The intellectual legacy of Phil Anderson

I am looking forward to reading Andrew Zangwill's book, A Mind Over Matter: Philip Anderson and the Physics of the Very Many, that should be available in January 2021.

Andy recently gave a beautiful talk at an ICAM meeting on the life and science of Phil Anderson. I highly recommend it. Yesterday, at the UQ condensed matter theory group meeting we watched it and discussed it.

A few things that stood out to me, partly because some were new to me.

``PWA was a brilliant intuitionist who did more than any other person to transform the patchwork of ideas and techniques of what was formerly called solid state physics into the deep, subtle, and intellectually coherent discipline know as condensed matter physics.''

Phil's wife, Joyce, had an MA in English literature and edited all his prose pieces. This may explain how well written his writing for general audiences, such as Physics Today columns and book reviews in The Times Higher Education Supplement were so well written. In contrast, Phils talks and some papers were rather obscure.

PWA was a contrarian. He did not follow the pack. This is embodied in the fact that he chose to work on his PhD at Harvard with van Vleck, rather than Schwinger, who was chosen by eleven of his peers! van Vleck said "follow the data". During this time he was a friend of Tom Lehrer, a mathematics graduate student who became famous for writing and performing satirical songs with a strong social justice theme.

Phil did a BS in Electronic Physics (essentially Radio Engineering) and did not learn any modern physics. He did a PhD in chemical physics. It was only at Bell Labs that he started working on condensed matter problems. There he had three significant mentors: Conyers Herring, Gregory Wannier, and Charles Kittel.

Phil's 1952 paper on antiferromagnetism contained the idea of spontaneous symmetry breaking. But, this was not appreciated for a decade.

Phil's 1957 localisation paper and his 1961 magnetic impurities paper [the two works cited for his Nobel Prize] were both stimulated by talking to experimentalists at Bell Labs [George Feher and Berndt Matthias, respectively].

Concepts in Solids, based on his graduate lectures at Cambridge in 1961-2, was revolutionary for the time because the focus was on the properties of model Hamiltonians, rather than detailed phenomenology.

Phil's criticisms of high energy physics, its reductionism and drawing resources away from "tabletop" science, began as early as 1971, when he wrote a New Scientist article on the subject. 

But there is a lot more. Watch the video!

Fun facts about phonons

Today we just take it for granted that crystals are composed of periodic arrays of interacting atoms. However, that was only established definitively one hundred years ago.
I have been brushing up on phonons with Marder's nice textbook, Condensed Matter Physics.
There are two historical perspectives that I found particularly fascinating. Both involve Max Born.

In a solid the elastic constants completely define the speeds of sound (and the associated linear dispersion relationship). In a solid of cubic symmetry, there are only three independent elastic constants, C_11, C_44, and C_12.
Cauchy and Saint Venant showed that if all the atoms in a crystal interact through pair-wise central forces then C_44=C_12. However, in a wide range of elemental crystals, one finds that C_12 is 1-3 times larger than C_44. This discrepancy caused significant debate in the 19th century but was resolved in 1914 by Born who showed that angular forces between atoms could explain the violation of this identity. From a quantum chemical perspective, these angular forces arise because it costs energy to bend chemical bonds.

The first paper on the dynamics of a crystal lattice was by Born and von Karman in 1912. This preceded the famous x-ray diffraction experiment of von Laue that established the underlying crystal lattice. In 1965, Born reflected

The first paper by Karman and myself was published before Laue's discovery. We regarded the existence of lattices as evident not only because we knew the group theory of lattices as given by Schoenflies and Fedorov which explained the geometrical features of crystals, but also because a short time before Erwin Madelung in Göttingen had derived the first dynamical inference from lattice theory, a relation between the infra-red vibration frequency of a crystal and its elastic properties.... 

Von Laue's paper on X-ray diffraction which gave direct evidence of the lattice structure appeared between our first and second paper. Now it is remarkable that in our second paper there is also no reference to von Laue. I can explain this only by assuming that the concept of the lattice seemed to us so well established that we regarded von Laue's work as a welcome confirmation but not as a new and exciting discovery which it really was.

This raises interesting questions in the philosophy of science. How much direct evidence do you need before you believe something? I can think of two similar examples from more recent history: the observation of the Higgs boson and gravitational waves. Both were exciting, and rightly earned Nobel Prizes.
However, many of us were not particularly surprised.
The existence of the Higgs boson made sense because it was a necessary feature of the standard model, which can explain so much.
Gravitational waves were a logical consequence of Einstein's theory of general relativity, which had been confirmed in many different ways. Furthermore, gravitational waves were observed indirectly through the decay of the orbital period of binary pulsars.

A comparative appreciation of P.W. Anderson and Linus Pauling

Andrew Zangwill contacted me because he is working on scientific biography of Phil Anderson. I think this is overdue. I would argue that Phil is the greatest theoretical physicist of the second half of the twentieth century. I would argue this on similar grounds to why I think Linus Pauling was the greatest theoretical chemist of the first half of the twentieth century. Crucially, their scientific legacies have extended far beyond condensed matter physics and chemistry, respectively.

Specifically, Pauling did not just make essential contributions to our understanding of chemical bonding, x-ray crystallography, and quantum chemistry. His impact went far beyond chemistry. Francis Crick said Pauling was the "father of molecular biology." He proposed and elucidated alpha helices and beta sheets in proteins. Furthermore, he began the whole field of molecular medicine, by showing the molecular basis of a specific disease, sickle cell anemia.

Phil Anderson has made incredibly diverse and valuable contributions to condensed matter physics (anti-ferromagnetism, localisation, weak localisation, magnetic impurities in metals, Kondo problem, poor mans scaling, superfluid 3He, spin liquids, RVB theory of superconductivity... ).
I can think of three significant and profound influences of Phil beyond condensed matter physics.

Codifying and elucidating the concept of emergence (and the limitations of reductionism) in all of science, in More is Different in 1972.

Laying ground work for the Higgs boson in 1963 by connecting spontaneous gauge symmetry breaking and mass. 

Elucidating spin glasses in a way that was key to John Hopfield's development of a particular neural network and to the notion of a "rugged landscape", relevant in protein folding and evolution. Anderson described these connections nicely in two pages in Physics Today in 1990.

Are there other examples?

Who do you think is the greatest theoretical physicist of the second half of the twentieth century?
[n.b. If you are thinking Feynman, he did path integrals and QED before 1950].

Some ultra-cold atom experiments I would like to see

I have been having some stimulating interactions with my Australian cold atom colleagues, including Matt Davis, Chris Vale, Andy Martin, and Kris Helmerson.

As I see it ultracold atomic gases and solid-state materials have complementary strengths and weaknesses for investigating emergent quantum many-body phenomena. Solid state materials are much easier to bring to spatially uniform thermal equilibrium, achieve temperatures much less than characteristic temperatures (such as the Fermi temperature), and perform high precision thermometry. On the other hand it is hard to drive solid state systems far from equilibrium, to investigate non-equilibrium phenomena such as turbulent charge flows, and the time scales for relaxation to equilibrium are often too fast to be observed.

In contrast, ultra-cold atomic gases make it is much easier to access non-equilibrium states, and image them and their time evolution. The two platforms are also complementary in the access they provide to tune-ability, control and design. Solid state systems can be tuned considerably by temperature, pressure, magnetic field, electric field, and chemical substitution. However, sometimes it is hard to know how these variations produce changes in the underlying microscopic interactions between the constituent particles. In contrast, some of the underlying interatomic interactions in ultracold atom systems can be readily tuned from weak to strong in a precise and the known manner. However, a major challenge remains to expand the repertoire of possible tune able interactions, particularly to include some of the more common interactions found in solid state systems (e.g., the coupling of orbital motion of fermions to a magnetic field and the Heisenberg antiferromagnetic spin interaction in Mott insulators).

Here a few experiments that I would particularly like to see done and may be "relatively straight-forward", i.e, feasible in the next few years. Of particular interest would be observing these phenomena in fermionic atom systems in which one can tune the strength of the interactions, observe the BEC-BCS crossover, and universal behaviour associated with scattering close to unitarity.

Probing Thermoelectric transport with cold atoms
and
Quantum oscillations in ultracold Fermi gases: Realizations with rotating gases or artificial gauge fields
Charles Grenier, Corinna Kollath, Antoine Georges

The "Higgs boson"!
Visibility of the amplitude (Higgs) mode in condensed matter
Daniel Podolsky, Assa Auerbach, and Daniel P. Arovas

For bosonic systems there is a recent experimental paper from Immanuel Bloch's group
The ‘Higgs’ amplitude mode at the two-dimensional superfluid/Mott insulator transition

This then connects to
Conductivity of hard core bosons: A paradigm of a bad metal
by Lindner and Auerbach
An earlier post discussed this paper, suggesting calculation of the thermopower.

Observation of an d-wave pseudogaps. For the s-wave case see
Observation of a pairing pseudogap in a two dimensional Fermi gas.

The Higgs boson in social context

A week ago I gave a talk "The Higgs Boson: scientific reality vs. media hype" at the Centre for Science, Religion, and Society at Emmanuel College at UQ. You can see the slides on my other blog.

One minute physics

Maybe you all know all about Minute physics.
But only this week I got introduced (by my wife!) .
We watched Why the Higgs is the missing link and

I think they highlight the value of simple whiteboard talks.

Marketing the Higgs boson

The level of media coverage (and hype) associated with the Higgs boson announcement in July caught me by surprise. But, then I realised that if you spend $10 billion on an experiment there must be some very small fraction associated with publicity and outreach. So I did some Googling and found this CERN document which gives the annual marketing budget as slightly less than $2 million. 
Combining this with 10,000 physicists from around the world hitting their local media outlets I should not have been surprised at the level of publicity.

2012 Nobel Prize predictions

People are starting to make predictions. A post from last year links to prediction from other bloggers, mostly in Chemistry.

1. Experiments for testing Bell inequalities and elucidating the role of entanglement in quantum physics
Alan Aspect, John Clauser, and Anton Zeilinger
They received the Wolf Prize in 2010, a common precursor to the Nobel.

2. Duncan Haldane and David Thouless
Showing the important role of topology in low-dimensional condensed matter

This should be a precursor to any prize for topological insulators. I remain to be convinced that there should be a prize for that. Also note Haldane and Thouless both wrote papers that were foundational for topological insulator theory.

I was convinced of the importance of Haldane and Thouless by Rajiv Singh several years ago.
I think their contributions are more original, significant and profound than Berry and Aharonov. But, I think the latter are probably more popular and likely.
Also, Haldane has not received the Wolf Prize yet.

3. Higgs, Kibble, and Englert?
They must be hot candidates and CERN will be lobbying hard. But, I hope it won't happen this year. I would like to see more statistics and checks on the experimental data. Also it has not yet been established that the Higgs field is the origin of the mass of fermions.

I welcome alternative views and suggestions.

Is this test of the Standard Model impressive?

A week ago we had an interesting physics colloquium The Higgs Boson at the Large Hadron Collider by Elizabetta Barberio, who works in the ATLAS detector collaboration.

It was nice to hear a talk about the Higgs boson which simply discussed the physics and the actual experimental results, without any hype.

To me one of the most interesting and impressive figures shown in the talk actually had nothing to do with the Higgs! I found it here on the CERN website.

It shows the measured cross sections for the production of different particle products (horizontal scale).
Note the vertical scale varies by four orders of magnitude.
Basically, it shows that the results from the ATLAS detector are consistent with the Standard Model.

One thing I would like to know is how many independent parameters (coupling constants) are involved in determining these cross sections from the Standard Model?
Is the agreement between experiment and theory impressive? Or are there so many parameters in the Standard Model that this plot is really just saying what those parameters are? But, all the cross sections can't be independent of one another.

The Higgs boson enters cocktail party chit-chat

It is amazing to me how much the Higgs boson has featured in the press and entered the public consciousness lately. I fear this is partly because CERN has such a large and effective press office. This was particularly brought home to me when my wife sent me the above cartoon which one of her friends had posted on Facebook.

On the one hand, I think it is good that physics is getting all this publicity. On the other hand I think the scientific significance of this discovery is being blown out of proportion, driven by the large budgets involved....

Clarifying the origins of mass and the Higgs boson

There is a nice article by Frank Close, Higgs boson: beginning of the end or end of the beginning.
It gives a succinct discussion of the background to the recent discovery and what it does and does not mean for elementary particle physics.

A couple of points I found helpful.
Reports in the media that "the Higgs boson is responsible for mass" are misleading.

First, almost all the mass in our bodies comes from neutrons and protons, and more than 99% of their mass comes from the binding energy of quarks (due to quantum chromodynamics) and not from the mass of isolated quarks.
The latter are hypothesized to get their mass from the Higgs field.
[Aside: the boson and the field are not the same thing. The boson is one specific excitation of the field].

Secondly, the CERN experiments do not establish that leptons and quarks obtain their mass from the Higgs field. Rather, only that the gauge bosons in electro-weak theory obtain their mass from the Higgs field.
Further experiments at CERN in the next few years may establish this though.

But, the existence of the Higgs field is relevant to chemistry in the following sense. Nuclei are so compact because of the large energy of pions, which is a reflection of the mass of quarks. Furthermore, the size of hydrogen atom is determined by the
mass of the electron.

The Higgs boson and condensed matter physics

This week at the Quantum Science seminar Ben Powell gave a tutorial about the Higgs boson, highlighting its conceptual origin in condensed matter physics. The talk followed some of Section 12.6 of Piers Coleman's nice book Introduction to Many Body Physics (free online). It is a nice clear and helpful discussion.

One of the key ideas first emphasized by Phil Anderson in 1963 was that a massless gauge field can aquire a mass in the presence of a coupling to a spontaneously broken field. A concrete realisation of this occurs in superconductors. In the Meissner effect a superconductor thicker than the penetration depth expels magnetic fields. This is like the photon acquires a mass.

In the electro-weak theory of Weinberg-Salam there is a combined U(1) x SU(2) gauge symmetry. Due to coupling to the Higgs field (whose symmetry is spontaneously broken)
one gauge field remains massless (the photon) and the other three become massive. These massive particles are the W+, W-, and Z bosons.

In a type II superconductor, vortices are allowed in the superconducting order parameter field. Can such vortices occur in the Higgs field? They may have been important in the early universe.
On fascinating thing I learnt is that for the Higgs field the crucial ratio [between the London penetration length and the superconducting coherence length] that determines whether type II behaviour is possible is the ratio of Higgs boson mass to W mass. The LHC results suggest that type II behaviour is possible!

In summary, here is an extract from Coleman's book (page 246).

Shortly after the importance of this mechanism for relativistic Yang Mills theories was noted by Higgs and Anderson, Weinberg and Salem independently applied the idea to develop the theory of “electro-weak” interactions. According to this picture, the universe we live is a kind of cosmological Meissner phase, formed in the early universe, which excludes the weak force by making the vector bosons which carry it, become massive. It is a remarkable thought that the very same mechanism that causes superconductors to levitate lies at the heart of the weak nuclear force responsible for nuclear fusion inside stars. In trying to discover the Higg’s particle, physicists are in effect trying to probe the cosmic superconductor above its gap energy scale.

Aside: Later Coleman discusses how (in a slave boson formulation) "the Anderson-Higgs effect in the Kondo problem endows the composite f−electron with charge."

Quantum physics as a political metaphor

There is a somewhat amusing column Our Political Black Hole in the New York Times by Gail Collins. It considers the fictional response of US presidential candidates to the discovery of the Higgs boson. I found it somewhat amusing, but in someways it is a bit painfully close to the truth.
This is a bit how I feel when I watch the classic BBC political comedy, Yes Minister.

Perhaps Gail Collins use of physics metaphor was inspired by David Javerbaum's earlier NYT column A Quantum Theory of Mitt Romney.

Remembering Coulson

Charles Coulson is definitely one of my heroes and I found this nice memorial talk by Roy McWeeny on a history of quantum chemistry site. It emphasizes how Coulson made the transition from applied mathematics to theoretical chemistry:

The broadening of his philosophy is summed up in a sentence .... in a lecture on mathematical models, .... "It is likely that one cannot be a good applied mathematician unless one has the ability to simplify to the point of absurdity!" — recalling at the same time a remark by Eddington that "If the model is right, the rest is easy".

Two trivia about Coulson I also learned:
He was chairman of Oxfam from 1965-1971.
He was Ph.D supervisor of Peter Higgs (of Higgs boson fame).

The LHC makes me yawn

This post may just reflect my ill informed prejudices. Please correct me.
Sorry, but I cannot get excited about the Large Hadron Collider (LHC). I find it hard to see how it is going to reveal the secrets to the universe, or even to produce new scientific insights comparable to the expense and effort involved.

First, I find it hard to believe that the Higgs boson will not be found. My limited knowledge of particle physics and the standard model is that it just has to be there. Spontaneous symmetry breaking and the associated dynamical mass generation is well established in other areas of physics (e.g. the Meissner effect in superconductors can be viewed as photons acquiring mass, as first emphasized by Anderson). Hence, I won't be surprised if it also works / is present in the Standard model via the Higgs boson.

On the one hand, the LHC (search for the Higgs boson) is an experiment that should certainly be done, in a world in with almost unlimited resources for science.
On the other hand, I remain to be convinced that the LHC is a much better investment than "tabletop science." The latter has produced Graphene, violations of Bell inequalities, spin ice, fractional statistics in the quantum Hall effect, and cuprate superconductors. To me anyone of those is of comparable importance to confirming the Higgs boson is really there.

An earlier post considered the second of Two questions physics can no longer avoid, asked by Martin Gutzwiller in a Letter to Physics Today, published in August 1994.

His first question was, "Has particle physics fulfilled its promise?"