Symmetry is the origin of all interactions

In Phil Anderson's review of Lucifer's Legacy: The Meaning of Asymmetry by Frank Close, Anderson makes the following profound and cryptic comment.

In a book focusing, as this does, on symmetry, it seems misleading not to explain the fundamental principle that all interaction follows from symmetry: the gauge principle of London and Weyl, modelled on and foreshadowed by Einstein's derivation of gravity from general relativity (Einstein seems to be at the root of everything). The beautiful idea that every continuous symmetry implies a conservation law, and an accompanying interaction between the conserved charges, determines the structure of all of the interactions of physics. It is not appropriate to try to approach advanced topics such as electroweak unification and supersymmetry without this foundation block.

To see how this plays out in electrodynamics see here.

A pioneering condensed matter physicist

In terms of institutional structures, Condensed Matter Physics did not really exist until the 1970s. A landmark being when the Division of Solid State Physics of the American Physical Society changed its name. On the other hand, long before that people were clearly doing CMP! If we think of CMP as a unified approach to studying different states of matter that enterprise began in earnest during the twentieth century.

Kamerlingh Onnes (1853-1924) was a pioneer in low-temperature physics but is best known for the discovery of superconductivity in 1911. In many ways, Onnes embodied the beginning of an integrated and multi-faceted approach to CMP: development of experimental techniques, the interaction of theory and experiment, and addressing fundamental questions.

1. Onnes played the long game, spending years developing and improving experimental methods and techniques, whether glass blowing, sample purification, or building vacuum pumps. He realized that this approach required a large team of technicians, each with particular expertise and that teamwork was important. The motto of Onnes’ laboratory was Door meten tot weten (Through measurement to knowledge). Techniques were a means to a greater end.

2. In Leiden, Onnes sought out theoretical advice from his colleague Johannes van der Waals (1837-1923).  [Almost 10 years ago I gave a talk about van der Waals legacy].

3. Onnes’ experiments were driven by a desire to answer fundamental questions. Questions he helped answer included the following.
Can any gas become liquid?
For gases is there a universal relationship between their density, pressure, and temperature?
How are gas-liquid transitions related to interactions between the constituent molecules in a material? At very low temperatures is the electrical conductivity of a pure metal zero, finite, or infinite?

The first of these questions motivated Onnes to pursue being the first to cool helium gas to low enough temperatures that it would become liquid. At the time all other known gases had been liquified. In 1908 his group observed that helium became liquid at a temperature of 4.2 K. This discovery was of both fundamental importance and great practical significance. Liquid helium became extremely useful in experimental physics and chemistry as a means to cool materials and scientific instruments. Indeed liquid helium enabled the discovery of superconductivity, which resulted from addressing the last question.

The figure shows Onnes (left) in his lab with van der Waals.

The discussion above closely follows Steve Blundell's Superconductivity: A Very Short Introduction.

Common examples of symmetry breaking

In his beautiful book, Lucifer's Legacy: The Meaning of Asymmetry, Frank Close gives several nice examples of symmetry breaking that make the concept more accessible to a popular audience.

One is shown in the video below. Consider a spherical drop of liquid that hits the flat surface of a liquid. Prior to impact, the system has continuous rotational symmetry about an axis normal to the plane of the liquid and through the centre of the drop. However, after impact, a structure emerges which does not have this continuous rotational symmetry, but rather a discrete rotational symmetry.



Another example that Close gives is illustrated below. Which napkin should a diner take? One on their left or right? Before anyone makes a choice there is no chirality in the system. However, if one diner chooses left others will follow, symmetry is broken and a spontaneous order emerges.

My tentative answers to some big questions about CMP

In my last post, I asked a number of questions about Condensed Matter Physics (CMP) that my son asked me. On reflection, my title ``basic questions" was a misnomer, because these are actually rather profound questions. Also, it should be acknowledged that the answers are quite personal and subjective. Here are my current answers.

1. What do you think is the coolest or most exciting thing that CMP has discovered? 

Superconductivity.

explained?

BCS theory of superconductivity.
Renormalisation group (RG) theory of critical exponents.

2. Scientific knowledge changes with time. Sometimes long-accepted ``facts''  and ``theories'' become overturned.  What ideas and results are you presenting that you are almost absolutely certain of? 

Phase diagrams of pure substances.
Crystallography.
Landau theory and symmetry breaking as a means to understand almost all phase transitions.
RG theory.
Bloch's theorem and band theory as a framework to understand the electronic properties of crystals.
Quantisation of vortices.
Quantum Hall effects.
Emergence.

What might be overturned?

I will be almost certain of everything I will write about in the Very Short Introduction. This is because it centers around concepts and theories that have been able to explain a very wide swathe of experiments on diverse materials and that have been independently reproduced by many different groups.
I am deliberately avoiding describing speculative theories and the following.
Ideas, results, and theories based on experiments that did not involve the actual material claimed, involved significant curve fitting, or large computer simulations.
Many things published in luxury journals during the last twenty years.

3. What are the most interesting historical anecdotes? 

These are so interesting and relevant to major discoveries that they are worth including in the VSI.
Graphene and sellotape.
Quasi-crystals.
Bardeen's conflict with Josephson.
Abrikosov leaving his vortex lattice theory in his desk drawer because Landau did not like it.

What are the most significant historical events? 

Discovery of x-ray crystallography
Discovery of superconductivity.
Landau's 1937 paper.
BCS paper.
Wilson and Fisher.

Who were the major players?

They are so important that they are worthy of a short bio in the text.
Onnes.
Landau.
Bardeen.
Anderson.
Wilson.

4. What are the sexy questions that CMP might answer in the foreseeable future?

Is room-temperature superconductivity possible?

Basic questions about condensed matter

I am trying out draft chapters of Condensed matter physics: A very short introduction, on a few people who I see as representative of my target audience. My son is an economist but has not studied science beyond high school. He enjoys reading widely. He kindly agreed to give me feedback on each draft chapter. Last week he read the first two chapters and his feedback was extremely helpful. He asked me several excellent questions that he thought I should answer.

1. What do you think is the coolest or most exciting thing that CMP has discovered? explained?

2. Scientific knowledge changes with time. Sometimes long-accepted ``facts''  and ``theories'' become overturned? What ideas and results are you presenting that you are almost absolutely certain of? What might be overturned?

3. What are the most interesting historical anecdotes? What are the most significant historical events? Who were the major players?

4. What are the sexy questions that CMP might answer in the foreseeable future?

I have some preliminary answers. But, to avoid prejudicing some brainstorming, I will post later.
What answers would you give?

The global massification of universities

A recent issue of The Economist has an interesting article about the massive expansion in higher education, both private and public, in Africa.
The thing I found most surprising and interesting is the graphic below.

It compares the percentage of the population within 5 years of secondary school graduation are enrolled in higher education, in 2000 and 2017. In almost all parts of the world the percentage enrollment has doubled in just 17 years!
I knew there was rapid expansion in China and Africa, but did not realise it is such a global phenomenon.

Is this expansion good, bad, or neutral?
It is helpful to consider the iron triangle of access, cost, and quality. You cannot change one without changing at least one of the others.

I think that this expansion is based on parents, students, governments, and philanthropies holding the following implicit beliefs uncritically. Based on the history of universities until about the 1970s. Prior to that universities were fewer, smaller, more selective, had greater autonomy (both in governance, curriculum, and research).

1. Most students who graduated from elite institutions went on to successful/prosperous careers in business, government, education, ...

2. Research universities produced research that formed the foundation for amazing advances in technology and medicine, and gave profound new insights into the cosmos, from DNA to the Big Bang.

Caution: the first point does not imply that a university education was crucial to the graduates' success. Correlation and causality are not the same thing. The success of graduates may be just a matter of signaling.  Elite institutions carefully selected highly gifted and motivated individuals who were destined for success. The university just certified that the graduates were ``hard-working, smart, and conformist.''

But the key point is these two observations (beliefs) concern the past and not the present. Universities are different.  Massification and the stranglehold of neoliberalism (money, marketing, management, and metrics) mean that universities are fundamentally different, from the student experience to the nature of research.

According to Wikipedia,

Massification is a strategy that some luxury companies use in order to attain growth in the sales of product. Some luxury brands have taken and used the concept of massification to allow their brands to grow to accommodate a broader market.

What do you think?
Are these the key assumptions?
Will massification and neoliberalism undermine them?

J.R. Schrieffer (1931-2019): quantum many-body theorist

Bob Schrieffer died last month, as reported in a New York Times obituary.

Obviously, Schrieffer's biggest scientific contribution was coming up with the variational wave-function for the BCS theory of superconductivity. BCS theory was an incredible intellectual achievement on many levels. Many great theoretical physicists had failed to crack the problem. The elegance of the theory was manifest in the fact that it was analytically tractable, yet could give a quantitative description of diverse physical properties in a wide range of materials. BCS also showed the power of using quantum-field-theory techniques in solid state theory. This was a very new thing in the late 50s. Then there was the following cross-fertilisation with nuclear physics and particle physics (e.g. Nambu).

Another significant contribution was the two-page paper from 1966 that used a unitary transformation to connect the Kondo model Hamiltonian to that of the Anderson single impurity model. In particular, it gave a physical foundation for the Kondo model, which at the time was considered somewhat ad hoc.
John Wilkins wrote a nice commentary on the background history and significance of the Schrieffer-Wolff transformation.

The SW transformation is an example of a general strategy of finding an effective Hamiltonian for a reduced Hilbert space. This can also be done via quasi-degenerate perturbation theory. In different words, when one ``integrates out'' the charge degrees of freedom in the Anderson model one ends up with the Kondo model.

There is also the Su-Schrieffer-Heeger model, that is related to Heeger's Nobel Prize in Chemistry. However, although this spawned a whole industry (that I worked in as a postdoc with Wilkins) its originality and significance is arguably not comparable to BCS and SW.

Because of when he was born, like many of the pioneers of quantum many-body theory, Schrieffer may have been born for success?

I am somewhat (scientifically) descended from Schrieffer because I did a postdoc with John Wilkins, who was one of Schrieffer's first PhD students. My main interaction with Schrieffer was during 1995-2000. Each year I would visit my collaborator, Jim Brooks, at the National High Magnetic Field Laboratory, and would have some helpful discussions with Schrieffer. During one of those visits, I stumbled across a compendium of reprints from a Japanese lab. [This was back in the days when some people snail-mailed out such things to colleagues]. It had been sent to Schrieffer and contained a copy of a paper by Kino and Fukuyama on a Hubbard model for organic charge transfer salts. That was the starting point for my work on that topic.