theory. Today for specific materials where superconductivity is known to be due to electron-phonon coupling and the electron gas is weakly correlated one can now work upwards using computational methods such as Density Functional Theory (DFT) for Superconductors or the Eliashberg theory with input parameters calculated from DFT-based methods. However, in reality this has debatable success. The superconducting transition temperatures calculated typically vary with the approximations used in the DFT such as the choice of functional and basis set, and often differ from experimental results by the order of 50 percent. This illustrates how hard prediction is for emergent phenomena.

Potential and pitfalls of mean-field theory. 

Mean-field approximations and theories can provide a useful guide as what emergent properties are possible and as a starting point to map out properties such as phase diagrams. For some systems and properties, they work incredibly well and for others they fail spectacularly and are misleading. 

Ginzburg-Landau theory and BCS theory are both mean-field theories. For three-dimensional superconductors they work extremely well. However, in two dimensions as long-range order and breaking of a continuous symmetry cannot occur and the physics associated with the Berezinskii-Kosterlitz-Thouless transition occurs. Nevertheless, the Ginzburg-Landau theory provides the background to understand the justification for the XY model and the presence of vortices to proceed. Similarly, the BCS theory fails for strongly correlated electron systems, but a version of the BCS theory does give a surprisingly good description of the superconducting state.

Cross-fertilisation of fields. 

Concepts and methods developed for the theory of superconductivity bore fruit in other sub-fields of physics including nuclear physics, elementary particles, and astrophysics. Considering the matter fields (associated with the electrons) coupled to electromagnetic fields (a U(1) gauge theory) the matter fields can be integrated out to give a theory in which the photon has mass. This is a perspective on the Meissner effect in which the magnitude of an external magnetic field decays exponentially as it penetrates a superconductor. This idea of a massless gauge field acquiring a mass due to spontaneous symmetry breaking was central to steps towards the Standard Model made by Nambu and by Weinberg. 

Topological defects determine the strength and growth rate of crystals

 The quantum theory of solids developed in the 1920s provided a theoretical estimate of the ideal strength of crystals. The problem was that this estimate was a thousand times greater than the measured strength of metals. This paradox was resolved in 1934, when Egon Orowan, Michael Polanyi and G. I. Taylor, independently proposed that plastic deformation could be explained in terms of the theory of dislocations. Aside: this is an example of how macroscopic properties can be determined by structures at the mesoscale rather than microscopic properties.

By 1940 the accepted theory of crystal growth was that it occurred by nucleation of successive close-packed layers of the crystal and this provided algebraic expressions for growth rates that were consistent with experiment. However, around 1950 Keith Burton estimated the parameters in the theory and pointed out that it predicted a growth rate that was smaller than observed growth rates by a factor 10^1000, i.e., 1000 orders of magnitude!

This quantitative discrepancy was resolved by Burton, Nicolas Cabrera and Charles Frank in 1951 who showed the central role played by screw dislocations. A crystal does not grow by the independent nucleation of separate layers. Rather it grows from just one layer that heloicoidally overlapping itself. A signature of this growth mode is the presence of spiral steps on crystal surfaces and they were subsequently observed.

This history is beautifully recounted in the introduction to a review article on Snow Crystals published by Charles Frank in 1982. It was reprinted in 2009 with an introduction by Andrew Fisher.

Following the introduction Frank discusses how snow is an important example of crystal growth that is not attributable to the presence of screw dislocations.

In 2015, D.P. Woodruff wrote a commentary on the classic 1951 paper by Burton, Cabrera, and Frank.

From Leo Szilard to the Tasmanian wilderness

Richard Flanagan is an esteemed Australian writer. My son recently gave our family a copy of Flanagan's recent book, Question 7. It is a personal memoir that masterfully weaves together a dizzying array of topics, from nuclear physics to the Tasmanian wilderness. I mention it on this blog because of its endearing and fascinating portrayal of Leo Szilard, arguably one of the twentieth century's most creative, unconventional, and eccentric physicists.

The paragraph below gives an overview of the narrative that is used to weave together all the disparate topics.

“Without Rebecca West’s kiss H. G. Wells would not have run off to Switzerland to write a book in which everything burns, and without H. G. Wells’s book [The World Set Free] Leo Szilard would never have conceived of a nuclear chain reaction and without conceiving of a nuclear chain reaction he would never have grown terrified and without growing terrified Leo Szilard would never have persuaded Einstein to lobby Roosevelt and without Einstein lobbying Roosevelt there would have been no Manhattan Project and without the Manhattan Project there is no lever at 8.15 am on 6 August 1945 for Thomas Ferebee to release 31,000 feet over Hiroshima, there is no bomb on Hiroshima and no bomb on Nagasaki and 100,000 people or 160,000 people or 200,000 people live and my father dies. Poetry may make nothing happen, but a novel destroyed Hiroshima and without Hiroshima there is no me and these words erase themselves and me with them.”

You can read an extract here and a review in The Guardian here.

John Hopfield on what physics is

A decade ago John Hopfield reflected on his scientific life in Annual Reviews in Condensed Matter Physics, Whatever Happened to Solid State Physics?

"What is physics? To me—growing up with a father and mother who were both physicists—physics was not subject matter. The atom, the troposphere, the nucleus, a piece of glass, the washing machine, my bicycle, the phonograph, a magnet—these were all incidentally the subject matter. The central idea was that the world is understandable, that you should be able to take anything apart, understand the relationships between its constituents, do experiments, and on that basis be able to develop a quantitative understanding of its behavior. 

Physics was a point of view that the world around us is, with effort, ingenuity, and adequate resources, understandable in a predictive and reasonably quantitative fashion. Being a physicist is a dedication to the quest for this kind of understanding."

He describes how this view was worked out in his work in solid state theory and moved into biological physics and the paper for which he was awarded the Nobel Prize. 

"Eventually, my knowledge of spin-glass lore (thanks to a lifetime of interaction with P.W. Anderson), Caltech chemistry computing facilities, and a little neurobiology led to the first paper in which I used the word neuron. It was to provide an entryway to working on neuroscience for many physicists..."

After he started working on biological physics in the late 1970s he got an offer from Chemistry and Biology at Caltech and Princeton Physics suggested he take it. 

"In 1997, I returned to Princeton—in the Molecular Biology Department, which was interested in expanding into neurobiology. Although no one in that department thought of me as anything but a physicist, there was a grudging realization that biology could use an infusion of physics attitudes and viewpoints. I had by then strayed too far from conventional physics to be courted for a position in any physics department. So I was quite astonished in 2003 to be asked by the American Physical Society to be a candidate for vice president. And, I was very happy to be elected and ultimately to serve as the APS president. I had consistently felt that the research I was doing was entirely in the spirit and paradigms of physics, even when disowned by university physics departments."

Autobiography of John Goodenough (1922-2023)

 John Goodenough was an amazing scientist. He made important contributions to our understanding of strongly correlated electron materials, magnetism, solid state chemistry, and materials science and engineering. He developed materials that are widely used in computer RAMs and rechargeable lithium batteries. He kept working in the laboratory and writing papers into his early 90s. Goodenough was awarded the Nobel Prize in Chemistry in 2019. Here is his Nobel Lecture, including text, slides, and video.

In 2008 he published Witness to Grace, a brief autobiography that chronicles his personal, scientific, and spiritual journeys. It is a fascinating story. The book is now out of print and the publisher is out of business. I have scanned a copy. You can download it here. I thank David Purdy for bringing to my attention the need to preserve the book.

Physics on Netflix

The Netflix series, 3-body Problem, features physics and physicists throughout. I am not a big fan of science fiction, but watched the first episode, to try and get a sense of why the series is attracting so much attention. The opening scene (in the video above) is rooted in history. It depicts a "struggle session" during the Cultural Revolution, featuring the denunciation and killing of a physics professor, who is the father of the main character in the series.

For some more on the intellectual and political background see

Organized criticism of Einstein and relativity in China, 1949–1989, by Danian Hu

Effective quantum field theories and hierarchial reality

 Over the last hundred years, there has been a fruitful cross-fertilisation of concepts and techniques between the theory of condensed matter and the quantum theory of elementary particles and fields. Examples include spontaneous symmetry breaking, renormalisation, and BCS theory. Sometimes, these efforts have occurred in parallel and only later did people realise that two different communities were doing essentially the same thing but using different language. Other times, one community adopted ideas or techniques from the other.

Central to condensed matter theory are ideas of emergence, a hierarchy of scales, and effective theories that are valid at a particular scale. Elementary particle theorists such as Steven Weinberg often distinguish themselves as reductionists with different goals and approaches. I only recently became aware that effective field theories have become a big thing in the elementary particle community, and Weinberg has been one of the leaders of this!

There is a helpful article in the CERN Courier, published just a year ago.

A theory of theories

Michèle Levi takes a tour through the past, present and future of Effective Field Theory, with applications ranging from LHC physics to cosmology.

The figure below, taken from the article, shows a hierarchy of energy scales and the corresponding effective field theories (EFTs).

n.b. Energy increases from bottom to top. [This may be confusing for condensed matter physicists, as we tend to put the high-energy theories at the bottom].

SM is the standard model

HQET is heavy quark effective theory in which the heavy quark degrees of freedom are integrated out.

EW breaking is Electro-Weak symmetry breaking which occurs on the scale of the Higgs boson.

The smallest energy scale in the figure is Lamda_QCD which is of the scale of the mass of the proton.

The standard model is now considered an effective field theory.

For the associated history and philosophy, I found this article helpful. Effective Field Theories, Reductionism and Scientific Explanation, by Stephan Hartmann

The decoupling theorem, proved by Appelquist and Carazzone in 1975, [cited 2,500 times] is central to EFTs and a hierarchy of scales. 

In its simplest case, this theorem demonstrates that for two coupled systems with different energy scales m1 and m2 (with m2 > m1) and described by a renormalisable theory, there is always a renormalisation condition according to which the effects of the physics at scale m2 can be effectively included in the theory with the smaller scale m1 by changing the parameters of the corresponding theory. The decoupling theorem implies the existence of an EFT at scale m1 which will, however, cease to be applicable once the energy gets close to m2.

There are two distinct approaches to finding effective theories at a particular scale, referred to as bottom-up and top-down approaches. 

Top-down requires one to have a theory at a higher energy scale and then integrate out the high energy degrees of freedom (fields and particles) to find the effective theory for the lower energy scale. This is what Wilson did in his RG approach to critical phenomena. Another example is how string theorists try to derive GR and the Standard Model starting with strings.

Bottom-up can always be done because one does not need to know the higher energy theory. One can often write down the Lagrangian for the EFT based on symmetry considerations and phenomenology. An example is Fermi's theory of beta decay and the weak interactions.

In a previous post, I considered Bei Lok Hu's discussion of these two different routes to developing a quantum theory of gravity.

A major outstanding challenge in the theory of elementary particles and fields is the hierarchy problem: the measured values of some masses and coupling constants are many orders of magnitude different from the "bare" values used in the Lagrangian.

The articles I have read about the role of effective field theories make no mention of the corresponding issues in condensed matter or how emergence is involved. Emergence occurs in systems where there are many interacting components. Here those components are the quantum fields and their components with different momenta/energy. Hence, I would say that emergence is at the heart of big questions in the theory of elementary particles and fields.