Macroscopic quantum effects in superconductors and superfluids

Quantisation of magnetic flux in a superconductor

Magnets and electrical currents produce magnetic fields, regions of space where other magnets and electrical wires experience a mechanical force. For a circle of wire in the presence of a magnetic field the magnetic flux is defined as the strength of the magnetic field passing through the circle multiplied by the area of the circle. A law of electromagnetism states that if the field varies with time, then a voltage is produced in the wire with a magnitude that is proportional to the rate at which the magnetic flux through the circle changes. This is the physics behind all electrical motors and electrical generators. In the everyday world magnetic flux can have any value and can be varied continuously by changing the strength of magnetic field. In the quantum world that is not the case. Magnetic flux is quantised.

In 1961, two experimental groups independently reported the first observation of a macroscopic quantum effect, the quantisation of the magnetic flux passing through a superconducting cylinder (Figure 30). One team was Bascom Deaver and William Fairbank and the other Robert Doll and Martin Nabauer. A tall thin cylinder made of tin was placed in a magnetic field and cooled down to a low enough temperature that it entered the superconducting state. The magnetic flux passing through the cylinder was then measured as the magnetic field was varied. The resulting graph has four noteworthy features. First, there are clear steps, showing that the magnetic flux has discrete values. In contrast, in the normal metallic state the graph was a straight line. Secondly, the magnitude of the steps was the same, to within about one per cent, suggesting quantisation of a single unit of magnetic flux. Thirdly, the value of this quantum of magnetic flux was equal to the value of h/2e. Thus, it was completely determined by the two fundamental constants, h and e, Planck’s constant and the charge on an electron, respectively. And fourthly, graphs with the same three features noted above were later observed in other superconducting materials and cylinders. This showed that flux quantisation is independent of details such as the chemical composition and dimensions of the cylinder. This flux quantisation is a macroscopic quantum effect. It is macroscopic because the system is macroscopic, and the magnetic flux is a macroscopic property. It is quantum as and the magnitude of the quantisation is determined by Planck’s constant.

                                                                       (b)

Figure 30. Quantisation of magnetic flux in a superconducting cylinder. (a) A tall thin cylinder of tin was placed in a magnetic field. (b) The graph shows the value of the magnetic flux passing through the cylinder as the magnetic field was varied. Note the step like structure, showing quantisation of the flux.

The quantum of magnetic flux is denoted Φ0 (= h/2e) and has the value 2.067833848...×10−15   tesla (metre)2. This number also determines the scale of quantum interference effects between two superconductors, as we will see shortly. The flux quantum is also relevant to vortices that form when some superconductors are placed in a magnetic field (Figure 20). A persistent electrical current flows around the vortex and the magnetic field penetrates the core of the vortex. It can also be shown, both theoretically and experimentally, that the magnetic flux associated with each vortex is exactly equal to one quantum of flux. Something similar happens in superfluids.

Macroscopic quantum effects in superfluids

When a cylinder containing a fluid is rotated about an axis passing down the centre of the cylinder the fluid will also rotate. The faster the cylinder is rotated the faster the fluid rotates. A physical quantity known as the circulation is proportional to the speed of rotation and the diameter of the cylinder. With a variable speed motor, the rotation speed can be continuously varied and in normal fluids the circulation has continuous values. But not in a superfluid, as shown in a beautiful experiment done by W.F. Vinen in 1961 using liquid 4He. He observed that when the liquid was cooled below the superfluid transition temperature that the circulation could only take on discrete values. Furthermore, these discrete values are multiples of h/M where h is Planck’s constant and M is the mass of one atom of helium. This value was predicted by Lars Onsager in 1949 who identified h/M with the circulation of a single vortex in the superfluid. This is another macroscopic quantum effect.

The quantisation of magnetic flux in superconductors and of circulation in superfluids showed that both superconductors and superfluids can be classified as quantum states of matter. The close similarity of these quantum phenomena, even though superconductivity occurs in solids and superfluidity in liquids. This indicates a deep underlying unity, demonstrated through the study of condensed matter physics. 

This is an extract from Chapter 7, Quantum Matter, in Condensed Matter Physics: A Very Short Introduction.

Philosophical perspectives on the emergence of molecular structure

 In philosophical discussions of emergence and reductionism in chemistry, molecular structure has received significant attention and debate. Sometimes molecular structure is used to justify strong emergence, i.e., that molecular cannot be predicted, even in principle, solely from quantum theory.

Primas was one of the first to claim that molecular structure could not be reduced to quantum physics. Consider the following statements.

“From a physical point of view the crucial point of a Born–Oppenheimer description is not a simplification of the mathematical problem, but the replacement of the basic theory by a related but qualitatively new one…

[the structure of benzene] does not exist in a full quantum-theoretical description since electrons and nuclei are entangled by Einstein-Podolsky–Rosen correlations. The concept of molecular structure does not follow from first principles - all molecules with the same empirical formula have the same Schrödinger equation, so that, at this level, the shape of a molecule as the main feature of molecular chemistry is simply not in evidence. In a quantum theoretical description the molecular shape emerges by abstracting from the actually existing Einstein-Podolsky–Rosen correlations between the electrons and the nuclei. Historically, the structure concept has been introduced into quantum chemistry by the so called Born-Oppenheimer approximation. But this terminology is misleading since the main issue is not an approximation, but the breaking of a holistic symmetry.”

I have italicised claims that are contestable and that I will discuss further below.

Cartwright has given philosophical arguments as to why chemistry cannot be reduced to physics. In this context, she claims (pp. 106-7)

“The typical method of quantum-mechanical treatment of molecules begins with the Born–Oppenheimer approximation…

This approximation treats the atomic nucleus as a classical particle. But this fundamentally violates quantum mechanics which, following the Heisenberg uncertainty principle, maintains that we cannot have a simultaneous assignment of fixed positions and fixed momenta. The approximations that provide the reduction violate the very theory that the chemistry is being reduced to… the success of quantum chemistry relies fundamentally on assumptions that belong to classical chemistry.” 

This claim that the BOA violates the Heisenberg uncertainty principle was rebutted in an earlier post and discussed in more detail by Huggett et al. Nevertheless, Lombardi et al. are not satisfied by the rebuttal.

Hendry claimed molecular structure is evidence of strong emergence and/or downward causation. In a similar spirit, Ellis and Drossel argued that crystal structures in solid state physics are evidence of strong emergence. The arguments of Hendry have been criticised by Seifert. The arguments centre around the fact that the molecular structure is a classical entity and a concept that is imposed, whereas a logically self-consistent approach would treat both electrons and nuclei quantum mechanically. It is claimed that the existence of molecular structures is assumed and not derived in quantum chemistry calculations as they assume the Born-Oppenheimer approximation (BOA). 

Scerri responded to these arguments claiming that chemistry (particularly the concept of molecular structure) is irreducible to quantum physics. He claimed these arguments are not valid because they misunderstand the role of the BOA. It does not violate the uncertainty principle and in practice chemists can and do perform non-BOA approximations. 

Fortin et al. rejected the view that decoherence can explain isomerism, as decoherence does not resolve issues associated with the quantum measurement problem. 

Franklin and Seifert claim “the problem of molecular structure just is the quantum measurement problem.” This is debatable. Most molecular structures can be understood in terms of the nuclear probability density having a unique maximum and decoherence then is not relevant. Decoherence and the collapse of the nuclear wavefunction are only relevant in systems such as ammonia and stereoisomers in which there are molecular structures with equal energy and separated by high energy barriers.

I now respond to some of the contestable claims of Primas.

“electrons and nuclei are entangled by Einstein-Podolsky–Rosen correlations”

It is possible to quantify and calculate the amount of entanglement between electrons and nuclei in a specific quantum state. In an EPR state the entanglement is maximal. In the BOA wavefunction entanglement is present, but is absent in the crude BOA. The entanglement has been estimated in benzene and is very small. The only molecules where the entanglement may be significant are those, such as isomers, where there are two degenerate molecular structures and the overlap of the associated nuclear wavefunctions is small (i.e., the tunnel splitting is small). But then, in most chemical situations decoherence will wash out this entanglement.

“all molecules with the same empirical formula have the same Schrödinger equation, so that, at this level, the shape of a molecule as the main feature of molecular chemistry is simply not in evidence.”

This is the problem of isomers. It is resolved because isomers are present in the solution to the Schrödinger equation, as I argued earlier.

“the crucial point of a Born–Oppenheimer description is not a simplification of the mathematical problem, but the replacement of the basic theory by a related but qualitatively new one… the main issue is not an approximation, but the breaking of a holistic symmetry.”

This seems subjective to me. I see the BOA as just a well-justified approximation. The electrons and nuclei are treated differently because they are. They have vastly different masses and this affects how they can be treated in any solution to the full Hamiltonian. Nevertheless, the BOA is a quantum theory and the nuclei are described by a wavefunction.

As discussed earlier, for small molecules in practise it is no longer necessary to use the BOA and the electrons and nuclei can be treated on an equal footing. Molecular structure is present in solutions to the full Schrödinger equation.

I wonder if the objection to use of the BOA is any different to the use of approximations in other theories? For example, consider theoretical treatments of the motion of planets in the solar system. The effects of all the planets are not treated on an equal footing. The effect of other planets on a planet of interest are treated perturbatively.

In conclusion, the arguments that molecular structure is evidence of strong emergence are weak. Some confusion may partly arise from misinterpreting the significance of the following valid observations.

i. Molecular structures were first conjectured before quantum theory was proposed.

ii. The BOA was proposed to explain molecular structure from quantum theory.

iii. Today, almost all calculations of molecular structure assume BOA.

iv. Chemists talk about molecular structures largely in classical not quantum terms.

However, the scientific reality is that for small molecules their structure, can be understood, described, and calculated in purely quantum terms. Yet, that understanding provides a strong justification for the validity of the BOA and for the convenience of using classical language to describe molecular structure.

I stress that the weakness of the arguments for the strong emergence of molecular structure, does not mean that an emergent perspective is not relevant to chemistry. Molecular structure is emergent, when defined in terms of novelty. This leads to effective theories defined in terms of potential energy surfaces. Furthermore, as the next section argues chemistry exhibits novel properties, concepts, and theories that are not present in physics.

This post is extracted from Section 15, of my review article "Emergence: from physics to biology, sociology, and computer science."

Tony Leggett (1938-2026): condensed matter theorist

Tony Leggett died last week. The New York Times has a nice obituary. One measure of his influence on me is that more than 20 posts on this blog feature his work. He received the Nobel Prize in 2003 for developing the theory of superfluid 3He.

In 1972, a graduate student at Cornell, Doug Osheroff, discovered a phase transition around a temperature of 2 mK in liquid 3He. In the 1960s liquid 3He was established to be a Fermi liquid that was beautifully described by Landau's theory. Osheroff and his advisors, David Lee and Robert Richardson, incorrectly identified the phase transition as arising from antiferromagnetic order in the solid phase of 3He.

However, Leggett argued that it was actually due to superfluidity that there were two distinct superfluid phases, A and B, with different order parameters. 

Lee, Osheroff, and Richardson shared the Nobel Prize in 1996 for their discovery.

Leggett was primed to make rapid progress, as in 1965 and 1966 he had written three papers about superfluidity in liquid 3He, albeit assuming s-wave pairing. Indeed, by 1975 he wrote a comprehensive review article on the two superfluid phases.

For many reasons superfluid 3He was significant for the broader field of condensed matter. BCS showed that in elemental metals, superconductivity resulted from Cooper pairing of electrons due to an attractive electron-phonon interaction.  The order parameter (Cooper pair wave function) had s-wave spin singlet symmetry.

In contrast, superfluid 3He showed that Cooper pairing could also occur in a neutral Fermi liquid, and have non-trivial symmetry, i.e., p-wave symmetry and spin triplet. The order parameter has 18 components, compared to only 2 for elemental superconductors. There is spontaneous symmetry breaking of the local gauge symmetry, and spin or orbital rotational symmetries. 

The Cooper pairing in superfluid 3He is not due to a fermion-phonon interaction but due to spin fluctuations.

The fact that Cooper pairing was possible for different symmetries and mechanisms than for elemental superconductors was significant in that it meant it was reasonable to consider this possibility for superfluidity in neutron stars, and superconductivity in cuprates, strontium ruthenate, heavy fermions, and organic charge transfer salts.

There is rich physics associated with the symmetry breaking: 18 collective modes of the order parameter, textures such as boojums, and exotic vortex cores. For vortices, there is also some (controversial) connection to cosmic strings, including experiments that test the Kibble-Zurek mechanism and the electro-weak phase transition in the early universe.

Aside: My Ph.D. thesis was on the theory of the non-linear interaction of zero sound with the order parameter collective modes in the B-phase.

Leggett's development of the theory of superfluid 3He was amazing and certainly worthy of a Nobel. However, I think he made an even greater contribution to physics through his work on the theory of macroscopic quantum effects in Josephson junctions. This work was the basis for the experimental work that was honoured with the Nobel Prize last year.

With his student Amir Caldeira, Leggett performed concrete calculations of the effects of decoherence on quantum tunnelling in Josephson junctions.

[The NY Times obituary mistakenly says this work began after Leggett moved to Urbana. It was done while he was still at Sussex].

The formalism they developed involving the spectral density is the basis for most theoretical treatments of decoherence in superconducting qubits. A relevant toy model is the spin-boson model, and in 1987 Leggett published a seminal (but rather dense) review on the subject.

Leggett aided our understanding of cuprate superconductors. He contributed to the theoretical ideas that were the basis of the phase-sensitive measurements that established the d-wave nature of the order parameter. He also showed that experiments with inconsistent with  Anderson's interlayer tunneling theory.

I recommend reading Leggett's own scientific autobiography, Matchmaking Between Condensed Matter and Quantum Foundations, and Other Stories: My Six Decades in Physics and his book, The Problems of Physics

2025 Nobel Prize in Physics: Macroscopic quantum effects

John Clarke, Michel H. Devoret, and John M. Martinis received the prize  “for the discovery of macroscopic quantum mechanical tunnelling and energy quantisation in an electric circuit.”

The work was published in three papers in PRL in 1984 and 1985. The New York Times has a nice discussion of the award, including comments from Clarke, Martinis, Tony Leggett, and Steve Girvin.

There is some rich, subtle, and beautiful physics here. As a theorist, I comment on the conceptual and theoretical side, but don't want to minimise that doing the experiments was a technical breakthrough.

The experiments were directly stimulated by Tony Leggett, who, beginning in the late 70s, championed the idea that Josephson junctions and SQIDs could be used to test whether quantum mechanics was valid at the macroscopic level. Many in the quantum foundations community were sceptical. Leggett and Amir Caldeira, performed some beautiful, concrete, realistic calculations of the effect of decoherence and dissipation on quantum tunneling in SQUIDs. The results suggested that macroscopic tunneling should be observable.

Aside: Leggett rightly received a Nobel in 2003 for his work on the theory of superfluid 3He. Nevertheless, I believe his work on quantum foundations is even more significant.

Subtle point 1. What do we mean by a macroscopic quantum state?

It is commonly said that superconductors and superfluids are in a macroscopic quantum state. Signatures are the quantisation of magnetic flux in a superconducting cylinder and how the current through a Josephson junction oscillates as a function of the magnetic flux through the junction. I discuss this in the chapter on Quantum Matter in my Very Short Introduction.

Leggett argued that these experiments are explained by the Josephson equations, which treat the phase of the superconducting order parameter as a classical variable. For example, in a SQUID, it satisfies a classical dynamical equation. 

If the state is truly quantum, then the phase variable should be quantised.

Aside: a nice microscopic derivation, starting from BCS theory and using path integrals, of the effective action to describe the quantum dynamics was given in 1982 by Vinay Ambegaokar, Ulrich Eckern, Gerd Schön

Subtle point 2. There are different signatures of quantum theory: energy level quantisation, tunnelling, coherence (interference), and entanglement.

In 1984-5, Clarke, DeVoret, and Martinis observed the first two. Macroscopic quantum coherence is harder to detect and was only observed in 2000. 

In a nice autobiographical article

Matchmaking Between Condensed Matter and Quantum Foundations, and Other Stories: My Six Decades in Physics

Leggett commented in 2020,

Because of the strong prejudice in the quantum foundations community that it would never be possible to demonstrate characteristically quantum-mechanical effects at the macroscopic level, this assertion made us [Leggett and Garg, 1985] the target of repeated critical comments over the next few years. Fortunately, our experimental colleagues were more open-minded, and several groups started working toward a meaningful experiment along the lines we had suggested, resulting in the first demonstrations (29, 30) of MQC [Macroscopic Quantum Coherence] in rf SQUIDs (by then rechristened flux qubits) at the turn of the century. However, it would not be until 2016 that an experiment along the lines we had suggested (actually using a rather simpler protocol than our original one) was carried out (31) and, to my mind, definitively refuted macrorealism at that level.  

I find it rather amusing that nowadays the younger generation of experimentalists in the superconducting qubit area blithely writes papers with words like “artificial atom” in their titles, apparently unconscious of how controversial that claim once was.

Two final comments on the sociology side.

Superconductivity and superfluidity have now been the basis for Nobel Prizes in six years and four years, respectively.

The most widely cited of the three PRLs that were the basis of the Prize is the one on quantum tunnelling with about 500 citations on Google Scholar. (In contrast, Devoret has more than 20 other papers that are more widely cited). From 1986 to 1992 it was cited about a dozen times per year. Between 1993 and 2001 is was only cited a total of 30 times. Since, 2001 is has been cited about 20 times per year.

This is just one more example of how citation rates are a poor measure of the significance of work and a predictor of future success.

Nobel Prize predictions for 2025

 This week Nobel Prizes will be announced. I have not done predictions since 2020. This is a fun exercise. It is also good to reflect on what has been achieved, including outside our own areas, and big advances from the past we may now take for granted.

Before writing this I looked at suggestions from readers of Doug Natelson's blog, nanoscale views, an article in Physics World, predictions from Clarivate based on citations, and recent recipients of the Wolf Prize.

Please enter you own predictions below.

Although we know little about how the process actually works or the explicit criteria used, I have a few speculative suggestions and observations.

1. The Wolf Prize is often a precursor.

2. Every now and then, they seem to surprise us.

3. Every few years, the physics committee seems to go for something technological, sometimes arguably outside physics, perhaps to remind people how important physics is to modern technology and other areas of science.

4. They seem to spread the awards around between different areas of physics.

5. Theory only gets awards when it has led to well-established experimental observations. Brilliant theoretical discoveries that motivate large research enterprises (more theory and experimental searches) are good enough. This is why predictions based on citation numbers may be misleading.

6. Once an award has been made on one topic, it is unlikely that there will be another award for a long time, if ever, on that same topic. In other words, there is a high bar for a second award.

7. I don't think the logic is to pick an important topic and then choose who should get the prize for the topic. This approach works against topics where many researchers independently made contributions that were all important. The awardee needs to be a standout who won't be a debatable choice.

What do you think of these principles?

For some of the above reasons, I discuss below why I am sceptical about some specific predictions.

My top prediction for physics is Metamaterials with negative refractive index, going to John Pendry (theory) and David Smith (experiment). This is a topic I know little about.

Is it just a matter of time before twisted bilayer graphene wins a prize? This might go to Allan MacDonald (theory) and Pablo Jarillo-Herrero (experiment). They recently received a Wolf Prize. One thing that convinced me of the importance of this discovery was a preprint on moiré WSe2 with beautiful phase diagrams such as this one.

The level of control is truly amazing. Helpful background is the recent Physics Today article by Bernevig and Efetov.

This is big enough to overcome 6. and the earlier prize for graphene.

Unfortunately, my past prediction/wish of Kondo and heavy fermions won't happen as Jun Kondo died in 2022. This suggestion also always went against Principle 6, with the award to Ken Wilson citing his solution of the Kondo problem.

The prediction of Berry and Aharonov for topological phases in quantum mechanics is reasonable, except for questions about historical precursors.

The prediction of topological insulators is going against 6. and the award to Haldane in 2016.

Clarivate's predictions of DiVincenzo and Loss (for qubits based on electron spin in quantum dots) goes against 5. and 7. It is just one of many competing proposals for a scaleable quantum computer and a large-scale device is still elusive.

Predictions of a prize for quantum algorithms (Shor, Deutsch, Brassard, Bennett) go against 5. 

Chemistry 

I don't know enough chemistry to make meaningful predictions. On the other hand, in 2019 I did correctly predicted John Goodenough for lithium batteries.  I do like the prediction from Clarivate for Biomolecular condensates (Brangwynne, Hyman, and Rosen). I discussed them briefly in my review article on emergence.

What do you think about my 7 "principles"?

What are your predictions?

My review article on emergence

I just posted on the arXiv a long review article on emergence

Emergence: from physics to biology, sociology, and computer science

The abstract is below.

I welcome feedback. 

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Many systems of interest to scientists involve a large number of interacting parts and the whole system can have properties that the individual parts do not. The system is qualitatively different to its parts. More is different. I take this novelty as the defining characteristic of an emergent property. Many other characteristics have been associated with emergence are reviewed, including universality, order, complexity, unpredictability, irreducibility, diversity, self-organisation, discontinuities, and singularities. However, it has not been established whether these characteristics are necessary or sufficient for novelty. A wide range of examples are given to show how emergent phenomena are ubiquitous across most sub-fields of physics and many areas of biology and social sciences. Emergence is central to many of the biggest scientific and societal challenges today. Emergence can be understood in terms of scales (energy, time, length, complexity) and the associated stratification of reality. At each stratum (level) there is a distinct ontology (properties, phenomena, processes, entities, and effective interactions) and epistemology (theories, concepts, models, and methods). This stratification of reality leads to semi-autonomous scientific disciplines and sub-disciplines. A common challenge is understanding the relationship between emergent properties observed at the macroscopic scale (the whole system) and what is known about the microscopic scale: the components and their interactions. A key and profound insight is to identify a relevant emergent mesoscopic scale (i.e., a scale intermediate between the macro- and micro- scales) at which new entities emerge and interact with one another weakly. In different words, modular structures may emerge at the mesoscale. Key theoretical methods are the development and study of effective theories and toy models. Effective theories describe phenomena at a particular scale and sometimes can be derived from more microscopic descriptions. Toy models involve minimal degrees of freedom, interactions, and parameters. Toy models are amenable to analytical and computational analysis and may reveal the minimal requirements for an emergent property to occur. The Ising model is an emblematic toy model that elucidates not just critical phenomena but also key characteristics of emergence. Many examples are given from condensed matter physics to illustrate the characteristics of emergence. A wide range of areas of physics are discussed, including chaotic dynamical systems, fluid dynamics, nuclear physics, and quantum gravity. The ubiquity of emergence in other fields is illustrated by neural networks, protein folding, and social segregation. An emergent perspective matters for scientific strategy, as it shapes questions, choice of research methodologies, priorities, and allocation of resources. Finally, the elusive goal of the design and control of emergent properties is considered.

Emergence and quantum theories of gravity

Einstein’s theory of General Relativity successfully describes gravity and large scales of length and mass. In contrast, quantum theory describes small scales of length and mass. Emergence is central to most attempts to unify the two theories. Before considering specific examples, it is useful to make some distinctions.

First, a quantum theory of gravity is not necessarily the same as a theory to unify gravity with the three other forces described by the Standard Model. Whether the two problems are inextricable is unknown.

Second, there are two distinct possibilities on how classical gravity might emerge from a quantum theory. In Einstein’s theory of General Relativity, space-time and gravity are intertwined. Consequently, the two possibilities are as follows.

i. Space-time is not emergent. Classical General Relativity emerges from an underlying quantum field theory describing fields at small length scales, probably comparable to the Planck length.

ii. Space-time emerges from some underlying granular structure. In some limit, classical gravity emerges with the space-time continuum. 

Third, there are "bottom-up" and "top-down" approaches to discovering how classical gravity emerges from an underlying quantum theory, as was emphasised by Bei Lok Hu.

Finally, there is the possibility that quantum theory itself is emergent, as discussed in an earlier post about the quantum measurement problem. Some proposals of Emergent Quantum Mechanics (EQM) attempt to include gravity.

I now mention several different approaches to quantum gravity and for each point out how they fit into the distinctions above.

Gravitons and semi-classical theory

A simple bottom-up approach is to start with classical General Relativity and consider gravitational waves as the normal modes of oscillation of the space-time continuum. They have a linear dispersion relation and move with the speed of light. They are analogous to sound waves in an elastic medium. Semi-classical quantisation of gravitational waves leads to gravitons which are a massless spin-2 field. They are the analogue of phonons in a crystal or photons in the electromagnetic vacuum. However, this reveals nothing about an underlying quantum theory, just as phonons with a linear dispersion relation reveal nothing about the underlying crystal structure.

On the other hand, one can start with a massless spin-2 quantum field and consider how it scatters off massive particles. In the 1960s, Weinberg showed that gauge invariance of the scattering amplitudes implied the equivalence principle (inertial and gravitational mass are identical) and the Einstein field equations. In a sense, this is a top-down approach, as it is a derivation of General Relativity from an underlying quantum theory. In passing, I mention Weinberg used a similar approach to derive charge conservation and Maxwell’s equations of classical electromagnetism, and classical Yang-Mills theory for non-abelian gauge fields. 

Weinberg pointed out that this could go against his reductionist claim that in the hierarchy of the sciences, the arrows of the explanation always point down, saying “sometimes it isn't so clear which way the arrows of explanation point… Which is more fundamental, general relativity or the existence of particles of mass zero and spin two?”

More recently, Weinberg discussed General Relativity as an effective field theory

"... we should not despair of applying quantum field theory to gravitation just because there is no renormalizable theory of the metric tensor that is invariant under general coordinate transformations. It increasingly seems apparent that the Einstein–Hilbert Lagrangian √gR is just the least suppressed term in the Lagrangian of an effective field theory containing every possible generally covariant function of the metric and its derivatives..."

This is a bottom-up approach. Weinberg then went on to discuss a top-down  approach:

“it is usually assumed that in the quantum theory of gravitation, when Λ reaches some very high energy, of the order of 10^15 to 10^18 GeV, the appropriate degrees of freedom are no longer the metric and the Standard Model fields, but something very different, perhaps strings... But maybe not..."

String theory 

Versions of string theory from the 1980s aimed to unify all four forces. They were formulated in terms of nine spatial dimensions and a large internal symmetry group, such as SO(32), where supersymmetric strings were the fundamental units. In the low-energy limit, vibrations of the strings are identified with elementary particles in four-dimensional space-time. A particle with mass zero and spin two appears as an immediate consequence of the symmetries of the string theory. Hence, this was originally claimed to be a quantum theory of gravity. However, subsequent developments have found that there are many alternative string theories and it is not possible to formulate the theory in terms of a unique vacuum.

AdS-CFT correspondence

In the context of string theory, this correspondence conjectures a connection (a dual relation) between classical gravity in Anti-deSitter space-time (AdS) and quantum conformal field theories (CFTs), including some gauge theories. This connection could be interpreted in two different ways. One is that space-time emerges from the quantum theory. Alternatively, the quantum theory emerges from the classical gravity theory.   This ambiguity of interpretation has been highlighted by Alyssa Ney, a philosopher of physics. In other words, it is ambiguous which of the two sides of the duality is the more fundamental. Witten has argued that AdS-CFT suggests that gauge symmetries are emergent. However, I cannot follow his argument.

Seiberg reviewed different approaches, within the string theory community, that lead to spacetime as emergent. An example of a toy model is a matrix model for quantum mechanics [which can be viewed as a zero-dimensional field theory]. Perturbation expansions can be viewed as discretised two-dimensional surfaces. In a large N limit, two-dimensional space and general covariance (the starting point for general relativity) both emerge. Thus, this shows how both two-dimensional gravity and spacetime can be emergent. However, this type of emergence is distinct from how low-energy theories emerge. Seiberg also notes that there are no examples of toy models where time (which is associated with locality and causality) is emergent.

Loop quantum gravity 

This is a top-down approach where both space-time and gravity emerge together from a granular structure, sometimes referred to as "spin foam" or a “spin network”, and has been reviewed by Rovelli. The starting point is Ashtekar’s demonstration that General Relativity can be described using the phase space of an SU(2) Yang-Mills theory. A boundary in four-dimensional space-time can be decomposed into cells and this can be used to define a dual graph (lattice) Gamma. The gravitational field on this discretised boundary is represented by the Hilbert space of a lattice SU(2) Yang-Mills theory. The quantum numbers used to define a basis for this Hilbert space are the graph Gamma,  the “spin” [SU(2) quantum number] associated with the face of each cell, and the volumes of the cells. The Planck length limits the size of the cells. In the limit of the continuum and then of large spin, or vice versa, one obtains General Relativity.

Quantum thermodynamics of event horizons

A bottom-up approach was taken by Padmanabhan. He emphasises Boltzmann's insight: "matter can only store and transfer heat because of internal degrees of freedom". In other words, if something has a temperature and entropy then it must have a microstructure. He does this by considering the connection between event horizons in General Relativity and the temperature of the thermal radiation associated with them. He frames his research as attempting to estimate Avogadro’s number for space-time.

The temperature and entropy associated with event horizons has been calculated for the following specific space-times:

a. For accelerating frames of reference (Rindler space-time) there is an event horizon which exhibits Unruh radiation with a temperature that was calculated by Fulling, Davies and Unruh.

b. The black hole horizon in the Schwarzschild metric has the temperature of Hawking radiation.

c. The cosmological horizon in deSitter space is associated with a temperature proportional to the Hubble constant H, as discussed in detail by Gibbons and Hawking.

Padmanabhan considers the number of degrees of freedom on the boundary of the event horizon, Ns, and in the bulk, Nb. He argues for the holographic principle that Ns = Nb. On the boundary surface, there is one degree of freedom associated with every Planck area, Ns = A/Lp2, where Lp is the Planck length and A is the surface area, which is related to the entropy of the horizon, as first discussed by Bekenstein and Hawking. In the bulk, classical equipartition of energy is assumed so the bulk energy E = Nb k T/2. 

Padmanabhan gives an alternative perspective on cosmology through a novel derivation of the dynamic equations for the scale factor R(t) in the Friedmann-Robertson-Walker metric of the universe in General Relativity. His starting point is a simple argument leading to 

V is the Hubble volume, 4\pi/3H^3, where H is the Hubble constant, and Lp is the Planck length. The right-hand side is zero for the deSitter universe, which is predicted to be the asymptotic state of our current universe.

He presents an argument that the cosmological constant is related to the Planck length, leading to the expression  

where mu is of order unity and gives a value consistent with observation.

Could quantum mechanics be emergent?

One of the biggest challenges in the foundations of physics is the quantum measurement problem. It is associated with a few key (distinct but related) questions.

i. How does a measurement convert a coherent state undergoing unitary dynamics to a "classical" mixed state for which we can talk about probabilities of outcomes?

ii. Why is the outcome of an individual measurement always definite for the "pointer states" of the measuring apparatus?

iii. Can one derive the Born rule, which gives the probability of a particular outcome?

Emergence of the classical world from the quantum world via decoherence

A quantum system always interacts to some extent with its environment. This interaction leads to decoherence, whereby quantum interference effects are washed out. Consequently, superposition states of the system decay into mixed states described by a diagonal density matrix. A major research goal of the past three decades has been understanding decoherence and the extent to which it does provide answers to the quantum measurement problem. One achievement is that decoherence theory seems to give a mechanism and time scale for the “collapse of the wavefunction” within the framework of unitary dynamics. However, this is not the case because decoherence is not the same as a projection (which is what a single quantum measurement is). Decoherence does not produce definite outcomes but rather statistical mixtures. Decoherence only resolves the issue if one identifies ensembles of measured states with ensembles of the decohered density matrix (the statistical interpretation of quantum mechanics). Thus, it seems decoherence only answers the first question above, but not the last two. On the other hand, Zurek has pushed the decoherence picture further and given a “derivation” of the Born rule within its framework. In other words, decoherence does not solve the quantum measurement problem: measurements always produce definite outcomes.

One approach to solving the problem is to view quantum theory as only an approximate theory. In particular, it could be an effective theory for some underlying theory valid at time and length scales much smaller than those for which quantum theory has been precisely tested by experiments. 

Emergence of quantum field theory from a “classical” statistical theory

Einstein did not accept the statistical nature of quantum theory and considered it should be derivable from a more “realistic” theory. In particular, he suggested “a complete physical description, the statistical quantum theory would …. take an approximately analogous position to the statistical mechanics within the framework of classical mechanics.”

Einstein's challenge was taken up in a concrete and impressive fashion by Stephen Adler in a book, “Quantum Theory as an Emergent Phenomenon: The Statistical Mechanics of Matrix Models as the Precursor of Quantum Field Theory”, published in 2004.  A helpful summary is given in a review by Pearle.

The starting point is "classical" dynamical variables qr and pr which are NxN matrices, where N is even. Half of these variables are bosonic, and the others are fermionic. They all obey Hamilton's equations of motion for an unspecified Hamiltonian H. Three quantities are conserved: H, the fermion number N, and (very importantly) the traceless anti-self-adjoint matrix, 

where the first term is the sum for all the bosonic variables of their commutator, and the second is the sum over anti-commutators for the fermionic variables.

Quantum theory is obtained by tracing over all the classical variables with respect to a canonical ensemble with three (matrix) Lagrange multipliers [analogues of temperature and chemical potential in conventional statistical mechanics] corresponding to the conserved quantities H, N, and C. The expectation values of the diagonal elements of C are assumed to all have the same value, hbar!

An analogy of the equipartition theorem in classical statistical mechanics (which looks like a Ward identity in quantum field theory) leads to dynamical equations (trace dynamics) for effective fields. To make these equations look like regular quantum field theory, an assumption is made about a hierarchy of length, energy, and "temperature" [Lagrange multiplier] scales, which cause the Trace dynamics to be dominated by C rather than H, the trace Hamiltonian. Adler suggests these scales may be Planck scales. Then, the usual quantum dynamical equations and the Dirac correspondence of Poisson brackets and commutators emerge. Most of the actual details of the trace Hamiltonian H do not matter; another case of universality, a common characteristic of emergent phenomena.

The “classical” field C fluctuates about its average value. These fluctuations can be identified with corrections to locality in quantum field theory and with the noise terms which appear in the modified Schrodinger equation of "physical collapse" models of quantum theory.

More recently, theorists including Gerard t’Hooft and John Preskill have investigated how quantum mechanics can emerge from other deterministic systems. This is sometimes known as the emergent quantum mechanics (EmQM) hypothesis.

Underlying deterministic systems considered include

Hamilton-Randers systems defined in co-tangent spaces of large-dimensional configuration spaces, 

neural networks,

cellular automata,

fast-moving classical variables, and the

 boundary of a local classical model with a length that is exponentially large in the number of qubits in the quantum system. 

In most of these versions of EmQM the length scale at which the underlying theory becomes relevant is conjectured to be of the order of the Planck length.

The fact that quantum theory can emerge from such a diverse range of underlying theories again illustrates universality.

The question of quantum physics emerging from an underlying classical theory is not just a question in the foundations of physics or in philosophy. Slagle points out that Emergent Quantum Mechanics may mean that the computational power of quantum computers is severely limited. He has proposed a specific experimental protocol to test for EmQM. A large number d of entangling gates (the circuit depth d) are applied to n qbits in the computational basis, followed by the inverse gates. This is followed by measurement in the computational basis. The fidelity should decay exponentially with d, whereas for EmQM will decay much faster above some critical d, for sufficiently large n.

Independent of experimental evidence, EmQM provides an alternative interpretation to quantum theory that avoids the thorny issues such as the many-worlds interpretation.

Quantum BS: piling it higher

Hans Bachor recently gave a talk at UQ, Hype and Trust in Quantum Technologies

Trust is a core value in science, trust in data, analysis, concepts, models. This is achieved in physics by open publishing, scientific discourse, testing, repeating experiments, asking critical questions and designing new tests. Fortunately, science is self-correcting in the long term. Hype includes predictions which sensationalise scientific discoveries and exaggerate the future impact. Increasing competition for funding, visibility or job security can make this more attractive. But it also erodes trust in science by the public and investors and has negative social effects on us the researchers. How can we balance them?

I think this problem more broadly reflects the way universities have become to imitate the social context they are imbedded in, rather than being a critique of those societies.

The sociologist Christian Smith eloquently described the emergence of BS in universities, several years ago.

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

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

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

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

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

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

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

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

I look forward to hearing others' reflections.

Are gravity and spacetime really emergent in AdS-CFT?

There is an interesting Scientific American article by Adam Becker

What Is Spacetime Really Made Of?

Spacetime may emerge from a more fundamental reality. Figuring out how could unlock the most urgent goal in physics—a quantum theory of gravity

It considers two different approaches to quantum gravity (loop quantum gravity and AdS-CFT beloved by string theorists). Compared to some Scientific American articles it is moderately balanced and low on hype. The article has a nice engagement with some philosophers of physics. It is clear to me how loop quantum gravity has a natural interpretation that gravity and space-time are emergent. However, that is not clear for AdS-CFT.

 The following paragraph is pertinent.

But there are other ways to interpret the latest findings. The AdS/CFT correspondence is often seen as an example of how spacetime might emerge from a quantum system, but that might not actually be what it shows, according to Alyssa Ney, a philosopher of physics at the University of California, Davis. 

“AdS/CFT gives you this ability to provide a translation manual between facts about the spacetime and facts of the quantum theory,” Ney says. “That’s compatible with the claim that spacetime is emergent, and some quantum theory is fundamental.” 

But the reverse is also true, she says. The correspondence could mean that quantum theory is emergent and spacetime is fundamental—or that neither is fundamental and that there is some even deeper fundamental theory out there. Emergence is a strong claim to make, Ney says, and she is open to the possibility that it is true. “But at least just looking at AdS/CFT, I’m still not seeing a clear argument for emergence.”

What is really fundamental in science?

What do we mean when we say something in science is fundamental? When is an entity or a theory more fundamental or less fundamental than something else? For example, are quarks and leptons more fundamental than atoms? Is statistical mechanics more fundamental than thermodynamics? Is physics more fundamental than chemistry or biology? In a fractional quantum Hall state, are electrons or the fractionally charged quasiparticles more fundamental?

Answers depend on who you ask. Physicists such as Phil Anderson, Steven Weinberg, Bob Laughlin, Richard Feynman, Frank Wilczek, and Albert Einstein have different views.

In 2017-8, the Foundational Questions Institute (FQXi) held an essay contest to address the question, “What is Fundamental?” Of the 200 entries, 15 prize-winning essays have been published in a single volume. The editors give a nice overview in the Introduction.

This post is mostly about the essay, Fundamental? of the first prize winner, Emily Adlam, a philosopher of physics. She contrasts two provocative statements.

Fundamental means we have won. The job is done and we can all go home.

Fundamental means we have lost. Fundamental is an admission of defeat.

This raises the question of whether being fundamental is objective or subjective.

Examples are given from scientific history to argue that what is considered to be fundamental has changed with time. The reductionism has led to the drive to explain everything in terms of smaller and smaller entities, that are deemed 'more fundamental". But we find that smaller does not always mean simpler.

Perhaps we should ask what needs explaining and what constitutes a scientific explanation. For example, Adlam asks whether explaining the fact that the initial state of the universe had a low entropy [the "past hypothesis"] is really possible or should be an important goal.

She draws on the issue of the distinction between objective and subjective probabilities. Probabilities in statistical mechanics are subjective: they are a statement about our own ignorance about the details of the motion of individual atoms and not any underlying randomness in nature. In contrast, probabilities in quantum theory reflect objective chance.

as realists about science we must surely maintain that there is a need for science to explain the existence of the sorts of regularities that allow us to make reliable predictions... but there is no similarly pressing need to explain why these regularities take some particular form rather than another. Yet our paradigmatic mechanical explanations do not seem to be capable of explaining the regularity without also explaining the form, and so increasingly in modern physics we find ourselves unable to explain either. 

It is in this context that we naturally turn to objective chance. The claim that quantum particles just have some sort of fundamental inbuilt tendency to turn out to be spin up on some proportion of measurements and spin down on some proportion of measurements does indeed look like an attempt to explain a regularity (the fact that measurements on quantum particles exhibit predictable statistics) without explaining the specific form (the particular sequence of results obtained in any given set of experiments). But given the problematic status of objective chance, this sort of nonexplanation is not really much better than simply refraining from explanation at all. 

Why is it that objective chances seem to be the only thing we have in our arsenal when it comes to explaining regularities without explaining their specific form? It seems likely that part of the problem is the reductionism that still dominates the thinking of most of those who consider themselves realists about science

In summary, (according to the Editors) Adlam argues that "science should be able to explain the existence of the sorts of regularities that allow us to make reliable predictions. But this does not necessarily mean that it must also explain why these regularities take some particular form." 

we are in dire need of another paradigm shift. And this time, instead of simply changing our attitudes about what sorts of things require explanation, we may have to change our attitudes about what counts as an explanation in the first place. 

Here, she is arguing that what is fundamental is subjective, being a matter of values and taste.

In our standard scientific thinking the fundamental is elided with ultimate truth: getting to grips with the fundamental is the promised land, the endgame of science. 

She then raises questions about the vision and hopes of scientific reductionists. 

In this spirit, the original hope of the reductionists was that things would get simpler as we got further down, and eventually we would be left with an ontology so simple that it would seem reasonable to regard this ontology as truly fundamental and to demand no further explanation. 

But the reductionist vision seems increasingly to have failed. 

When we theorise beyond the standard model [BSM] we usually find it necessary to expand the ontology still more: witness the extra dimensions required to make string theory mathematically consistent.

It is not just strings. Peter Woit has emphasised how BSM theories, such as supersymmetry, introduce many more particles and parameters.

... the messiness deep down is a sign that the universe works not ‘bottom-up’ but rather ‘top-down,’ ... in many cases, things get simpler as we go further up.

Our best current theories are renormalisable, meaning that many different possible variants on the underlying microscopic physics all give rise to the same macroscopic physical theory, known as an infrared fixed point. This is usually glossed as providing an explanation of why it is that we can do sensible macroscopic physics even without having detailed knowledge of the underlying microscopic theories. 

For example, elasticity theory, thermodynamics and fluid dynamics all work without knowing anything about atoms, statistical mechanics, and quantum theory.

But one might argue that this is getting things the wrong way round: the laws of nature don’t start with little pieces and build the universe from the bottom up, rather they apply simple macroscopic constraints to the universe as a whole and work out what needs to happen on a more fine-grained level in order to satisfy these constraints.

This is rather reminiscent of Laughlin's views about what is fundamental.

Finally, I mention two other essays that I look forward to reading as I think they make particularly pertinent points.

Marc Séguin (Chap. 6) distinguishes "between epistemological fundamentality (the fundamentality of our scientific theories) and ontological fundamentality (the fundamentality of the world itself, irrespective of our description of it)."

"In Chap. 12, Gregory Derry argues that a fundamental explanatory structure should have four key attributes: irreducibility, generality, commensurability, and fertility."

[Quotes are from the Introduction by the Editors].

Some would argue that the Standard Model is fundamental, at least on some level. But it involves 19 parameters that have to be fixed from experiment. Related questions about the Fundamental Constants, have been explored in a 2007 paper by Frank Wilczek.

Again, I thank Peter Evans for bringing this volume to my attention.

Two distinctly different routes to a quantum theory of gravity

 Emergence in condensed matter physics may provide some valuable insights into the elusive search for a quantum theory of gravity. There was a helpful discussion by Bei Lok Hu  in Emergent/quantum gravity: macro/micro structures of spacetime

Hu makes a distinction between two approaches that he characterises as "bottom-up" and "top-down". Both have the common goal of understanding how space-time and Einstein's classical theory of gravity can emerge from some more "fundamental" theory that describes physics at higher energies and shorter distances, such as the Planck scale.

1. Going from the micro- to the macro-

Examples of this approach are string theory (a la Schwarz, Green, and Witten) and loop quantum gravity. The respective microscopic entities are strings and spin foam. This approach is motivated by the success of the standard model of elementary particles and gauge fields. One starts with a well-defined "classical" action inspired by symmetry (and broken symmetry) and uses quantum field theory to calculate observable properties. Generally, one is quantising the classical theory of gravity. Perhaps, we should not be surprised that this approach has not borne fruit as we know from condensed matter that deducing emergent (macro-)properties from microscopic theory is extremely hard.

This picture is taken from a recent Scientific American article

Hu also has the following valuable insight about whether quantising classical theory is the right approach.

[quantising the classical theory of spacetime] will not lead to a microscopic theory of spacetime. In the analogy of a crystal made of atoms quantizing the vibrational models yields phonons, not atoms. Finding the atomic structure of matter does not come from simply quantizing its collective degrees of freedom, but takes a very different path.

àMä?ÍaËdÌMä£ã􏰹î2Ê􏰅à­Ò?ÍEÊVáHu calls this approach "top-down" as it involves going from high energies down to low energies. I found this confusing as I tend to think of this approach means going up in distance, i.e. from the bottom structures (small distances) up to the top structures (long distances). 

2. Going from the macro- to the micro-

This approach is also ambitious. By considering the macroscopic theory (classical space-time and General Relativity) and the associated observed structures the goal is to deduce something about the microscopic theory, even without probes to investigate reality on very short distance scales. 

History suggests this is not completely fanciful. Consider for example the path to the belief that liquids and crystals were actually made of atoms. Einstein's theory of Brownian motion and Perrin's experiments were not at the atomic scale. People had deduced that crystals were made of arrays of atoms before the discovery of x-ray diffraction from crystals.

Space-time and the metric are viewed as collective variables, like order parameters in condensed matter.

Hu calls this approach "bottom-up", advocates it, and explores some possible ways to pursue it.

I thank Gerard Milburn for rekindling my interest in these issues.

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.

Quantum matters for the public

I have now finished my first draft of  Chapter 7 of Condensed Matter Physics: A Very Short Introduction. The main purpose of the chapter is to introduce quantum states of matter. It is arguably the most challenging of the chapters to write and to understand. But, it is potentially the most fascinating.

I welcome comments and suggestions. However, bear in mind that my target audience is not the typical reader of this blog, but rather your non-physicist friends and family.

I think it still needs a lot of work, particularly to be less technical. For example, I should probably drop Aharonov Bohm ...

The goal is for the chapter to be interesting, accessible, and bring out the excitement and importance of condensed matter physics.

Why Josephson matters

Reflecting on macroscopic quantum effects in condensed matter I have come to the view that Brian Josephson is a key figure. But, the observation of magnetic flux quantisation in superconducting cylinders is also a landmark.

The significance of Josephson is nicely laid out in a fascinating article published by in Physics Today in 2001 by Donald G. McDonald

The Nobel Laureate Versus the Graduate Student 

John Bardeen, the leading condensed matter theorist of his day, was quite wrong when he dismissed a startling prediction by the unknown Brian Josephson. 

The article nicely lays out several important precursors to Josephson's work that all occurred after BCS theory in 1957.

1. The experimental (unanticipated) discovery by Ivar Giaever in 1960 of single-particle tunneling in SIS junctions [superconductor-insulator-superconductor sandwiches]. I-V curves clearly showed the structure of the BCS energy gap.

[Aside. This discovery was also laid the foundation for John Rowell's tunneling experiments that allowed a quantitative (strong-coupling BCS) analysis of the electron-phonon interaction responsible for superconductivity.]

2. The discovery by Hans Meissner [not the discoverer of the Meissner effect!] in 1960 of the proximity effect, where superconductivity is induced in a non-superconducting metal, by close proximity to a superconductor.

3. The discovery in 1961 by two independent experimental groups that the magnetic flux inside a cylinder was quantised in units of h/2e where h is Planck's constant and e is the electronic charge. This effect had been predicted by Fritz London in 1948, albeit without the factor of 2.

These experiments provided ``the first direct demonstration of a macroscopic quantum effect.''

The data above is from a 1971 paper, observing flux quantisation within one-half of a per cent.

A nice article on the history of the discovery is

50 Years of Fluxoid Quantization: 2e or Not 2e by Dietrich Einzel 

 Aside. These experiments also clearly showed the physical nature of the magnetic vector potential, A, and illustrated the Aharonov-Bohm effect.

4. Josephson's attendance at a series of lectures ``Concepts in Solids" that Phil Anderson gave to graduate students at Cambridge in 1961-1962. In particular, at the end, Anderson introduced the concept of broken symmetry as an organising principle to describe ``condensed systems" such as antiferromagnets, superfluid 4He, ferroelectrics, and superconductors.

Distinctly quantum phenomena are tunneling, superposition (and the associated coherence and interference), and entanglement. Josephson junctions can be used to illustrate all of these at the macroscopic scale.

This is explored in a nice autobiographical article by Tony Leggett.

Matchmaking Between Condensed Matter and Quantum Foundations, and Other Stories: My Six Decades in Physics

Because of the strong prejudice in the quantum foundations community that it would never be possible to demonstrate characteristically quantum-mechanical effects at the macroscopic level, this assertion made us [Leggett and Garg] the target of repeated critical comments over the next few years. Fortunately, our experimental colleagues were more open-minded, and several groups started working toward a meaningful experiment along the lines we had suggested, resulting in the first demonstrations (29, 30) of MQC [Macroscopic Quantum Coherence] in rf SQUIDs (by then rechristened flux qubits) at the turn of the century. However, it would not be until 2016 that an experiment along the lines we had suggested (actually using a rather simpler protocol than our original one) was carried out (31) and, to my mind, definitively refuted macrorealism at that level. I find it rather amusing that nowadays the younger generation of experimentalists in the superconducting qubit area blithely writes papers with words like “artificial atom” in their titles, apparently unconscious of how controversial that claim once was.