The emergence of hadronic matter from interacting quarks and gluons

 A characteristic of emergent phenomena is how novel and complex properties can emerge from apparently simple laws. Quantum ChromoDynamics (QCD) describes the interaction of quarks and gluons. The classical Lagrangian is remarkably simple.

It has an SU(3) local gauge symmetry and the A_v^mu are the associated gauge fields (gluons).

The quarks are fermions with fractional electrical charge. The only parameters in the theory are the coupling constant g_s, which describes the self-interaction of the gluons, and the bare masses of the quarks, m_f. The gluons are massless. In the limit where the bare mass of quarks vanishes, the Lagrangian has chiral symmetry, which transforms quarks with left-handed symmetry into right-handed.

Frank Wilczek states that QCD "is conceptually simple. Its realisation in nature, however, is usually very complex. But not always."

Hadronic matter (nucleons and mesons) has properties that are qualitatively different from its components (interacting quarks and gluons). In other words, it is emergent. In hadronic matter, there are no particles with fractional electrical charge or massless bosons. Chiral symmetry is broken. Consequently, hadrons do not come in pairs with opposite parity and equal energy. Quarks are confined and this is associated with a string tension. The order parameter associated with confinement is the Polyakov (or Wilson) loop. The connection between chiral symmetry breaking and confinement is subtle. For a long time they were thought to be intimately connected but now that is not the case.

Although the underlying Lagrangian is simple, the spectrum of hadrons and their interactions is complex. There is a "zoo" of particles. This all comes from a single coupling constant!

On the one hand, this complexity is surprising. On the other hand, it is similar to how there is a simple coupling constant (the electronic charge) in the Hamiltonian that describes most of chemistry and condensed matter physics. Most of the particles are unstable and can be viewed as quasiparticles as they have a finite lifetime, even in the absence of electroweak interactions. 

The emergent state of hadronic matter only exists at "low" temperatures and densities. It "melts" at the high temperatures associated with the Big Bang, relativistic heavy ion colliders, or the high densities associated with neutron stars. But that and the associated phase diagram of QCD is another story...

Update. I revised this post due to some helpful clarifications from Chris Allton, who was visiting UQ this week.

A golden age for precision observational cosmology

Yin-Zhe Ma gave a nice physics colloquium at UQ last week, A Golden Age for Cosmology

I learnt a lot. Too often, colloquia are too specialised and technical for a general audience.

There are three pillars of experimental evidence for the Big Bang model: Hubble expansion of the universe, relative abundance of light nuclei due to nucleosynthesis in the first few minutes, and the Cosmic Microwave Background.

Ma showed Hubble's original data from 1929 for redshift versus distance of galaxies. There was a lot of noise in the data. Nevertheless, Hubble was right.

Big Bang Nucleosynthesis

This was first proposed in 1948 by Ralph Alpher and George Gamow. (Hans Bethe was an honorary author of the paper as a joke so that the author list would sound like the first three letters of the Greek alphabet. Gamow had a mischievous sense of humour.)

The chain of nuclear reactions that will produce the lightest elements and isotopes is shown below.

Because the binding energy of 4He is so large, it could have only been formed at an extremely high temperature of about 10^10 K. (Or is the issue activation energy for formation, not binding energy?)

Detailed calculations using parameters from terrestrial nuclear physics give the observed relative abundances of the elements. In particular, the universe is 74% hydrogen and 24 per cent helium.

The astrophysicist's periodic table showing the origin of the different chemical elements is rather cute.

Giving credit to George Gamow

Gamow, who died in 1968, made impressive contributions to theoretical physics. His Wikipedia page is worth reading. He claimed that he predicted the Cosmic Microwave Background in the late 1940s and did not receive sufficient credit when it was discovered in 1964. The 2019 Nobel Prize citation for James Peebles also minimises Gamow's early contributions. Whether this is fair or not can be debated.

Anisotropies in the Cosmic Microwave Background.

The past two decades have seen amazing advances in precision measurements of these anisotropies. The radiation is isotropic to one part in 25000, with a temperature of 2.72548±0.00057 K.

Measurements of the anisotropies have allowed precise determinations of key cosmological parameters by fitting theoretical predictions to the data shown below from the 2018 Planck collaboration. Different peaks have different physical origins. 

The level of precision in the data is truly amazing.

The solid line is a fit to theory involving six parameters. What would Enrico Fermi say? This is not "making the tale of an elephant wiggle" because the fit parameters are all consistent with independent determination of the cosmological parameters from Hubble expansion and the relative abundance of the light elements.

Aside. The paper from the Planck 2 collaboration has been cited 19000 times, but has almost 200 authors. How does one use that information in evaluating individual authors in job and promotion applications? How are they to be compared to a single-author paper with 100 citations or a five-author paper with 500 citations?

Is this a golden age for cosmology? 

Yes, in terms of precision measurements. 

On the theoretical side, the golden age may have passed. It is not clear that new concepts or theories will emerge. The outstanding questions are:

What is the nature and origin of dark matter? of dark energy? 

Why is the cosmological constant so small? Why is it so fine-tuned?

Can the validity of inflation be pinned down?

Does quantum gravity matter?

A lot of smart people have spent decades on these problems and made little progress. That fact does not preclude the possibility of a theoretical breakthrough. However, it does not make me optimistic. I hope I am wrong.

The role of superconductivity in development of the Standard Model

In 1986, Steven Weinberg published an article, Superconductivity for Particular Theorists, in which he stated

"No one did more than Nambu to bring the idea of spontaneously broken symmetries to the attention of elementary particle physicists. And, as he acknowledged in his ground-breaking 1960 article  "Axial Current Conservation in Weak Interactions'', Nambu was guided in this work by an analogy with the theory of superconductivity,..."

In the 1960 PRL, referenced by Weinberg, Nambu states that in the BCS theory, as refined by Bogoliubov, [and Anderson]

"gauge invariance, the energy gap, and the collective excitations are logically related to each other as was shown by the author. [Y. Nambu, Phys. Rev. 117, 648 (1960)] In the present case we have only to replace them by (chiral) (gamma_5) invariance, baryon mass, and the mesons." 

This connection is worked out explicitly in two papers in 1961. The first is

Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. I

Y. Nambu and G. Jona-Lasinio

They acknowledge, 

"that the model treated here is not realistic enough to be compared with the actual nucleon problem. Our purpose was to show that a new possibility exists for field theory to be richer and more complex than has been hitherto envisaged,"

Hence, I consider this to be a toy model for an emergent phenomena.

The model consists of a massless fermion field with a quartic interaction that has chiral invariance, i.e., unchanged by global gauge transformations associated with the gamma_5 matrix. (The Lagrangian is given above.) At the mean-field level, this symmetry is broken. Excitations include massless bosons (associated with the symmetry breaking and similar to those found earlier by Goldstone) and bound fermion pairs. It was conjectured that these could be analogues of mesons and baryons, respectively. The model was proposed before quarks and QCD. Now, the fermion degrees of freedom would be identified with quarks, and the model illustrates the dynamical generation of quark masses. When generalised to include SU(2) or SU(3) symmetry the model is considered to be an effective field theory for QCD, such as chiral effective theory.

The triumphs of lattice gauge theory

When first proposed by Ken Wilson in 1974, lattice gauge theory was arguably a toy model, i.e., an oversimplification. He treated space-time as a discrete lattice purely to make analysis more tractable. Borrowing insights and techniques from lattice models in statistical mechanics, Wilson could then argue for quark confinement, showing that the confining potential was linear with distance.

Earlier, in 1971, Wegner had proposed a Z2 gauge theory in the context of generalised Ising models in statistical mechanics to show how a phase transition was possible without a local order parameter, i.e., without symmetry breaking. Later, it was shown that the phase transition is similar to the confinement-deconfinement phase transition that occurs in QCD. [A nice review from 2014 by Wegner is here]. This work also provided a toy model to illustrate the possibility of a quantum spin liquid.

Perhaps, what was not anticipated was that lattice QCD could be used to calculate accurately properties of elementary particles.

The discrete nature of lattice gauge theory means it is amenable to numerical simulation. It is not necessary to have the continuum limit of real spacetime because of universality. Due to increases in computational power over the past 50 years and innovations in algorithms, lattice QCD can be used to calculate properties of nucleons and mesons, such as mass and decay rates, with impressive accuracy. The figure below is taken from a 2008 article in Science. 

The mass of three mesons is typically used to fix the mass of the light and strange quarks and the length scale. The mass of nine other particles, including the nucleon, is calculated with an uncertainty of less than one per cent, and in agreement with experimental values.

An indication that this is a strong coupling problem is that about 95 per cent of the mass of nucleons comes from the interactions. Only about 5 per cent is from the rest mass of the constituent quarks.

For more background on computational lattice QCD, there is a helpful 2004 Physics Today article, which drew a critical response from Herbert Neuberger. A recent (somewhat) pedagogical review by Sasa Prelovsek just appeared on the arXiv.

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.

A very effective Hamiltonian in nuclear physics

Atomic nuclei are complex quantum many-body systems. Effective theories have helped provide a better understanding of them. The best-known are the shell model, the (Aage) Bohr-Mottelson theory of non-spherical nuclei, and the liquid drop model. Here I introduce the Interacting Boson Model (IBM), which provides somewhat of a microscopic basis for the Bohr-Mottelson theory. Other effective theories in nuclear physics are chiral perturbation theory, Weinberg's theory for nucleon-pion interactions, and Wigner's random matrix theory.

The shell model has similarities to microscopic models in atomic physics. A major achievement is it explains the origins of magic numbers, i.e., nuclei with atomic numbers 2, 8, 20, 28, 50, 82, and 126 are particularly stable because they have closed shells. Other nuclei can then be described theoretically as an inert closed shell plus valence nucleons that interact with a mean-field potential due to the core nuclei and then with one another via effective interactions.

For medium to heavy nuclei the Bohr-Mottelson model describes collective excitations including transitions in the shape of nuclei.

An example of the trends in the low-lying excitation spectrum  to explain is shown in the figure below. The left spectrum is for nucleus with close to a magic number of nuclei and the right one for an almost half-filled shell. R_4/2 is the ratio of the energies of the J=4+ state to that of the 2+ state, relative to the ground state. B(E2) is the strength of the quadrupole transition between the 2+ state and the ground state.

The Interacting Boson Model (IBM) is surprisingly simple and successful. It illustrates the importance of quasi-particles, builds on the stability of closed shells, and neglects many degrees of freedom. It describes even-even nuclei, i.e., nuclei with an even number of protons and an even number of neutrons. The basic entities in the theory are pairs of nucleons. These are taken to be either an s-wave state or a d-wave state. There are five d-wave states (corresponding to the 2J+1 possible states of total angular momentum with J=2). Each state is represented by a boson creation operator and so the Hilbert space is six-dimensional. If the states are degenerate [which they are not] the model has U(6) symmetry.

The IBM Hamiltonian is written in terms of the most general possible combinations of the boson operators. This has a surprisingly simple form.

Note that it involves only four parameters. For a given nucleus these parameters can be fixed from experiment, and in principle calculated from the shell model. The Hamiltonian can be written in a form that gives physical insight, connects to the Bohr-Mottelson model and is amenable to a group theoretical analysis that makes calculation and understanding of the energy spectrum relatively simple.

Central to the group theoretical analysis is considering subalgebra chains as shown below

 

An example of an energy spectrum is shown below.

The fuzzy figures are taken from a helpful Physics Today article by Casten and Feng from 1984 (Aside: the article discusses an extension of the IBM involving supersymmetry, but I don't think that has been particularly fruitful).

The figure below connects the different parameter regimes of the model to the different subalgebra chains.

The nucleotide chart below has entries that have colour shading corresponding to their parameter values for the IBM model according to the symmetry triangle above.

The different vertices of the triangle correspond to different nuclear geometries and allow a connection to Aage Bohr's model for the surface excitations. 

This is discussed in a nice review article, which includes the figure above.

Quantum phase transitions in shape of nuclei

Pavel Cejnar, Jan Jolie, and Richard F. Casten

Aside: one thing that is not clear to me from the article concerns questions that arise because the nucleus has a finite number of degrees of freedom. Are the symmetries actually broken or is there tunneling between degenerate ground states?   

Emergence, structuralism, realism, and quarks

"Structuralism as an influential intellectual movement of the twentieth century has been advocated by Bertrand Russell, Rudolf Carnap, Nicholas Bourbaki, Noam Chomsky, Talcott Parsons, Claude Levi-Strauss, Jean Piaget, Louis Althusser, and Bas van Fraassen, among many others, and developed in various disciplines such as linguistics, mathematics, psychology, anthropology, sociology, and philosophy." 

In different words, structuralism and post-structualism have been and are still a really big deal in the humanities and social sciences. Structuralism is central to the rise and fall of a multitude of academic fashions, careers and reputations.  

"As a method of enquiry, it takes a structure as a whole rather than its elements as the major or even the only legitimate subject for investigations. Here, a structure is defined either as a system of stable relations among a set of elements, or as a self-regulated whole under transformations, depending on the specific subject under consideration. The structuralist maintains that the character or even the reality of a whole is mainly determined by its structuring laws, and cannot be reduced to its parts; rather, the existence and essence of a part in the whole can only be defined through its place in the whole and its relations with other parts."

In a sense, structuralism favours emergence over reductionism. But, note some of the strong exclusivist language highlighted in bold in the quote above. Structuralism seems to be an overreaction to extreme reductionism. 

Condensed matter physics has something concrete to contribute to these debates. Consider the case of Ising models defined on a range of lattices, as I discussed in a previous post. We do not have an exclusive interest in the whole system or in the parts of the system. Rather, we want to know the relationship between macroscopic properties [different ordered states], mesoscopic properties [domains, long-range correlations, networks], and microscopic properties [the individual spins and their local interactions].

That is the main point of this post. But for more context, keep reading.

The quotations above are taken from a book by Tian Yu Cao. 

From Current Algebra to Quantum Chromodynamics: A Case for Structural Realism

Cao is interested in a broad range of philosophical questions related to QCD, such as "If quarks cannot be observed in isolation should they be considered to be real?"

He continues:

In the epistemically interesting cases involving unobservable entities, the structuralist usually argues that it is only the structure and the structural relations of its elements, rather than the elements themselves (properties or entities with properties) that are empirically accessible to us. It is obvious that such an anti-reductionist holistic stance has lent some support to phenomenalism. 

However, as an effort to combat compartmentalization, which urge is particularly strong in mathematics, linguistics, and anthropology, the structuralist also tries to uncover the unity among various appearances, in addition to invariance or stable correlation under transformations, which can help discover the deep reality embodied in deep structures. Furthermore, if we accept the attribution of reality to structures, then the antirealist implications of the underdetermination thesis [which claims that since evidence cannot uniquely determine (or, worse, can even support conflicting) theoretical claims about certain unobservable entities, no theoretical entities should be taken as representation of reality], is somewhat neutralized, because then we can talk about the realism of structures, or the reality of the structural features of unobservable entities exhibited in evidence, although we cannot directly talk about the reality of the entities themselves that are engaged in the structural relations. In fact, this realist implication of structuralism was one of the starting points of current interests in structural realism.

Emergence and the stratification of physics into sub-fields

The concept of emergence is central to understanding sub-fields of physics and how they are related, and not related, to other sub-fields.

The table below shows a stratum of sub-disciplines of physics. For each strata there are a range of length, time, and energy scales that are relevant. There are distinct entities that are composed of the entities from lower strata. These composite entities interact with one another via effective interactions that arise due to the interactions present at lower strata and can be described by an effective theory. Each sub-discipline of physics is semi-autonomous. Collective phenomena associated with a single strata can be studied, described, and understood without reference to lower strata.

Table entries are not meant to be exhaustive but to illustrate how emergence is central to understanding sub-fields of physics and how they are related to one another.

What do you think of the table? Is it helpful? Have you seen something like this before?

I welcome suggestions about entries that I could add.

Emergence in nuclear physics

Nuclear physics exhibits many characteristics associated with emergent phenomena. These include a hierarchy of scales, effective interactions and theories, and universality.

The table below summarises how nuclear physics is concerned with phenomena that occur at a range of length and number scales. At each level of the hierarchy, there are effective interactions that are described by effective theories. Some of the biggest questions in the field concern how the effective theories that operate at each level are related to the levels above and below.

Moving from the bottom level to the second top level, relevant length scales increase from less than a femtometre to several femtometres.

The challenge in the 1950s was to reconcile the liquid drop model and the nuclear shell model. This led to the discovery of collective rotations and shape deformations. The observed small moments of inertia were explained by BCS theory. Integration of the liquid drop and shell models led to the award of the1975 Nobel Prize in Physics to Aage Bohr, Ben Mottelson, and Rainwater.

Since the 1980s a major challenge is to show how the strong nuclear force between two nucleons can be derived from Quantum Chromodynamics (QCD). The figure below illustrates how the attractive interaction between a neutron and a proton can be understood in terms of the creation and destruction of a down quark-antiquark pair. The figure is taken from here.

An outstanding problem concerns the equation of state for nuclear matter, such as found in neutron stars. A challenge is to learn more about this from the neutron star mergers that are detected in gravitational wave astronomy.

Characteristics of universality are also seen in nuclear physics. Landau’s Fermi liquid theory provides a basis for the nuclear shell model which starts from assuming that nucleons can be described in terms of weakly interacting quasiparticles moving in an average potential from the other nucleons. The BCS theory of superconductivity can be adapted to describe the pairing of nucleons, leading to energy differences between nuclei with odd and even numbers of nucleons. 

Universality is also evident in the statistical distribution of energy level spacings in heavy nuclei. They can be described by random matrix theory which makes no assumptions about the details of interactions between nucleons, only that the Hamiltonian matrix has unitary symmetry. Random matrix theory can also describe aspects of quantum chaos and zeros of the Riemann zeta function relevant to number theory.

Hollywood and a Physical Review paper

 I am not sure I have seen this before. If you watched the movie Oppenheimer, you may have noticed that a one point a student excitedly showed Oppenheimer the latest issue of Physical Review and the following image flashed across the movie screen.

On Continued Gravitational Contraction

J. R. Oppenheimer and H. Snyder

A beautiful blog post just appeared on 3 Quarks Daily,

 

September 1, 1939: A Tale Of Two Papers

by Ashutosh Jogalekar

The post describes the scientific and historical significance of the paper, including how it attracted no interest for twenty years, being eclipsed by a paper in the same issue of Physical Review.

The Mechanism of Nuclear Fission

Niels Bohr and John Archibald Wheeler

Have you ever seen a Hollywood movie that explicitly showed the page of a scientific journal article.

Science and the universe are awesome

Since we are surrounded by scientific knowledge. We are so used to it that we can take science for granted and not reflect on how amazing science truly is. And how amazing the universe is that science reveals. Things that we know, learn, and do today in science would have been inconceivable decades ago, let alone centuries ago.

What specific things do you think are particularly awesome? This question was stimulated by Frank Wilczek's recent book, Fundamentals: Ten Keys to Reality. In writing the book, he says "what began as an exposition grew into a contemplation."

 My answer to the question has some significant overlap with Wilczek's ten. 

Below I list some of the things that I find awesome. I consider two classes: what science can do and what we learn about the universe from science.

Science works! It is amazing what science can do.

We can understand the material world.

Einstein said, "The most incomprehensible thing about the world is that it is comprehensible." In a previous post, I explored some different dimensions of the fact that the universe is comprehensible. The mystery includes human capabilities, both intellectual and physical, and the malleability of the material world.

We can make precise measurements.

Scientists have created incredibly powerful and specialised instruments for making very precise measurements such as spectrometers, telescopes and microscopes. Scientists can measure the tension in a single strand of DNA, the magnetic moment of an electron to a precision of one part in one billion billion, the spectrum of light emitted by a galaxy that is ten billion light years away, ...

We can predict the outcome of new experiments.

Scientists construct theories in their minds, on pieces of paper, in mathematical equations, and in computers. One way to evaluate the possible validity of a theory is to propose new experiments and predict the outcome. Famous examples include the existence of the chemical element aluminium, the existence of the planet Neptune, radio waves, a specific excited quantum state of the atomic nucleus of carbon atoms, the pollinator moth for Darwin's orchid, the deflection of the path of light from a distant star by our sun, gravitational waves, the Cosmic Microwave Background, quarks, the Higgs boson, the Berezinskii-Kosterlitz-Thouless phase transition, the hexatic phase, edge states in integer spin antiferromagnetic chains, topological insulators, ... Predictions are particularly impressive when they are unexpected and controversial.

We can use mathematics. 

Eugene Wigner received the Nobel Prize in Physics in 1963. In 1960 he published an essay "The Unreasonable Effectiveness of Mathematics in the Natural Sciences that concludes

The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. 

We can manipulate and control nature.

Scientists and engineers can move single atoms, design drugs, make computers, build atom bombs, heart pacemakers, and mobile phones, manipulate genes, ......

We know so much but we know so little. 

On the one hand, the achievements of science are amazing. Yet, in spite of this, there are still significant mysteries and challenges. Examples include the nature of dark matter or human consciousness, a quantum theory of gravity, fine-tuning of fundamental constants, the quantum-classical boundary, protein folding, the nature of glasses, and how to calculate the properties of complex systems.

It is awesome what science reveals to us about the universe.

The immense scales of the observable universe

Our sun is just one star among the more than two hundred billion that make up our galaxy, the Milky Way. And that is just one of one trillion galaxies in the whole universe. It takes light from the most distant galaxies tens of billions of years to travel to us.

Length, time, and energy scales over many many orders of magnitude

These go far beyond our everyday experience and what we can see with the naked eye (from a millimetre to a kilometre). On the large scale, the visible universe involves distances of billions of light years (10^25 metres). On the small scale, there is the sub-structure of nucleons, which is smaller than femtometres (10^-15 m).  This wide range of length scales is nicely illustrated in the wonderful movie Powers of Ten and its update, The Cosmic Eye. There are corresponding time, energy, and temperature scales varying over many many orders of magnitude. For example, as one goes from ultracold atomic gases to quark-gluon plasmas, the  relevant energy and temperature scales vary over more than 20 orders of magnitude! At every scale, there are distinct phenomena and structures. 

Universal laws that are simple to state

The universe exhibits a diversity of rich and complex behaviour. Yet it can understand much of it in terms of simple universal laws that are easy to state, e.g., Newton's laws of motion, the laws of thermodynamics, Maxwell's equations of electromagnetism, Schrodinger's equation of quantum mechanics, the genetic code, ....  And, these are just a few of these laws. One does not need a multitude of laws to describe a multitude of instances of a multitude of phenomena.

Just a few building blocks

There are just a few fundamental particles in the standard model (leptons, neutrinos, and gauge bosons). Everything is made of them. They are the building blocks of atoms. They each have just a few physical properties: charge, spin, mass, and colour. Every single particle of a particular type in the universe has exactly the same properties. Exactly. As far as we know, they have been exactly the same throughout time, going back to the beginning of the universe, and whether they are in your body, or in a star in a distant galaxy.

Atoms are the building blocks of chemical compounds. Every single atom of a particular chemical element (and nuclear isotope) is absolutely identical. This allows astronomers to determine the chemical composition of distant stars, galaxies, and dust clouds.

Humans, plants, and animals all have the same molecular building blocks and there are just a few of them. Any DNA molecule is composed of just four different base pairs (denoted A, G, T, C) and proteins are composed of just twenty different amino acids.

There are two amazing things here. First, there are just so few building blocks. Second, every one of these building blocks is absolutely identical.

Emergence: simple rules produce complex behaviour

Humans, cells, and crystals can be viewed as systems composed of many interacting components. The components and their interactions can often be understood and described in simple terms. Nevertheless, from these interactions complex structures and properties can emerge.

Nature appears to be fine-tuned for life

This covers not just the values of fundamental physical constants that lead to the notion of fine-tuning and the anthropic principle. Water has unique physical and chemical properties that allow it to play a crucial role in life, such as the surface of lakes freezing before the bottom and aiding protein folding.

The intricate and subtle "machinery" of biomolecules

Proteins have very unique structures that are intimately connected to their specific functions, whether as catalysts or light sensors.

What do you think are the most amazing things about science and what we learn from it?

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.

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?

The emergence of condensed matter as a fundamental force in physics

What shapes the emergence and influence of a specific new academic discipline or research field? How much does context matter?

How is the discipline defined? By the objects studied, methods used, central concepts, questions asked, goals, or key discoveries? And, who gets to define the discipline: text-book authors, current researchers, distinguished academics, or university managers?

It may depend on who you ask. A discipline can be viewed from intellectual, historical, institutional, political, economic, and sociological perspectives. It all depends on what questions you ask.

Arguably, for most of the twentieth-century physics was considered the dominant field of science. We also observe today that condensed matter physics is a dominant force in physics. This is reflected in many different measures, such as numbers of practitioners, journal articles, PhDs, citations, and Nobel Prizes.

How did this happen? 

Joseph Martin is a historian who explores this question in his 2018 book, Solid State Insurrection: How the Science of Substance Made American Physics Matter. He looks particularly at physics in the USA in the political and economic context of the Cold War, focusing on the rise of solid-state physics, and its metamorphosis into condensed matter physics. The role of institutions such as government, industry, and the American Physical Society (journals, conferences, divisions) is carefully examined. Public testimony of Phil Anderson against the SSC (Superconducting SuperCollider) in 1989 is considered to be a watershed moment and highly symbolic. 

The book is carefully researched, beautifully written, and contains important new insights. I highly recommend it.

In exploring these issues I think it important to find a balance between two extremes. On the one side, there are purists and idealists who claim that physicists are the best (or even only) people to provide a useful and reliable perspective. Science is all about reality, facts, and truth, and contexts (social, political, economic) are completely irrelevant. At the other extreme are the social constructivists who think science is just about politics and power, both inside and outside the university community. Martin is to be commended that he does not tend towards either of these extremes.

A Physics Today article is adapted from the book When condensed-matter physics became king and gives a useful summary.

To whet your appetite for the whole book, a good place to start is the concluding chapter. Martin offers two fascinating counterfactual histories: one where the Manhattan Project failed, one where APS did not keep industrial physicists in the fold.

the most active frontier of the twentieth century was not the high-energy frontier, but the complexity frontier. It was the demystification of the properties of complex matter and the applications of those properties, which remade our technological world, from home computing, stereo equipment, and cookware to communication, transportation, medicine, and warfare.

This is a tendentious framing, but it serves a purpose: it exposes the historiographical contingency of the disproportionate focus on nuclear physics, high energy physics, and cosmology, alongside the historical contingency of the dominance those fields assumed over public discourse about physics in the second half of the twentieth century. Two counterfactual scenarios help to probe that contingency further, each of which offers heuristic utility by throwing into relief the role solid state physics played, despite lacking the public acclaim of its sibling subfields, in securing the prominence of American physics.

First, given the high degree of institutional volatility in the early post–Second World War era, it is easy to imagine a counterfactual scenario in which solid state physicists migrate away from physics and into chemistry, metallurgy, and engineering, much as electrical engineering had some decades earlier. It was a contingency about which the field’s founders actively worried, and the American Physical Society council was demonstrably squeamish about clearing the type of institutional space that would give the society a more industrial flavor. Without solid state, which accounted for a large proportion of the postwar population boom, physics would have stayed smaller and grown more slowly.

We can imagine a second counterfactual scenario in which the Manhattan Project never acquired the scale or resources it needed to construct a working bomb before the end of the war in the Pacific... Suppose, for whatever reason, the Second World War ends without a dramatic, public demonstration of the power of the nucleus...  In this second scenario, solid state physicists would have been well positioned to become much more politically influential in the early Cold War, in particular on the strength of radar research,..

Aside. Earlier I posted about a nice article Martin wrote about public perceptions about condensed matter physics.

Radioactive science for the masses

 My wife and I watched the movie, Radioactive, based on the life of Marie Sklodowska Curie. She was an amazing scientist who showed incredible perseverance, particularly in the face of discrimination by the scientific establishment in France at the beginning of the twentieth century, and attacks in the media because of her gender, nationality, and personal life.

 

The movie is good entertainment and creative, maybe a bit too creative at times. But they be a matter of personal taste. There were many things that I learnt, some substantial and others just interesting trivia, particularly after reading more on Wikipedia. Here are a few.

Curie did not only discover radioactivity, the elements radium and polonium (named after her native Poland), but also was the founder of nuclear medicine. 

One can easily forget that more than a century ago, chemistry labs were very basic and that producing pure samples was a tedious process. For example, a tonne of pitchblende (uranium oxide ore) had to be crushed and processed to produce just one-tenth of a gram of radium chloride.

Back then the boundaries between physics and chemistry were fuzzy. Marie received a Nobel Prize in both. I wonder whether the legacy of joint chemistry-physics institutes in France was essential to de Gennes's work in soft matter.

Both Curie's started out in solid-state physics. Pierre Curie and his older brother discovered piezoelectricity. Pierre discovered the transition temperature for ferromagnetism (Curie temperature), and the Curie law for the temperature dependence of the magnetic susceptibility in a paramagnet. He followed his wife into nuclear research.

After her husband's tragic death, she had an affair with Paul Langevin and was vilified in the press.

A strong critique of the movie is by Geraldine McGinty. On the one hand, I agree with her concerns. On the other hand, I am just happy that "Hollywood" is exposing people to this extraordinary woman and her science. Maybe my hopes and expectations are just too low. 

This relates to an ongoing debate about to what extent movies based on historical figures have to be historically accurate in every detail. The Crown (which I love) has brought these debates to the fore. Simon Jenkins states The Crown's fake history is as corrosive as fake news. Recent movies about scientists also raise the question to what extent the science must be absolutely accurate.

What do you think?

I welcome other comments on the movie, particularly from women.

It's not complicated. It's Complex!

When is a system "complex"?
Even though we have intuition (e.g. complexity is associated with many interacting degrees of freedom) coming up with definitive criteria for complexity is not easy.

I just finished reading, Complexity: A Very Short Introduction, by John Holland.
His perspective is that a system is "complicated" if it has many interacting degrees of freedom, but is "complex" if in addition it exhibits emergent properties.
The criteria for emergence is the existence of new hierarchies, containing new entities or agents (defined by the formation of boundaries) that are coupled by new interactions, and described by new "laws".

Holland distinguishes complex physical systems (CPS) from complex adaptive systems (CAS).
The latter involve elements (agents) that can change (learn or adapt) in response to interactions with other agents.
Cellular automata and pattern formation in biology are CPS, whereas genetic algorithms, economics, and sociology are examples of CAS.

The book gives a rather dense (but worthwhile) introduction to key concepts in complexity theory including the emergence of specialists (e.g., division of labor, according to Adam Smith in economics), the role of diversity, co-evolution (e.g. Darwin's orchid and moth), and evolutionary niches (fixed points of Markov matrices!).

Holland smoothly flits backwards and forwards between examples in biology, economics, linguistics, and computer science.

Holland's definition of emergence is consistent with how I think in condensed matter. For example, the formation of weakly interacting quasi-particles in a Fermi liquid. The emergent "boundaries" define the spatial size of the quasi-particle.
What struck me is that the interactions should be viewed as emergent, just as much as the quasi-particles.
For example, if we start with quarks and QCD (quantum chromodynamics), then at "low" temperatures and densities, nucleons form and the nuclear force emerges.

David Pines (1924-2018): quantum-many body theorist

I learnt today that David Pines died last week. He was a pioneer in quantum many-body theory, applying it not just to solid state physics but also to nuclear physics and astrophysics (neutron stars).  Furthermore, he was a great advocate of the importance of emergence in science, writing a classic paper, "The Theory of Everything," together with Bob Laughlin.

David also left a legacy of creative new institutions, being a co-founder of the Sante Fe Institute and the International Institute for Complex Adaptive Matter (I2CAM). Indeed, starting this blog was stimulated by David Pines and I2CAM. In January 2009, I attended the annual meeting of I2CAM in Cambridge and David organised a session on public outreach, including a presentation on blogging.

Piers Coleman, a current co-Director of I2CAM, has written a nice obituary which gives more details about David's contributions, both scientific and institutional.

Universality in mathematics

Physicists tend to think of universality (the details don't matter)  as a physical phenomena. However, in the early days of this blog I posted about how I became aware that the central limit theorem in mathematics is an example of universality.

Terence Tao has a nice article intended for a popular audience ,“E pluribus unum: from complexity, universality” that gives several examples of universality in mathematics and physics. The figures are particularly nice.
Some of the examples given include the law of large numbers, the central limit theorem, and Benford's law.

 "A histogram of the first two digits of accounts payable data of a major software company, together with the Benford's law prediction. (Source: Journal of Accountancy)"

The nicest part of the article is the discussion of the connections between random matrix theory, energy level spacings in nuclear physics, and the spacing of prime numbers and zeros of the Riemann zeta function. Universality is reflected in them all being described by the same probability distribution.

"A histogram of spacings between bus arrival times in Cuernavaca (Mexico), in crosses; the solid line is the prediction from random matrix theory. (Source: Krbalek-Seba, J. Phys. A., 2000)"

"Spacing distribution for a billion zeroes of the Riemann zeta function, and the corresponding prediction from random matrix theory. (Source: Andrew Odlyzko, Contemp. Math. 2001)"

These connections between mathematics and physics raise subtle philosophical questions as to whether the emergence of universality in physics is "just" a reflection of universality in mathematics.

Low temperature physics without nuclear weapons

Liquid 3He is amazing stuff. Below temperatures of a few hundred milliKelvin it forms a model (and the original inspiration for) Landau Fermi liquid. Furthermore, below about 1 mK it forms two different superfluid states, involving Cooper pairs in a spin triplet state. This is the model case for unconventional superconductivity.

Liquid 3He is actually of great practical use since it the crucial ingredient of dilution refrigerations that allow cooling from a few Kelvin to temperatures as low milliKelvin.
But where do labs get 3He from?
Well, it is a very useful by-product of nuclear weapons production.
Currently, the scientific community (which consumes only about 1% of the supply) is experience supply problems and dramatic price increases (a 15-fold increase between 2004 and 2010).
Why is this happening?
Thankfully, we are cutting back on nuclear weapons production!

One practical way to solve this problem is to develop alternative materials for ultra-low temperature refrigeration; one possibility is by adiabatic demagnetisation. Indeed, this is the method that was first developed in the 1930s using paramagnetic salts to achieve temperatures below about 0.3 K (and was the basis of the 1949 Nobel Prize in Chemistry) and is the basis for nice undergraduate problems in thermodynamics and statistical mechanics. Simply the entropy is a function of B/T (where B is the magnetic field and T the temperature). One cools the system down in a fixed magnetic field, then adiabatic isolates it and reduces the magnetic field slowly. In the last step the entropy must not change and so the temperature must decrease. (This is shown as the red horizontal arrow in the figure below). This is also known as the magnetocaloric effect. The problem is that most paramagnetic materials are insulators and one would prefer to have a metallic material that is a good thermal conductor and can be "machined".

I learnt some of this from an interesting paper (that I actually looked at in preparing an undergraduate thermodynamics lecture about Maxwell relations).

Large magnetocaloric effect and adiabatic demagnetization refrigeration with YbPt2Sn 
Dongjin Jang, Thomas Gruner, Alexander Steppke, Keisuke Mitsumoto, Christoph Geibel and Manuel Brando

The authors mention some basic unanswered science questions about why this material is a good candidate. Specifically, why is the Kondo temperature (associated with interaction of the magnetic moments of the Yb3+ ions with the conduction electrons) and the inter-ion magnetic interactions so low? This ensures that the spins act essentially like non-interacting spins (with a large entropy) down to less than 1 K.

A key figure is below, showing the entropy versus temperature at several different magnetic fields.