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. 

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.

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.

David Mermin on his life in science: funny, insightful, and significant

 David Mermin has posted a preprint with the modest title, Autobiographical Notes of a Physicist

There are many things I enjoyed and found interesting about his memories. A few of the stories I knew, but most I did not. He reminisces about his interactions with Ken Wilson, John Wilkins, Michael Fisher, Walter Kohn, and of course, Neil Ashcroft.

Mermin is a gifted writer and can be amusing and mischievous. He is quite modest and self-deprecating about his own achievements.

He explains why we should refer to the Hohenberg-Mermin-Wagner theorem, not Mermin-Wagner.

One of his Reference Frame columns in Physics Today, stimulated Paul Ginsbarg to start the arXiv.

I was struck by how Mermin's career belongs to a different era. The community was smaller and more personal. Doing physics was fun. Time was spent savouring the pleasure of learning new things and explaining them to others. Colleagues were friends rather than competitors. His research was curiosity-driven. This led to Mermin making significant contributions to quantum foundations. And, he only published about two papers per year!

Teaching was valued, enjoyable, and stimulated research. It was also a way to learn a subject, regardless of the level at which it was taught. For eight years, Mermin and Ashcroft spent half their time writing their beautiful textbook!

I look forward to hearing others' reflections.

Very Short Introductions Podcast on Condensed Matter Physics

The podcast episode where I talk about my book just came out.

It is available on a range of platforms, listed here, including SoundCloud and YouTube.

Condensed matter physics in 15 minutes!

Oxford University Press has a nice podcast on Very Short Introductions. 

In each episode, an author of a specific volume has 10-15 minutes to introduce themself and answer several questions.

What is X [the subject of the VSI]?

What got you first interested in X?

What are the key aspects of X that you would like everyone to know?

The ones I have listened to and particularly liked are Infinity, Philosophy of Science, Evangelicalism, Development, Consciousness, Behavioural Economics, and Modern China.

Tomorrow, I am recording an episode for Condensed Matter Physics: A Very Short Introduction.

Here is a practise version of the audio and the draft text is below. 

I welcome feedback.

VSI Podcast 

I am Ross McKenzie. I am an Emeritus professor of physics at the University of Queensland in Brisbane, Australia. I have spent the past forty years learning, teaching, and researching condensed matter physics. I really love the Very Short Introduction series and so I am delighted to share my experience by writing Condensed Matter Physics: A Very Short Introduction.

What is condensed matter physics? It is all about states of matter. At school, you were probably taught that there are only three states of matter: solid, liquid, and gas. This is wrong. There are many more states such as liquid crystal, glass, superconductor, ferromagnet, and superfluid. New states of matter are continually, and often unexpectedly, being discovered. Condensed matter physics investigates how the distinct physical properties of states of matter emerge from the atoms of which a material is composed.

What first got me interested in condensed matter physics?

After I finished an undergraduate degree in theoretical physics in Australia in 1982, I would not have been able to answer the question, “what is condensed matter physics?”, even though it is the largest sub-field of physics. I then went to Princeton University in the USA to pursue a Ph.D. in and I took an exciting course on the subject and began to interact with students and faculty working in the field. 

At Princeton was Phil Anderson, who had won a Nobel Prize in physics for work in condensed matter. At the time I did not appreciate his much broader intellectual legacy. In his recent biography of Anderson, Andrew Zangwill states “more than any other twentieth-century physicist, he [Anderson] transformed the patchwork of ideas and techniques formerly called solid-state physics into the deep, subtle, and intellectually coherent discipline known today as condensed matter physics.” Several decades later, my work became richer as Anderson gave me an appreciation of the broader scientific and philosophical significance of condensed matter physics, particularly its connection to other sciences, such as biology, economics, and computer science. When do quantitative differences become qualitative differences? Can simple models describe rich and complex behaviour? What is the relationship between the particular and the universal? How is the abstract related to the concrete?

So what are the key aspects of condensed matter physics that I would like everyone to know?

First, there are many different states of matter. It is not just solid, liquid, and gas. Consider the “liquid crystals” that are the basis of LCDs (Liquid Crystal Displays) in the screens of televisions, computers, and smartphones. How can something be both a liquid and a crystal? A liquid crystal is a distinct state of matter. Solids can be found in many different states. In everyday life, ice means simply solid water. But there are in fact eighteen different solid states of water, depending on the temperature of the water and the pressure that is applied to the ice. In each of these eighteen states, there is a unique spatial arrangement of the water molecules and there are qualitative differences in the physical properties of the different solid states.

Condensed matter physics is concerned with characterising and understanding all the different states of matter that can exist. These different states are called condensed states of matter. The word “condensed’’ is used here in the same sense as when we say that steam condenses into liquid water. Generally, as the temperature is lowered or the pressure is increased, a material can condense into a new state of matter. Qualitative differences distinguish the many different states of matter. These differences are associated with differences in symmetry and ordering.

Second, condensed matter physics involves a particular approach to understanding properties of materials. Every day we encounter a diversity of materials: liquids, glass, ceramics, metals, crystals, magnets, plastics, semiconductors, and foams. These materials look and feel different from one another. Their physical properties vary significantly: are they soft and squishy or hard and rigid? Shiny, black, or colourful? Do they absorb heat easily? Do they conduct electricity? The distinct physical properties of different materials are central to their use in technologies around us: smartphones, alloys, semiconductor chips, computer memories, cooking pots, magnets in MRI machines, LEDs in solid-state lighting, and fibre optic cables. Why do different materials have different physical properties? 

Materials are studied by physicists, chemists, and engineers, and the questions, focus, goals, and techniques of researchers from these different disciplines can be quite different. The focus of condensed matter physics is on states of matter. Condensed matter physics as a research field is not just defined by the objects that it studies (states of matter in materials), but rather by a particular approach to the study of these objects. The aim is to address fundamental questions and to find unifying concepts and organizing principles to understand a wide range of phenomena in materials that are chemically and structurally diverse. 

The central question of condensed matter physics is, how do the properties of a state of matter emerge from the properties of the atoms in the material and their interactions? 

Let’s consider a concrete example, that of graphite and diamond. While you will find very cheap graphite in lead pencils, you will find diamonds in jewelery. Both graphite and diamond are composed solely of carbon atoms. They are both solid. So why do they look and feel so different?  Graphite is common, black, soft, and conducts electricity moderately well. In contrast, diamond is rare, transparent, hard, and conducts electricity very poorly. We can zoom in down to the scale of individual atoms using X-rays and find the spatial arrangement of the carbon atoms relative to one another. These arrangements are qualitatively different in diamond and graphite.. Diamond and graphite are distinct solid states of carbon. They have qualitatively different physical properties, at both the microscopic and the macroscopic scale. 

Third, I want you to know about superconductivity, one of the most fascinating states of matter. I have worked on it many times over the past forty years. Superconductivity occurs in many metals when they are cooled down to extremely low temperatures, close to absolute zero (-273 ºC). In the superconducting state, a metal can conduct electricity perfectly; without generating any heat. This state also expels magnetic fields meaning one can levitate objects, whether sumo wrestlers or trains. 

The discovery of superconductivity in 1911 presented a considerable intellectual challenge: what is the origin of this new state of matter? How do the electrons in the metal interact with one another to produce superconductivity? Many of the greatest theoretical physicists of the twentieth century took up this challenge but failed. The theoretical puzzle was only solved 46 years after the experimental discovery. The theory turns out also to be relevant to liquid helium, nuclear physics, neutron stars, and the Higgs boson. New superconducting materials and different superconducting states continue to be discovered. A “holy grail” is to find a material that can superconduct at room temperature. 

I find superconductivity even more interesting when considering quantum effects. By 1930 it was widely accepted that quantum theory, in all its strangeness, describes the atomic world of electrons, protons, and photons. However, this strangeness does not show itself in the everyday world of what we can see and touch. You cannot be in two places at the same time. Your cat is either dead or alive. However, condensed matter physicists have shown that the boundary between the atomic and macroscopic worlds is not so clear cut. A piece of superconducting metal can take on weird quantum properties, just like a single atom, even though the metal is made of billions of billions of atoms. It is in two states at the same time, almost like Schrodinger’s famous cat.

Fourth, condensed matter physics is all about emergence; the whole is greater than the sum of the parts. A system composed of many interacting parts can have properties that are qualitatively different from the properties of the individual parts. Water is wet, but a single water molecule is not. Your brain is conscious, but a single neuron is not. Such emergent phenomena occur in many fields, from biology to computer science to sociology, leading to rich intellectual connections. Condensed matter physics is arguably the field with the greatest success at understanding emergent phenomena in complex systems, particularly at the quantitative level. This is not because condensed matter physicists are smarter than sociologists, economists, or neuroscientists. It is because the materials we study are much “simpler” than societies, economies, and brains. 

Finally, condensed matter physics is one of the largest and most vibrant sub-fields of physics. For example, in the past thirty years, the Nobel Prize in Physics has been awarded thirteen times for work on condensed matter. In the past twenty years, eight condensed matter physicists have received the Nobel Prize in Chemistry. 

I hope I have sparked your interest in condensed matter physics. I invite you to learn more about why I consider this field of science significant, beautiful, and profound. 

Condensed Matter Physics: A Very Short Introduction (hard copies) now available on Amazon USA

My book has finally been released by Amazon in the USA. I don't like Amazon but it is cheap and you can avoid shipping charges.

In Australia Amazon has listed under "Engineering and Transportation" and is currently out of stock. 

Condensed Matter Physics: A Very Short Introduction out now!

Hard copies of my book can now be purchased directly from Oxford University Press. 

After a long wait and a lot of work, it was great to finally see it in print. I am very happy with the quality of the typesetting and the figures.

I look forward to getting feedback from readers.

Condensed Matter Physics: A Very Short Introduction now available on Kindle

The good news is that if you read books on Kindle, my book Condensed Matter Physics: A Very Short Introduction can now be purchased as an e-book on Amazon for US$7.50.  It seems to only be available on the USA site but I used my USA Amazon account and downloaded it.

I am no fan of Amazon and minimise my purchases from them. They are my shop of last resort. I understand that some readers will not want to go this route.

The bad news is that the production of print copies continues to progress slowly. Depending on the country, different sites advertise it being available at various dates over the next three months...  

I look forward to readers feedback.

Condensed Matter Physics: A Very Short Introduction; almost there...

The publication of my book has been delayed a couple of months. It is now due for release in February in the UK and May in the USA.

It is available for pre-order.

If you are teaching a course for which the book could potentially be one of the texts you can request a free inspection copy.

OUP has produced a nice flyer to promote the book.

Eight amazing things physics has taught us

What are the most amazing things that we know about the physics of the universe? If you were to pick ten what would they be?

I recently read Fundamentals: Ten Keys to Reality (2021) a popular science book by Frank Wilczek. My interest in the book was piqued just to see what Wilczek's choices for his "ten" were. I got a copy from the public library and became entranced because I discovered what a gifted writer and expositor Wilczek is. I found I was learning some physics I did not know; or at least getting a deeper understanding of what I should know. I then bought my own copy so I could annotate it. I have previously enjoyed the insights in many of Wilczeks' Physics Today columns.

The book gives a popular presentation of some physics "basics" such as celestial mechanics, the Standard Model of elementary particles (which he renames the Core), and Big Bang cosmology.  I found it full of insights. I also appreciated that Wilczek does not have the hard reductionist or scientism edge found in the popular books of some distinguished theoretical physicists such as Weinberg and Hawking. However, a careful reading led me at times to be somewhat disappointed and irritated, for reasons that I discuss briefly below. In the end, this is because, not surprisingly, I have a much more emergentist perspective on reality, seeing it as stratified.

First, here are the ten things that Wilczek finds amazing, helpfully summarised in his chapter titles.

Part I. What There Is 

Chapter 1. There's Plenty of Space

Chapter 2. There's Plenty of Time

Chapter 3. There Are Very Few Ingredients

Chapter 4. There Are Very Few Laws

Chapter 5. There's Plenty of Matter and Energy

Part II. Beginnings and Ends 

Chapter 6. Cosmic History is an Open Book

Chapter 7. Complexity Emerges

Chapter 8. There's Plenty More to See

Chapter 9. Mysteries Remain

Chapter 10. Complementarity Is Mind-Expanding

Here are some of the ideas associated with each of the ten keys.

There's Plenty of Space

The scales of the universe are incredible. Beyond us, there is the vast numbers of stars and galaxies, and distances of more than ten billion light years. Within us, each of our bodies contains more atoms than there are stars in the universe. Our brains have as many neurons as there are stars in our galaxy. An atom is largely empty space.

There's Plenty of Time

Cosmic time is abundant. The quantity of time reaching back to the big bang dwarfs a human lifetime... [which] contains far more moments of consciousness than universal history contains human life spans. We are gifted with an abundance of inner time.

There Are Very Few Ingredients

Everything in the universe is made of just a few particles: leptons, quarks, and neutrinos. And forces and the associated bosons, such as photons, gravitons, and gluons. These particles have just a few properties: mass, charge, colour, and spin.

 "The most basic ingredients of physical reality are a few principles and properties. Four simple yet profound general principles govern how the world works.

1. The basic laws describe change.

2. The basic laws are universal.

3. The basic laws are local.

4. The basic laws are precise.

Newton realised locality was a problem. Fields rather than particles are the fundamenta building blocks of matter.

Quasiparticles are discussed. In high school, Wilczek was inspired by a visit to Bell Labs where he learnt that quanta of lattice vibrations are phonons. He describes how he introduced anyons in the early 1980s and how they were then identified with quasiparticles in fractional quantum Hall states.

There Are Very Few Laws

From forces we are led to fields, and from (quantum) fields, we are led to particles.

From particles we are led to (quantum) fields, and from fields, we are led to forces.

Thus, we come to understand that substance and force are two aspects of a common underlying reality.

The four fundamental forces (gravity, electromagnetism, weak nuclear, and strong nuclear) are described by just a few simple mathematical equations.

The art and science of spectroscopy is described as "Atoms sing songs that bare their souls, in light."

Wilczek's Ph.D. work on quark confinement and asymptotic freedom in Quantum Chromodynamics (QCD) was the beginning of QCD being accepted and used.

Newton's gravity theory presented the puzzle of the equivalence of inertial and gravitational mass. Einstein's gravity solved the puzzle and "fulfills Newton's aspiration for a theory of gravity based n local action". 

    "we can portray the majestic logic of general relativity in ten broad             strokes... "

    "John Wheeler, the poet of relativity, summed it up this way: "Space-time     tells matter how to move; matter tells space-time how to bend."

Wilczek makes the debatable and misleading claim that "The equations of QED, QCD, general relativity, and the weak force, ... have powered many advances, including lasers, transistors, nuclear reactors, MRIs, and GPS."

There's Plenty of Matter and Energy

The fact that the amount of solar energy falling on the surface of the earth is vastly greater than current human energy consumption.

The concept of "dynamical complexity" is introduced but not defined. "Music and ritual are purified expressions of dynamical complexity."

"The principle that the essence of human purposes is experienced through flows of information in dynamic complexity, rather than through details of chemistry and physiology, is both mind-expanding and liberating. It challenges us to imagine how minds could emerge elsewhere in the universe, and it prepares us to embrace those minds within our circle of empathy."

To me, this is "mumbo jumbo" and reflects the muddled thinking that occurs when Wilczek wildly extrapolates from "fundamental" physics to broader and deeper questions about humanity. The last chapter has similar weaknesses.

Cosmic History is an Open Book

A lucid short summary is presented of big bang cosmology. What we know and why we know it. The chapter ends with a brief reference to Augustine's prescient insights about time. It is what clocks measure and so time did not exist before the beginning of the universe.

Complexity Emerges

How did the featureless simple "soup" that existed a million years after the big bang develop into the complex universe seen today with structures such as stars, galaxies, planets, and biological life? This short chapter (only eight pages) mostly talks about the role of gravity. The chapter could have been much richer by discussing the emergence of complexity in biology, psychology, and sociology. Again, simple laws can produce complex properties.

There's Plenty More to See

The discovery of the Higgs particle and gravitational wave astronomy are both described. Some speculations are made to connect "Quantum Perception and Self-Perception."

Mysteries Remain

What triggered the big bang? Could it hapen again?

Are there meaningful patterns hidden in the apparent sprawl of fundamental particles and forces?

How, concretely, does min emerge from matter? (Or does it?)

Wilczek describes violation of time reversal invariance (T) in elementary particle physics and the Peccei-Quinn proposal for a new field to explain this. The corresponding particle was dubbed the axion by Wilczek, which fulfilled his high school dream to give a particle that name when he encountered a laundry detergent with that name. The axion "cleans up a problem" in elementary particle physics.

Axions are candidates for dark matter.

Complementarity Is Mind-Expanding

Bohr's concept of complementarity (embodied in wave-particle duality in quantum theory) is embraced. 

Complementarity is the concept that one single thing, when considered from different perspectives, can seem to have very different or even contradictory properties. Complementarity is an attitude toward experiences and problems that Ive found eye-opening an extremely helpful. It has literally changed my mind. Through it, I've become larger: more open to imagination, and more tolerant.

I am no fan of this perspective. I am all for having an open mind, considering a range of perspectives, and living with dialectic (intellectual tensions). However, I do not use quantum theory to justify that. There is a multitude of moral, philosophical, social, and political reasons that provide much more compelling justifications for humility. Bohr's perspective and extrapolations from the atomic world to politics has a long and dubious history that has systematically been debunked by Mara Beller, including in Physics Today.  Nevertheless, these ideas just won't go away, as seen why a recent volume of papers on Quantizing International Relations.

In summary, I love Wilczek's discussions of physics, and I think eight of the ten chapters describe amazing things about the physical world that we have learnt and should contemplate with awe and wonder.  But, two of the chapters make speculations about how the type of theoretical physics that Wilczek has made seminal contributions to is profoundly relevant to technological, social, economic, and political reality. I would much rather draw on the insights and debates from the humanities and social sciences to understand those realities and our place in them.

Very Short Introduction can be pre-ordered

 

I am currently working on the proofs and index for Condensed Matter Physics: A Very Short Introduction. It is wonderful to have got to this stage.

It is slated for release on December 29. It can be pre-ordered from Oxford UP (GDP 9) , Amazon (US $12), Book Depository (US $16), ...

Famous last words

If you ever write a popular book about science I suggest you spend a lot of time honing your very last paragraph. If it is eloquent, grand, and hyperbolic it may be so widely quoted that many people will think that this is actually what the book is about or has proven. Here are a few examples that I often see.

Where then shall we find the source of truth and the moral inspiration for a really scientific socialist humanism? Only, we suggest, in the sources of science itself,..... it is the conclusion to which the search for authenticity necessarily leads. The ancient covenant is in pieces; man at last knows that he is alone in the unfeeling immmensity of the universe, out of which he emerged only by chance. Neither his destiny nor his duty have been written down. The kingdom above or the darkness below: it is for him to choose.''

Jacques Monod, Chance and Necessity: An Essay on the Natural Philosophy of Modem Biology, trans. Austryn Wainhouse (New York: Knopf, 1971), p. 167

But if there is no solace in the fruits of our research, there is at least some consolation in the research itself. Men and women are not content to comfort themselves with tales of gods and giants, or to confine their thoughts to the daily affairs of life; they also build telescopes and satellites and accelerators, and sit at their desks for endless hours working out the meaning of the data they gather. The effort to understand the universe is one of the very few things which lifts human life a little above the level of farce and gives it some of the grace of tragedy.

Steven Weinberg, The First Three Minutes (Basic Books, 1977), pages 154-155.

If we do discover a complete theory, it should in time be understandable in broad principle by everyone, .... Then we shall all ...[discuss] why it is that we and the universe exist. If we find the answer to that, it would be the ultimate triumph of human reason - for then we would truly know the mind of God.  

Stephen Hawking, A Brief History of Time

There is grandeur in this view of life, with its several powers, having been originally breathed by the Creator into a few forms or into one; and that, whilst this planet has gone circling on according to the fixed law of gravity, from so simple a beginning endless forms most beautiful and most wonderful have been, and are being evolved.

Charles Darwin, The Origin of Species

Can you think of any other examples of famous last paragraphs?

Chapter abstracts for A Very Short Introduction (part 2)

 Here are my draft abstracts and keywords for the whole book and for chapters 6-10. Context and chapters 1-5 were given in the previous post.

Comments and suggestions are welcome.

Condensed Matter Physics: A Very Short Introduction 

There are many more states of matter than just solid, liquid, and gas. Examples include liquid crystal, ferromagnet, glass, superfluid, and superconductor. New states are continually, and unexpectedly, being discovered. A superconductor can be like Schrodinger’s cat and in the macroscopic world exhibit the weirdness associated with the microscopic world of atoms, photons, and electrons, that is described by quantum theory. Condensed matter physics investigates how states of matter, and their distinct physical properties emerge from the atoms that a material is composed of. Such a system composed of many interacting parts can have properties that the parts do not have. Water is wet, but a single water molecule is not. Your brain is conscious, but a single neuron is not. Such emergent phenomena are central to condensed matter physics and occur in many fields, from biology to computer science to sociology, leading to rich intellectual connections. When do quantitative differences become qualitative differences? Can simple models describe rich and complex behaviour? What is the relationship between the particular and the universal? How is the abstract related to the concrete? Condensed Matter Physics: A Very Short Introduction is concerned with such big questions. The materials in silicon chips, liquid crystal displays, and magnetic computer memories, may have transformed society. But, understanding them has transformed how we think about complex systems. Key concepts explored include phase diagrams, phase transitions, symmetry, types of order, spontaneous symmetry breaking, spatial dimensionality, scaling, universality, macroscopic quantum states, topology, metrology, and emergence.

Keywords: condensed matter physics, states of matter, phase transition, broken symmetry, emergence, solid-state physics, superconductivity, Physics Nobel Prize, theoretical physics, metrology

Chapter 6. The critical point

“The critical point” in a phase diagram denotes the conditions under which a continuous transition between two states of matter occurs. Surprisingly, near the critical point diverse systems can have the same dependence of physical properties on parameters such as temperature is the same. The only details that determine the critical exponents are the symmetry of the order parameter and the spatial dimensionality of the system. This independence from chemical and structural details, known as universality, presented a major challenge to theoretical physics for decades. Theory must deal with the large fluctuations in the amount of order that occurs close the critical point. The successful theory developed in the 1970s exploits the fact that different states of a system and different systems can be related to one another by mathematically rescaling the length scales in the system. The mathematics can be made tractable by consider the abstract idea of a system with variable number of spatial dimensions. The idea of rescaling is illustrated with the results of computer simulations of an Ising model and with images of fractals.  

Keywords: Critical point, phase diagram, phase transition, critical exponent, universality, Ken Wilson, renormalisation group, scaling, fractals

7. Quantum matter

“Quantum matter” describes how some states of matter, such as superconductors and superfluids, have properties like those found in the strange quantum world of atoms, electrons, and photons. In quantum theory, properties such as energy cannot have any possible value, but are quantised. That is they come in discrete lumps. Also, particles can act like waves and so interfere with themselves. The weirdness of quantum theory is captured in the paradox of Schrödinger’s cat, where quantum effects occur on the macroscopic scale. This is realised in a superconductor, where the magnetic flux is quantised. Josephson proposed an electrical circuit that is the basis for a Superconducting Quantum Interference Device (SQUID). These devices are of technological significance as they are used in quantum computing, and to make precise measurements of fundamental physical constants and of magnetic field strengths. SQUIDs are now used in metrology, the science of precise measurements, being the basis for the international standard for the Volt, the unit of electrical voltage, and are used in quantum computing.  

Keywords: Schrödinger’s cat, quantum theory, Josephson effect, SQUID, superconductor, superfluid, metrology, magnetic flux, macroscopic quantum effect, quantum computing

8. Topology matters

“Topology matters” in condensed matter physics because topology provides a means to describe the unusual types of order found in some states of matter in which there is no symmetry breaking. Topology is the field of mathematics covering the properties of geometric objects that do not change when smoothly deformed. The Hall effect is the existence of a new type of electrical resistance in a conductor caused by an electric current moving transverse to a magnetic field. In a two-dimensional metal (Flatland) in a large magnetic field, the Hall resistance is quantised in units defined by fundamental constants. This is a macroscopic quantum effect and provides a means to make highly precise measurements of electrical resistance. This quantum Hall effect is now used in metrology, being the basis for the international standard for the ohm, the unit of electrical resistance. Topology helps explain why the Hall resistance is so precisely quantised and is independent of so many details such as the chemical composition of the material in which the electrons move. Haldane showed that topology is also key to understanding the unusual properties of chains of magnetic atoms. They exhibit new states of matter, quite distinct from those found in three-dimensional magnets. Haldane also laid the foundation for proposals of topological insulators, a state of matter which is an electrical conductor on its surfaces, but an insulator in its interior.

Keywords: Topology, quantum Hall effect, mathematics, topological invariant, metrology, Duncan Haldane, topological insulator, Flatland

9. Emergence: more is different

“Emergence: more is different” discusses how the concept of emergence is central to condensed matter physics. An emergent property of a system composed of many interacting parts is a property that the individual parts do not have. The whole is greater than the sum of the parts. Other characteristics of emergent properties such as irreducibility, universality, and unpredictability are discussed. Emergent properties are illustrated with an example involving language, grammar, and literature. States of matter are emergent, as are the quasiparticles present in many systems. Phil Anderson argued that a hierarchy of scales illuminates the relationship between different scientific disciplines and shows the limitations of reductionism. Emergence explains why condensed matter physics works as a unified discipline. Due to universality, there are concepts and theories that describe phenomena in a wide range of materials. An emergence perspective highlights how discerning the relevant scale is central to effective scientific strategies aiming to understand complex systems, whether in physics, biology, or sociology.

Keywords: Emergence, reductionism, condensed matter physics, universality, philosophy of science, Phil Anderson, biology, stratification, quasiparticles, complex systems

10. An endless frontier

“An endless frontier” discusses how is difficult to predict the future of condensed matter physics, but it is likely to be an exciting one as new discoveries of emergent phenomena, such as novel states of matter, are often not anticipated. Grand challenges are identified including understanding glasses, Schrödinger’s cat, and exploring new materials, and new extremes of temperature, pressure, and magnetic field. Condensed matter physics has a rich history of contributing concepts, techniques, and personnel to other fields, including chemistry, biology, computer science, and materials engineering. This interdisciplinarity is likely to continue with investigations of complex systems, soft matter, and the social sciences. New technologies will aid new discoveries in condensed matter physics and vice versa. Threats to the future vitality of the field are like those for other intellectual enterprises imbedded in institutions increasingly controlled by financial values: a preoccupation with short-term commercial outcomes, hype, metrics, and managerialism. Advances have historically come from individuals and groups working within contexts and institutions that valued intellectual freedom, creativity, patience, curiousity, and serendipity.

Keywords: condensed matter physics, glass, complexity, emergence, science funding, hype, scientific discovery, materials science, interdisciplinarity

Any suggestions for improvement?

Chapter abstracts for A Very Short Introduction (part 1)

I am pleased to announce that Condensed Matter Physics: A Very Short Introduction is scheduled to be published on December 29.

The manuscript is currently with copy editors and in production. 

For each chapter, I have been asked to provide abstracts and keywords for the online version of the book. This turns out to be somewhat interesting as it is an issue of marketing, using internet searches to sell books. There are no chapter abstracts for the hard copy. Here is some of the background provided by Oxford University Press.

High quality A&K (Abstracts and Keywords) are those that help readers get to the content they are looking for, first by making the relevant content appear high in search results, and then by accurately describing the work so that they can decide whether it will be relevant to their needs. High quality A&K become even more important when readers are able to choose and purchase the relevant content from the results. 

The availability of A&K is now an industry standard. Referrals from Google represent a higher percentage of total visits for sites that have free A&K (up to 40-70%), compared to those that do not (around 13-30%).

An example of an abstract is that for the first chapter of Globalisation: A Very Short Introduction which is one of the best-selling titles in the series.

Chapter abstracts should be 100–250 words.

Here are my current versions for the first five chapters. I welcome suggestions for improvement.

1. What is condensed matter physics?

What is condensed matter physics?  It is the science concerned with characterising and understanding all the possible states of matter that can exist. Solid, liquid, and gas are not the only states of matter. There is also liquid crystal, superconductor, superfluid, crystal, glass, ferromagnet, and antiferromagnet. The central question of condensed matter physics is “how do the physical properties of a state of matter emerge from the interactions between the atoms of which the material is composed?” This is illustrated with the distinct properties of graphite and diamond, two distinct solid states of carbon. The recent discovery of graphene, a material composed of single layer of carbon atoms, and its unique electrical properties is an example of how the field continues to produce exciting surprises. Condensed matter physics is one of the largest and most vibrant subfields of physics. As it is concerned with materials and with emergent phenomena there is significant cross-fertilisation of concepts and techniques with other sub-fields of physics, science, and engineering.

5–10 keywords that can be used for describing the content of the chapter

Condensed matter physics, states of matter, physical properties, graphite, diamond, graphene, materials science, emergence, Kamerlingh Onnes

2. A multitude of states of matter

There are “a multitude of states of matter”. Materials composed of just one or two types of atoms can form many different states of matter.  Each has qualitatively different physical properties. Transitions between distinct states are defined by abrupt changes in properties. Dramatic examples include superconductivity and superfluidity. Phase diagrams encode which state of a material is stable under specific conditions defined by variables such as temperature and pressure. The phase diagrams of water, carbon dioxide, and carbon are discussed. At the critical point there is no distinction between liquid and gas. Topics discussed are relevant to making artificial diamonds, freeze-dried food, decaffeinated coffee, and dry ice.

Keywords: tipping point, phase transition, phase diagram, critical points, temperature, superconductivity, superfluidity, magnetism, sublimation, supercritical fluid

3. Symmetry matters

“Symmetry matters” in condensed matter physics because the mathematics of symmetry is key to characterising the qualitative difference between distinct states of matter. The concept of symmetry is illustrated by considering how the appearance of specific objects do not change when they undergo transformations such as rotations, reflections, and translations. Crystals are composed of repeat units of atoms. Symmetry constrains the number of types of different repeat units that are possible. The spatial arrangement of the atoms in each repeat unit can be determined by diffraction of a beam of x-rays by the crystal. The symmetry of a state of matter constrains what physical properties it can have. Symmetry aids a connection between the macroscopic and microscopic properties of a state of matter, such as explaining why snowflakes have six-fold rotational symmetry. The unexpected discovery of a quasicrystal, a distinct state of matter, revised the definition of a crystal.

Keywords: symmetry, Bravais lattice, crystal, crystallography, x-ray diffraction, structure, quasicrystal, chemistry, molecular biology, Bragg

4. The order of things

“The order of things” describes how distinct states of matter are associated with distinct types of ordering, such as the regular pattern of atoms in the material. The change in symmetry between different states of matter can be quantified in terms of an “order parameter”. Determining the relevant symmetry and order parameter for a state of matter often takes decades as it requires significant scientific insight. Lev Landau proposed a general theory to describe the amount of ordering present in any material that undergoes a phase transition to a distinct state of matter. The associated concept of spontaneous symmetry breaking is central to condensed matter physics, and to the theory of elementary particles and fundamental forces and led to the prediction of the existence of the Higgs boson. There is a rigidity associated with the type of order in a state of matter, whether a crystal or a superconductor. This rigidity determines the type of deviations from perfect order that are possible. Examples of defects include dislocations in crystals and vortices in superconductors and superfluids.

Keywords: States of matter, rigidity, symmetry breaking, magnetism, Lev Landau, Higgs boson, order parameter, liquid crystal, vortex, topological defect

5. Adventures of Flatland

“Adventures of Flatland” describes how condensed matter physics is different in a two-dimensional world, than in our three-dimensional one. This Flatland can be accessed in a laboratory because it is possible to fabricate materials, such as graphene, that are two-dimensional or close to it. Theory can also be used to investigate this different world and led to predictions of new states of matter and new types of phase transitions. A simple theoretical model for magnetic phase transtions is the Ising model. The two-dimensional version of the model illustrates concepts such as spontaneous symmetry breaking, long-range order, critical points, emergence, and more. A class of (almost) two-dimensional materials of great interest are crystals consisting of layers of copper and oxygen atoms. These materials superconduct at higher temperatures than any other, have a rich phase diagram, exhibit unusual metallic states, and remain a theoretical puzzle.  

Keywords: Flatland,  spatial dimension, phase transition, Ising model, two-dimensional material, high-temperature superconductor, Kosterlitz-Thouless transition

What do you think? I welcome suggestions for improvement.

de Gennes enthuses about Chemistry and skewers Comte

Pierre-Gilles de Gennes (1932-2007) was arguably the founder of soft matter as a research field, as recognized by the Nobel Prize in Physics in 1991. After this de Gennes gave many lectures in French high schools, which were then published as a book, Fragile Objects: Soft Matter, Hard Science, and the Thrill of Discovery. Previously, I mentioned the book with regard to whether condensed matter physics is too abstract.

 One of many fascinating sections of the book is a chapter entitled, The Imperialism of Mathematics. de Gennes sings the praises of chemistry, and rants about the weaknesses of the French system, laying the blame at the feet of his compatriot Auguste Comte (1798-1857). Comte was one of the first philosophers of modern science and a founder of sociology and of positivism.

Below I reproduce some of the relevant text. When reading it bear in mind that de Gennes was a theoretical physicist and did work that often involved quite abstract mathematics and concepts.

        THE "AUGUSTE COMTE" PREJUDICE

I now come to a prejudice typical of French culture, inherited from the positivism of Auguste Comte. This nineteenth-century philosopher achieved some degree of fame by inventing a classification system of the sciences. 

At the top of his hierarchy was mathematics; at the bottom was chemistry, which according to him "barely deserved the name of science"; in the middle were astronomy and physics. This classification dismissed out of hand geography and mineralogy, sciences which were declared concrete and descriptive, retaining only those that were theoretical, abstract, and general. The tone was set! It is ironic that this philosophical concept came from an individual who had once written in a letter "The only absolute truth is that everything is relative," and who claimed to be steeped quasi-religiously in factually observable laws, in other words, laws verifiable by experiments. 

The "Auguste Comte" prejudice corrupts to this day the teaching of the sciences, the scientific disciplines, and even the scientists themselves. It also contains the seed of contempt for manual labor, which has interfered for years by curbing every attempt at reform to revalue the manual trades and their apprenticeship... 

An example comes to mind, of some graduates of the Polytechnic School of Paris attending an advanced program at Orsay to learn solid-state physics. They would often show up convinced that they knew everything on the basis of calculations. 

... But the typical Polytechnic graduate I inherited at the time would remain stumped in front of his bare blackboard. One of them finally blurted out (I will never forget his comment): "But, sir, what Hamiltonian should I diagonalize?" He was trying to hang on to theoretical ideas which had no connection whatsoever with this practical problem. This kind of answer explains, in large part, the weakness of French industrial research.

Among all the catastrophes brought about by the positivist prejudice, none is worse than the widespread contempt for chemistry. I have already pointed out the importance of this discipline for our industrial future, the importance of chemists, these marvelously inventive sculptors of molecules, to whom the French teaching establishment does not do nearly enough justice. An undergraduate math major once told me about a teacher who, on opening day, announced: "I personally dislike chemistry, but I have to talk about it. So, I will start by giving you two hours of chemical nomenclature: what the name of an obscure and com- plex molecule is, and the like." At the conclusion of the two hours, the entire class was turned off chemistry for life!

When Lucien Monnerie, the director of studies, and I took over re- sponsibility for courses at the Institute of Physics and Chemistry, we had to wage a determined battle to overcome the antichemistry prejudice. Just before our arrival, the students had organized a strike: they all wanted to become physicists. Slowly, we climbed back up the slope with a series of measures: changing labels, opening up several new channels, turning the entire curriculum upside down, and launching a verbal propaganda campaign. It was rather easy for me to sound persuasive; being a theoretical physicist, nobody could accuse me of protecting my own turf. But it took us 10 years to restore the proper balance. 

To anyone who wants to form a more precise idea of chemistry, of the life of a typical chemical engineer, I would advise reading the magnificent collection of essays by Primo Levi, The Periodic Table. They recount real-life stories. They possess an authenticity and a vitality which give a universal impact to the account of an ordinary fact, the description of minute events. It is an excellent antidote to the poison spread by Auguste Comte's classification scheme.

The Story of Science is a nice video series

 I am on the lookout for good video resources about science that I can recommend to others, particularly non-scientists. By chance, I recently came across the BBC production, The Story of Science: Power, Proof, and Passion, hosted by Michael Mosley.

There is also a beautiful book that goes with the series, containing more detail, including colour illustrations. I was able to get the DVDs and the book from my local public library.

I particularly appreciate that science is presented as a human endeavour and progress is influenced by local contexts (economic, political, religious, ...). That can be acknowledged and enjoyed without descending into a social constructivist view of scientific knowledge. In a similar vein, the series does not have an ideological edge, or embrace some common tropes that too often popular video treatments may promote such as science the saviour, science the moneymaker, science the spoiler, science the monster-maker, ... or that science is uncontrollable, is inscrutable, or is the domain of evil/eccentric geniuses,....

The series introduced me to several colourful characters who played key roles in the history of science, including Hennig Brand, Hans Sloan, Georges Cuvier, Horace-Benedict de Saussure, Simon Sevin, Richard Trevithick, ...

A Myth about Condensed Matter Physics?

What is condensed matter physics about? 

In his beautiful book, The Problems of Physics (originally published in 1987), Leggett has a nice chapter about condensed matter physics, Physics on a human scale. The abstract begins:

This chapter argues that the widespread notion that the discipline of condensed matter physics is devoted to deriving the properties of complex many-body systems from that of their atomic-level components is a myth, and that the analogy of map-making is much more appropriate.

Here are some quotes that clarify Leggett's argument.

a number of cases, particularly in the traditional areas of the physics of gases and crystalline solids, in which a model which treats the behaviour of the whole as essentially just the sum of that of its parts (atoms or electrons) has been quite successful; and a few more in which, even if a ‘one- particle’ picture fails, a description in terms of pairs of particles interacting in a way which is not particularly sensitive to the environment gives good results. But these cases, despite the fact that they totally dominate the presentation of the subject in most elementary textbooks, are actually the exception rather than the rule. 

In virtually all the frontier areas of modern condensed-matter physics, the relationship between our understanding of the behaviour of matter at the microscopic level of single atoms and electrons, and at the macroscopic level of (say) liquids and solids, is actually a good deal more complicated than this.

If the activity just described is not what condensed-matter physics is all about, then what is it about? I would claim that the most important advances in this area come about by the emergence of qualitatively new concepts at the intermediate or macroscopic levels—concepts which, one hopes, will be compatible with one's information about the microscopic constituents, but which are in no sense logically dependent on it. 

... [these new concepts] provide a new way of classifying a seemingly intractable mass of information, of selecting the important variables from the innumerable possible variables which one can identify in a macroscopic system;

All this is not to deny that an important role is played in condensed-matter physics by attempts to relate the macroscopic behaviour of bulk matter to our knowledge concerning its constituent atoms and electrons. Indeed, the theoretical literature on the subject is full of papers which at first sight seem to be claiming to ‘derive’ the former from the latter—that is, to do exactly what I have just said condensed-matter physicists do not do. 

It is precisely this compelling need to isolate, from a vast and initially undifferentiated mass of information, the features which are relevant to the questions one wishes to ask, which distinguishes condensed-matter physics qualitatively from areas such as atomic or particle physics...

In this situation I believe that it is sensible to reorient our view of the kinds of questions that we are really asking in condensed-matter physics. Rather than chasing after the almost certainly chimerical goal of deducing the behaviour of macroscopic bodies rigorously from postulates regarding the microscopic level, it may be better to view the main point of the discipline as, first, the building of autonomous concepts or models at various levels, ranging all the way from the level of atomic and subatomic physics to that of thermodynamics; and, second, the demonstration that the relation between these models at various levels is one not of deducibility but of consistency—that is, that there are indeed ‘physical approximations’ we can make which make the models at various levels mutually compatible.

In different words, condensed matter physics is all about emergence! [Although, I know Leggett does not like the way the word is used]. 

The centrality of intermediate scales was also emphasised by Tom McLeish in Soft Matter: A Very Short Introduction.

When I recently read Leggett's chapter I was concerned that this might be in conflict with my draft manuscript of Condensed Matter Physics: A Very Short Introduction.  In the first chapter, I wrote the following.

The central question of Condensed Matter Physics

Generally, condensed matter physicists grapple with one question. Because it is so important I state the question in three different ways.

• How do macroscopic properties emerge from microscopic properties? 

• How do the properties of a state of matter emerge from the properties of the atoms in the material and the interactions between the atoms?

• How do the many atoms in a material interact with one another to collectively produce a particular property of the material? 

I think this is consistent with Leggett's perspective, particularly because I do later emphasise emergence and intermediate scales. On the other hand, I may not have the same emphasis (or strong language) that Leggett does. 

Leggett's view is particularly pertinent today because a quarter of a century later there are probably a lot more people who would say that they are condensed matter physicists but would subscribe to the "myth". This is because of the rise of computational materials science due to massive increases in computational power and better computational methods such as those based on Density Functional Theory (DFT), using "better" functionals and DMFT (Dynamical Mean-Field Theory).

What do you think?

What to read after A Very Short Introduction?

On friday I finally sent my draft manuscript for Condensed Matter Physics: A Very Short Introduction off to the publisher. Yay!

At the end of the book there is the opportunity to make suggestions for what people might read next (assuming readers have been so inspired!).

This was not easy to write for condensed matter as there is a dearth of popular and accessible books. Here is my draft of Further Reading. What do you think?

Three years ago I asked about basic introductions to condensed matter for motivated and intelligent beginning undergrads and received some helpful suggestions. From this I will add to my list 

Fundamentals of Condensed Matter and Crystalline Physics: An Introduction for Students of Physics and Materials Science by David Sidebottom.

I welcome further suggestions.

PhD students and postdocs need to learn soft skills

 Most Ph.D. students and postdocs will end up employed outside academia and doing work that is not related to their current research. For this reason alone it is important to learn a broad range of skills beyond what is needed to publish that paper in a luxury journal that their supervisor craves. 

Furthermore, for faculty to survive, let alone flourish, in today's university (corporate) environment soft skills are very important.

David Sholl (a frequent commenter on this blog) has just published a relevant book. Here is the publisher blurb.

Long-term success in scientific research requires skills that go well beyond technical prowess. Success and Creativity in Scientific Research: Amaze Your Friends and Surprise Yourself is based on a popular series of lectures the author has given to PhD students, postdoctoral researchers, and faculty at the Georgia Institute of Technology. Both entertaining and thought-provoking, this essential work supports advanced students and early career professionals across a variety of technical disciplines to thrive as successful and innovative researchers.

If you read it please post some thoughts in the comments below.