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.

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.

Are gravity and space-time emergent?

Attempts to develop a quantum theory of gravity continue to falter and stagnate. Given this, it is worth considering approaches that start with what we know about gravity at the macroscale and investigate whether it provides any hints about some underlying more microscopic theory. One such approach was taken by Thanu Padmanabhan and is elegantly described and summarised in a book chapter.

Gravity and Spacetime: An Emergent Perspective

Insights about microphysics from macrophysics 

Padmanabhan 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.

The approach of trying to surmise something about microphysics from macrophysics has a long and fruitful history, albeit probably with many false starts that we do not hear about. Kepler's snowflakes may have been the first example. Before people were completely convinced about the existence of atoms, the study of crystal facets and of Brownian motion provided hints of the atomic structure of matter. Planck deduced the existence of the quantum from the thermodynamics of black-body radiation.

Arguably, the first definitive determination of Avogadro's number was from Perrin's experiments on Brownian motion which involved macroscopic measurements.

Comparing classical statistical mechanics to bulk thermodynamic properties gave hints of an underlying quantum structure to reality. The Sackur-Tetrode equation for the entropy of an ideal gas hints at the quantisation of phase space. The Gibbs paradox hints that fundamental particles are indistinguishable. The third law of thermodynamics hints at the idea of quantum degeneracy.

Puzzles in classical General Relativity

Padmanabhan reviews aspects of the theory that he considers some consider to be "algebraic accidents" but he suggests that they may be hints to something deeper. These include the role of boundary terms in variational principles and he suggests hint at a classical holography (bulk behaviour is determined by the boundary). He also argues that the metric of space-time should not be viewed as a field, contrary to most attempts to develop a quantum field theory for gravity.

Thermodynamics of horizons

The key idea that is exploited to find the microstructure is that can define a temperature and an entropy for null surfaces (event horizons). These have been calculated for specific systems (metrics) including the following:

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

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

The cosmological horizon in deSitter space is associated with a temperature proportional to the Hubble constant H. [This was discussed in detail by Gibbons and Hawking in 1977].

Estimating Avogadro's number for space-time

Consider the number of degrees of freedom on the boundary, N_s, and in the bulk, N_b. 

On the boundary surface, there is one degree of freedom associated with every Planck area (L_p^2) where L_p is the Planck length, i.e,  N_s = A/ L_p^2, where A is the surface area, which is related to the entropy of the horizon (cf. Bekenstein and Hawking).

In the bulk equipartition of energy is assumed so the bulk energy E = N_b k T/2 and he presents an argument for the holographic principle that N_s = N_b.

An alternative perspective on cosmology 

He presents 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, 4pi/3H^3, where H is the Hubble constant, and L_P 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.

Possible insights about the cosmological constant

One of the biggest problems in theoretical physics is to explain why the cosmological constant has the value that it does.

There are two aspects to the problem.
1. The measured value is so small, 120 orders of magnitude smaller than what one estimates based on the quantum vacuum energy!

2. The measured value seems to be finely tuned (to 120 significant figures!) to the value of the mass energy.

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

where mu is of order unity.

Details of his proposed solution are also discussed here.

I am not technically qualified to comment on the possible validity or usefulness of Padmanabhan's perspective and results. However, I think it provides a nice example of a modest and conventional scientific alternative to radical approaches, such as the multiverse, or ideas that seem to be going nowhere such as AdS/CFT that are too often invoked or clung onto to address these big questions. 

Aside. In the same book, there is also a short and helpful chapter, Quantum Spacetime on loop quantum gravity by Carlo Rovelli. He explicitly identifies the "atoms" of space-time as the elements of "spin foam".

Steven Weinberg's radical change of mind

What is a fundamental theory? As we go to smaller and smaller distances and higher energies we keep finding new entities: atoms, electrons, nuclei, neutrons, protons, quarks, gluons, ...When will it stop?

If we look at a theory, such as a quantum field theory, at a particular energy and length scale, there may be hints that something is going on, such as the existence of new entities, at higher energies. One way to approach this problem is through the renormalisation group and to look at how coupling constants behave as the energy increases. If they start to blow up (diverge) is that a hint of something? But, this requires starting with a renormalisable theory...

An alternative approach is to start with an effective theory that one assumes [hypothesises] is valid at some limited energy scale. This goes against a previous dogma that one should only study renormalisable theories. Amongst elementary particle theorists, led by Steven Weinberg, there was a significant shift in perspective in the 1970s.

In a paper published in 2016, Effective field theory, past and future, Steven Weinberg reflected on how he changed his mind about renormalisability being a fundamental requirement for quantum field theories and how he came to the view that the Standard Model should be viewed as an effective field theory. Here are some quotes from the article. He first describes how in the 1960s he developed a field theory to describe the interactions of nucleons and pions.

"During this whole period, effective field theories appeared as only a device for more easily reproducing the results of current algebra. It was difficult to take them seriously as dynamical theories, because the derivative couplings that made them useful in the lowest order of perturbation theory also made them nonrenormalizable, thus apparently closing off the possibility of using these theories in higher order. 

My thinking about this began to change in 1976. I was invited to give a series of lectures at Erice that summer, and took the opportunity to learn the theory of critical phenomena by giving lectures about it. In preparing these lectures, I was struck by Kenneth Wilson’s device of “integrating out” short-distance degrees of freedom by introducing a variable ultraviolet cutoff, ...

Non-renormalizable theories, I realized, are just as renormalizable as renormalizable theories.

For me in 1979, the answer involved a radical reconsideration of the nature of quantum field theory.

The advent of effective field theories generated changes in point of view and suggested new techniques of calculation that propagated out to numerous areas of physics, some quite far removed from particle physics. Notable here is the use of the power-counting arguments of effective field theory to justify the approximations made in the BCS theory of superconductivity. Instead of counting powers of small momenta, one must count powers of the departures of momenta from the Fermi surface. Also, general features of theories of inflation have been clarified by re-casting these theories as effective field theories of the inflaton and gravitational fields. 

Perhaps the most important lesson from chiral dynamics was that we should keep an open mind about renormalizability. The renormalizable Standard Model of elementary particles may itself be just the first term in an effective field theory that contains every possible interaction allowed by Lorentz invariance and the SU (3) × SU (2) × U (1) gauge symmetry, only with the non-renormalizable terms suppressed by negative powers of some very large mass M...

... 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...

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..."

In 2021 Weinberg gave a talk, with a similar point of view, which inaugurated an international seminar series [online during covid-19]. 

In response to that talk, Peter Woit has a blog post where he objects to Weinberg's point of view that the Standard Model is "just" an effective theory, only valid at low energies.

Reviews of Modern Physics recently published a review that discussed how Weinberg's perspective is worked out in detail.

The standard model effective field theory at work

Gino Isidori, Felix Wilsch, and Daniel Wyler

The discussion above fits naturally with an emergentist perspective: reality is stratified. Effective theories at one strata may have singularities around boundaries between strata, and new entities emerge, both physically and theoretically, as one moves to the next higher or lower strata.

Do arrows of explanation point down or up?

The figure above shows the stratification of objects that interest physicists. As one goes down the chain length and time scales get smaller and energy scales get larger.

A reductionist seeks to explain the objects at each strata in terms of the objects that occur at the next lower strata.

In 1987 Steven Weinberg gave a talk at the University of Cambridge at the Tercentenary Celebration of Newton's Principia.

The talk was published in Nature. Newtonianism, Reductionism, and the Art of Congressional Testimony

Part of the talk is about Weinberg's testimony to a US Congressional Committee making the case for the construction of the SSC (Superconducting Super Collider). Phil Anderson spoke against the SSC.

Weinberg argued that the SSC should be built because particle physics is "in some sense more fundamental than other areas of physics." He claims that this is because "the arrows of explanation point down", as in the diagram shown above.

A contrasting perspective is that of Andrew Steane. His book, Science and Humanity, contains the figure below.

In his picture of the explanatory relationship between physics, chemistry, and biology, Steane draws arrows pointing in both directions. The up arrow is denoted “supports [allows and physically embodies the expression of]” and the down arrow is denoted “enarches [exhibits the structures and behaviours that make sense in their own terms and are possible within the framework of].”

Weinberg's article is worth reading in full. It has many insights about science and physics worth considering, including the relationship between emergence and reductionism.

Aside: It is also reproduced in his book of essays, Facing Up: Science and Its Cultural Adversaries, published in 2001.

Effective theories in classical and quantum mechanics

Working in quantum many-body theory, I slowly learned that many key concepts and techniques have predecessors and analogues in classical systems and one-body quantum systems. Examples include Green's functions, path integrals, cumulants, the linked cluster theorem, Hubbard-Stratonavich transformation (completing the square), mean-field theory, localisation due to disorder, and BBGKY hierarchy. Learning a full-blown quantum many-body version is easier if you first understand simpler analogues.

This post is about effective theories in classical systems and one-body quantum systems, following my earlier post about effective theories in quantum field theories of elementary particles.

Michèle Levi has a pedagogical article

Effective field theories of post-Newtonian gravity: a comprehensive review

This is motivated by the use of EFTs to describe gravitational waves produced by the inspiraling and merging of binary black holes and neutron stars. She discusses the different scales involved and how there are effective theories at each scale. She also puts these EFTs in the broader context of other fields.

Analogues in one-body quantum mechanics are also discussed  in

Effective Field Theories, Reductionism and Scientific Explanation, by Stephan Hartmann

"In his beautiful book Qualitative Methods in Quantum Theory, Migdal (1977) discusses an instructive example from quantum mechanics. Let S be a system which is composed of a fast subsystem Sf and a slow subsystem Ss, characterised by two frequencies of and os. It can be shown that the effects of Sf on Ss can be taken into account effectively by adding a potential energy term to the Hamiltonian operator of Ss. In this case, as well as in many other cases, one ends up with an effective Hamiltonian operator for the subsystem characterised by the smaller frequency (or energy)."

An important example of this is the Born-Oppenheimer approximation which is based on the separation of time and energy scales associated with electronic and nuclear motion. It is used to describe and understand the dynamics of nuclei and electronic transitions in solids and molecules. The potential energy surfaces for different electronic states define an effective theory for the nuclei. Without this concept, much of theoretical chemistry and condensed matter would be incredibly difficult.

Effective quantum field theories and hierarchial reality

 Over the last hundred years, there has been a fruitful cross-fertilisation of concepts and techniques between the theory of condensed matter and the quantum theory of elementary particles and fields. Examples include spontaneous symmetry breaking, renormalisation, and BCS theory. Sometimes, these efforts have occurred in parallel and only later did people realise that two different communities were doing essentially the same thing but using different language. Other times, one community adopted ideas or techniques from the other.

Central to condensed matter theory are ideas of emergence, a hierarchy of scales, and effective theories that are valid at a particular scale. Elementary particle theorists such as Steven Weinberg often distinguish themselves as reductionists with different goals and approaches. I only recently became aware that effective field theories have become a big thing in the elementary particle community, and Weinberg has been one of the leaders of this!

There is a helpful article in the CERN Courier, published just a year ago.

A theory of theories

Michèle Levi takes a tour through the past, present and future of Effective Field Theory, with applications ranging from LHC physics to cosmology.

The figure below, taken from the article, shows a hierarchy of energy scales and the corresponding effective field theories (EFTs).

n.b. Energy increases from bottom to top. [This may be confusing for condensed matter physicists, as we tend to put the high-energy theories at the bottom].

SM is the standard model

HQET is heavy quark effective theory in which the heavy quark degrees of freedom are integrated out.

EW breaking is Electro-Weak symmetry breaking which occurs on the scale of the Higgs boson.

The smallest energy scale in the figure is Lamda_QCD which is of the scale of the mass of the proton.

The standard model is now considered an effective field theory.

For the associated history and philosophy, I found this article helpful. Effective Field Theories, Reductionism and Scientific Explanation, by Stephan Hartmann

The decoupling theorem, proved by Appelquist and Carazzone in 1975, [cited 2,500 times] is central to EFTs and a hierarchy of scales. 

In its simplest case, this theorem demonstrates that for two coupled systems with different energy scales m1 and m2 (with m2 > m1) and described by a renormalisable theory, there is always a renormalisation condition according to which the effects of the physics at scale m2 can be effectively included in the theory with the smaller scale m1 by changing the parameters of the corresponding theory. The decoupling theorem implies the existence of an EFT at scale m1 which will, however, cease to be applicable once the energy gets close to m2.

There are two distinct approaches to finding effective theories at a particular scale, referred to as bottom-up and top-down approaches. 

Top-down requires one to have a theory at a higher energy scale and then integrate out the high energy degrees of freedom (fields and particles) to find the effective theory for the lower energy scale. This is what Wilson did in his RG approach to critical phenomena. Another example is how string theorists try to derive GR and the Standard Model starting with strings.

Bottom-up can always be done because one does not need to know the higher energy theory. One can often write down the Lagrangian for the EFT based on symmetry considerations and phenomenology. An example is Fermi's theory of beta decay and the weak interactions.

In a previous post, I considered Bei Lok Hu's discussion of these two different routes to developing a quantum theory of gravity.

A major outstanding challenge in the theory of elementary particles and fields is the hierarchy problem: the measured values of some masses and coupling constants are many orders of magnitude different from the "bare" values used in the Lagrangian.

The articles I have read about the role of effective field theories make no mention of the corresponding issues in condensed matter or how emergence is involved. Emergence occurs in systems where there are many interacting components. Here those components are the quantum fields and their components with different momenta/energy. Hence, I would say that emergence is at the heart of big questions in the theory of elementary particles and fields.

The role of effective theories and toy models in understanding emergent properties

Two of the approaches to the theoretical description of systems with emergent properties that have been fruitful are effective theories and toy models. These leverage our limited knowledge of many details about a system with many interacting components.

Effective theories

An effective theory is valid at a particular range of scales. This exploits the fact that in complex systems there is often a hierarchy of scales (length, energy, time, or number). In physics, examples of effective theories include classical mechanics, general relativity, classical electromagnetism, and thermodynamics. The equations of an effective theory can be written down almost solely from consideration of symmetry and conservation laws. Examples include the Navier-Stokes equations for fluid dynamics and non-linear sigma models in elementary particle physics. Some effective theories can be derived by the “coarse-graining” of theories that are valid at a finer scale. For example, the equations of classical mechanics result from taking the limit of Planck’s constant going to zero in the equations of quantum mechanics. The Ginzburg-Landau theory for superconductivity can be derived from the BCS theory. The parameters in effective theories may be determined from more microscopic theories or from fitting experimental data to the predictions of the theory. For example, transport coefficients such as conductivities can be calculated from a microscopic theory using a Kubo formula.

Effective theories are useful and powerful because of the minimal assumptions and parameters used in their construction. For the theory to be useful it is not necessary to be able to derive the effective theory from a smaller scale theory, or even to have such a smaller scale theory. For example, even though there is no accepted quantum theory of gravity, general relativity can be used to describe phenomena in astrophysics and cosmology and is accepted to be valid on the macroscopic scale. Some physicists and philosophers may consider smaller-scale theories as more fundamental, but that is contested and so I will not use that language. There also are debates about how effective field theories fit into the philosophy of science.

Toy models

In his 2016 Nobel Lecture, Duncan Haldane said, “Looking back, … I am struck by how important the use of stripped down “toy models” has been in discovering new physics.” 

Here I am concerned with a class of theoretical models that includes the Ising, Hubbard, Agent-Based Models, NK, Schelling, and Sherrington-Kirkpatrick models. I refer to them as “toy” models because they aim to be as simple as possible, while still capturing the essential details of a particular emergent phenomenon. At the scale of interest, the model is an approximation, neglecting certain degrees of freedom and interactions. In contrast, at the relevant scale, effective theories are often considered to be exact because they are based on general principles.

Historical experience has shown that there is a strong justification for the proposal and study of toy models. They are concerned with a qualitative, rather than a quantitative, description of experimental data. A toy model is usually introduced to answer basic questions about what is possible. What are the essential ingredients that are sufficient for an emergent phenomena to occur? What details do matter? For example, the Ising model was introduced in 1920 to see if it was possible for statistical mechanics to describe the sharp phase transition associated with ferromagnetism.  

In his book The Model Thinker and online course Model Thinking, Scott Page has enumerated the value of simple models in the social sciences. An earlier argument for their value in biology was put by JBS Haldane in his seminal article about “bean bag” genetics. Simplicity makes toy models more tractable for mathematical analysis and/or computer simulation. The assumptions made in defining the model can be clearly stated. If the model is tractable then the pure logic associated with mathematical analysis leads to reliable conclusions. This contrasts with the qualitative arguments often used in the biological and social sciences to propose explanations. Such arguments can miss the counter-intuitive conclusions associated with emergent phenomena and the rigorous analysis of toy models. Such models can show what is possible, what are simple ingredients for a system sufficient to exhibit an emergent property, and how a quantitative change can lead to a qualitative change. In different words, what details do matter? 

Toy models can guide what experimental data to gather and how to analyse it. Insight can be gained by considering multiple models as that approach can be used to rule out alternative hypotheses. Finally, there is value in the adage, “all models are wrong, but some are useful.”

Due to universality, sometimes toy models work better than expected, and can even give a quantitative description of experimental data. An example is the three-dimensional Ising model, which was eventually found to be consistent with data on the liquid-gas transition near the critical point. Although, not a magnetic system, the analogy was bolstered by the mapping of the Ising model onto the lattice gas model. This success led to a shift in the attitude of physicists towards the Ising model. According to Martin Niss, from 1920-1950, it was viewed as irrelevant to magnetism because it did not describe magnetic interactions quantum mechanically. This was replaced with the view that it was a model that could give insights into collective phenomena. From 1950-1965, the view diminished that the Ising model was irrelevant to describing critical phenomena because it oversimplified the microscopic interactions.

Physicists are particularly good and experienced at the proposal and analysis of toy models. I think this expertise is a niche that they could exploit more in contributing to other fields, from biology to the social sciences. They just need humility to listen to non-physicists about what the important questions and essential details are.

Gravitational waves and ultra-condensed matter physics

In 2016, when I saw the first results from the LIGO gravitational wave interferometer my natural caution and skepticism kicked in. They had just observed one signal in an incredibly sensitive measurement. A lot of data analysis was required to extract the signal from the background noise. That signal was then fitted the results of numerical simulations of the solutions to Einstein's gravitational field equations describing the merger of two black holes. Depending on how you count about 15 parameters are required to specify the parameters of the binary system [distance from earth, masses, relative orientations of orbits, .... The detection events involve displacement of the mirrors in the interferometer by about 30 picometres!

What on earth could go wrong?!

After all, this was only two years after the BICEP2 fiasco which claimed to have detected anisotropies in the cosmic microwave background due to gravitational waves associated with cosmic inflation. The observed signal turned out to be just cosmic dust! It led to a book, by the cosmologist Brian Keating, Losing the Nobel Prize: A Story of Cosmology, Ambition, and the Perils of Science’s Highest Honor

Well, I am happy to be wrong, if it is good for science. Now almost one hundred gravitational wave events have been observed and one event GW170817 has been correlated with an x-ray observation.

But detecting some gravitational waves is quite a long way from gravitational wave astronomy, i.e, using gravity wave detectors as a telescope, in the same sense as the regular suite of optical, radio, X-ray, ... detectors. I was also skeptical about that. But it does not seem that gravity wave detectors are providing a new window into the universe.

A few weeks ago I heard a very nice UQ colloquium by Paul Lasky, What's next in gravitational wave astronomy?

Paul gave a nice overview of the state of the field, both past and future. 

A key summary figure is below. It shows different possible futures when two neutron stars merge.

The figure is taken from the helpful review

The evolution of binary neutron star post-merger remnants: a review, Nikhil Sarin and Paul D. Lasky

A few of the things that stood out to me.

1. One stunning piece of physics is that in the black hole mergers that have been observed the combined mass of the resulting black hole is three solar masses less than the total mass of the two separate black holes. The resulting loss of mass energy (E=mc^2) of three solar masses is converted into gravitational wave energy within seconds. During this time the peak radiant power was more than fifty times the power of all the stars in the observable universe combined!

I have fundamental questions about a clear physical description of this energy conversion process. First, defining "energy" in general relativity is a vexed and unresolved question with a long history. Second, is there any sense in which needs to describe this in terms of a quantum field theory: specifically conversion of neutron matter into gravitons?

2. Probing nuclear astrophysics in neutron stars. It may be possible to test the equation of state (relation between pressure and density) of nuclear matter. This determines the Tolman–Oppenheimer–Volkoff limit; the upper bound to the mass of cold, non-rotating neutron stars. According to Sarin and Lasky

The supramassive neutron star observations again provide a tantalising way of developing our understanding of the dynamics of the nascent neutron star and the equation of state of nuclear matter (e.g., [37,121,127–131]). The procedure is straight forward: if we understand the progenitor mass distribution (which we do not), as well as the dominant spin down mechanism (we do not understand that either), and the spin-down rate/braking index (not really), then we can rearrange the set of equations governing the system’s evolution to find that the time of collapse is a function of the unknown maximum neutron star mass, which we can therefore infer. This procedure has been performed a number of times in different works, each arriving at different answers depending on the underlying assumptions at each of the step. The vanilla assumptions of dipole vacuum spin down of hadronic stars does not well fit the data [37,127], leading some authors to infer that quark stars, rather than hadronic stars, best explain the data (e.g., [129,130]), while others infer that gravitational radiation dominates the star’s angular momentum loss rather than magnetic dipole radiation (e.g [121,127]).

As the authors say, this is a "tantalising prospect" but there are many unkowns. I appreciate their honesty. 

3. Probing the phase diagram of Quantum Chromodynamics (QCD)

This is one of my favourite phase diagrams and I used to love to show it to undergraduates.

Neutron stars are close to the first-order phase transition associated with quark deconfinement.

When the neutron stars merge it may be that the phase boundary is crossed.

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.”

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.

Emergence and philosophy

 A challenge in understanding and discussing emergence is that it means different things to different people. This is not surprising given emergence involves diverse and complex phenomena, occurs in a wide range of contexts, and is of interest to people in a diverse range of fields. Recently, I have started to be more precise about how emergence might be defined.

The subject interests philosophers, but it is hard for physicists to glean insights from (and critique) what philosophers say.  I find the following article from 2011 by Bei Lok Hu, helpful.

Emergence: Key physical issues for deeper philosophical inquiries

Hu is not a condensed matter physicist. He is more interested in emergence from its relevance to quantum decoherence and the possibility of space-time being emergent leading to a theory of quantum gravity. Thus, the article is a good entry into literature that I am not familiar with.

Hu gives a nice summary and critique of some of the main philosophical discussions and issues. Here are a few things I have grasped so far. With respect to defining what emergence is Hu writes about three "senses of emergence". The first is below.

Emergence in the sense of difference in manifestations– Role of coarse-graining:

* Different manifestations at different levels of structures, hierarchical in form, and corresponding interactions.

* Requires the identification of the range and precision of measurement, thus interfaces necessarily with an observer’s probing ability and observation range. Effective field theory is of this nature.

* Stability of emergent structures depends on the degree of coarse-graining

* Robustness of emergent structures against the variation of coarse-graining.

(Vaguely in philosopher’s language, the first two bullets correspond to novelty, and the latter two correspond to autonomy.)

I note that this definition of "novelty" is different to mine. I take the plainer definition that at higher levels the system has a property that it does not have at a lower level. A drop of water is wet, but a single molecule is not. A brain is conscious, but a single neuron is not. A lump of solid let is a superconductor, but a few atoms of lead are not. 

This illustrates how the same word can mean different things to physicists and philosophers. Other examples include "reductionism" and "fundamental". 

An important work that engages both physics and philosophy perspectives is "Is More Different? Emergent Properties in Physics," Oxford University DPhil thesis, by Paul Mainwood.

Mainwood summarizes, “... systemic properties are novel, if and only if it is practically impossible to derive them from the microphysical properties mentioned in microphysical supervenience.” ([40] p. 30)

Three proposals of novelty were examined by Mainwood ([40] Sec. 1.5): 

1) a failure of intertheoretic reduction; 

2) an impossibility of deducing the systemic properties from the properties of the parts; or 

3) a failure of mereological supervenience. 

The approaches appeal to three entirely separate distinctions between the properties of parts and wholes; thus according to Mainwood, there are three entirely different sets of criteria for emergence. 

Like me, Hu suggests ontology [reality] should come before epistemology [how we know]. Whereas, philosophers tend to start with epistemology and then try to use that to understand emergence. Understandably, consciousness and the philosophy of mind is a big thing for philosophers. It is often used a starting point for discussions about emergence. However, given consciousness is such a thorny, slippery, and difficult problem, to understand emergence it would be better to start with concrete and tractable examples from physics, such as emergence in condensed matter. 

The final sentence of the acknowledgements in the paper is poignant, amusing, and tragic.

This kind of non mission-driven, non utilitarian work addressing purely intellectual issues is not expected to be supported by any U.S. grant agency.

Something amazing about Einsteinian gravity

When I read Fundamentals by Frank Wilczek I learnt something that I found beautiful and amazing about general relativity and quantum field theory.

Any massless spin-2 field must couple to the stress–energy tensor in the same way that gravitational interactions do. This is an alternative means to derive Einstein's equation.

Furthermore, if a massless spin-2 particle is discovered, it must be the graviton. There is a nice discussion of this on physics.forums

According to Wikipedia, "For a comparison of the geometric derivation and the (non-geometric) spin-2 field derivation of general relativity, refer to box 18.1 (and also 17.2.5) of Misner, C. W.; Thorne, K. S.; Wheeler, J. A. (1973). Gravitation." 

In the 1960s, Steven Weinberg published a series of seminal papers, summarised below by one commenter in the physics.forums discussion. The results are also derived in chapter 5 of Weinberg's Quantum Field Theory text (volume 1).

S. Weinberg, “Photons and gravitons in S-matrix theory: derivation of charge conservation and equality of gravitational and inertial mass,” Phys. Rev. 135, B1049 (1964). 

S. Weinberg, “Photons and gravitons in perturbation theory: Derivation of Maxwell’s and Einstein’s equations,” Phys. Rev. 138, B988 (1965). 

S. Weinberg, “Infrared photons and gravitons", Phys. Rev. 140, B516 (1965).

1) Maxwell’s theory is the most general Poincare’ and gauge invariant theory of massless spin-1 particle. This can be easily proved by writing down the most general Poincare invariant amplitude for emitting a single photon in the so-called soft limit. Then, by demanding gauge invariance, you get charge conservation. 

2) Einstein’s GR is the most general Poincare’ and generally covariant theory for a massless spin-2 particle. The proof is similar to photon case. You write the most general amplitude for emitting a soft graviton. Then you see what happens when you demand general covariance, i.e., demand that the amplitude is “gauge” invariant. If you do that, you find that the equivalence principle pops out. That is, all particles couple to the massless spin-2 particle with equal strength. From this, he also concluded that the coupling strength must vanish when the spin of the massless particle is greater than 2. To some extent, this explains why we don’t see this kind of particle. 

3) Yang-Mill’s theory is the most general Poincare’ and gauge invariant theory for massless, self-interacting spin-1 particles. In this case, if you do the same exercise, you find that the coupling strengths of the interaction satisfy the Lie algebra of a compact group.

It is fascinating that these papers were just a warm-up for Weinberg's 1967 electro-weak unification paper, "A model for leptons" which is the basis of his Nobel Prize, and the most cited PRL ever.

Fun facts about phonons

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

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

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

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

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

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

Four distinct responses to the cosmological constant problem

One of the biggest problems in theoretical physics is to explain why the cosmological constant has the value that it does.
There are two aspects to the problem.
The first problem is that the value is so small, 120 orders of magnitude smaller than what one estimates based on the quantum vacuum energy!
The second problem is that the value seems to be finely tuned (to 120 significant figures!) to the value of the mass energy.

The problems and proposed (unsuccessful) solutions are nicely reviewed in an article written in 2000 by Steven Weinberg.

There seem to be four distinct responses to this problem.

1. Traditional scientific optimism.
A yet to be discovered theory will explain all this.

2. Fatalism. 
That is just the way things are. We will never understand it.

3. Teleology and Design.
God made it this way.

4. The Multiverse.
This finely tuned value is just an accident. Our universe is one of zillions possible. Each has different fundamental constants.

It is is amazing how radical 2, 3, and 4, are.

I have benefited from some helpful discussions about this with Robert Mann. There is a Youtube video where we discuss the multiverse. Some people love the video. Others think it incredibly boring. I think we are both too soft on the multiverse.

Entering the strange world of Kurt Godel

The picture below is of Godel's rotating universe. It represents an exact solution to Einstein's gravitational field equations and has the strange property of closed timelike curves (i.e. one can travel into the past!). This mathematical solution was found by Kurt Godel while he was employed by the Institute for Advanced Study at Princeton.

I think I first encountered this picture in my final undergraduate year in the classic book, The Large Scale Structure of Space-Time by Hawking and Ellis, while working on a research project in general relativity.

Godel's universe is just one example of the fascinating science and stories recounted in the book
Who Got Einstein's Office? Eccentricity and Genius at the Institute for Advanced Study by Ed Regis, first published 30 years ago.

I only read the book this past week and loved it. It is a captivating blend of science, mathematics, personalities, history, philosophy, humorous anecdotes, gossip, eccentricities ...
I was so captivated that I read it during two situations I would not normally read something so "heavy": during a long flight [normally I watch reruns of The Big Bang Theory or Upper Middle Bogan [need to laugh!] or recently a Warren Buffett documentary... sorry better not mention that again...], and during "down time" in the evening after a busy day.

Regis nicely describes the continuum hypothesis, Einstein-Podolsky-Rosen (EPR) "paradox" in quantum theory, von Neumann machines, cellular automata, the Bourbaki seminar, parity violation, the solar neutrino problem, fractals, the stability of matter, ...

The personalities covered include Godel, Einstein, Herman Weyl, John von Neumann, J. Robert Oppenheimer, Freeman Dyson, T.D. Lee,  C.N. Yang, Andre Weil, John Bahcall, Stephen Wolfram, Ed Witten, .....

It is amazing how much Regis packs into less than 300 pages (in a paperback).

The tragic mental health problems of Godel are described in a sensitive manner.

One pathetic story concerns the endless quibbles of T.D. Lee and C.N. Yang.
(Aside: They actually did their Nobel Prize winning work on parity violation at the IAS. This is in contrast to the countless Nobel laureates who at one time have been affiliated with the IAS but did not do their prize work there.)
Lee and Yang (or is it Yang and Lee?) argued constantly about the order in which their names should be listed, not just as co-authors, and at the Nobel ceremony, but even in newspaper and magazine articles about them. Furthermore, it is crazy to read the wildly different and self-serving accounts of certain concrete events. Great scientists are all too human ......

Some people consider the book is a bit of a "hatchet" job and has a mocking tone that paints the IAS in a poor light and questions its value and existence. I would not agree. I think it does show that the IAS has produced a lot of important scholarship. Regis does raise some important questions I mention below. But, I did think that he did refer to the IAS as "the One True Platonic Heaven" too many times.

Regis is implicitly critical of the fact that there is very little interaction between different research groups and disciplines within IAS. However, there is one important story he missed: when Freeman Dyson and the number theorist Hugh Montgomery were introduced at tea at the IAS and they made a connection between random matrix theory (quantum physics) and zeros of the Riemann zeta function.

Some questions the book raises for me include:

Can you really "manage" genius?

How do you create an institutional environment that increases the likelihood of truly great discoveries and scholarship?

What is the best way to hire "great" people?

What is a good mix of young and old staff?

What is a good mix of permanent faculty, postdocs, and short term senior visitors?

When is the absence of students in a research institute good or bad?

When is the absence of experimentalists in an institution bad/good for theoretical physics?

How do you foster a healthy synergy between pure mathematics and theoretical physics?

How might you foster some constructive interaction between distinct disciplines: philosophy, mathematics, theoretical physics, economics, history, ....?

Here is Feynman's perspective (partly quoted in the book):

I don't believe I can really do without teaching. The reason is, I have to have something so that when I don't have any ideas and I'm not getting anywhere I can say to myself, "At least I'm living; at least I'm doing something; I am making some contribution" -- it's just psychological. 

When I was at Princeton in the 1940s I could see what happened to those great minds at the Institute for Advanced Study, who had been specially selected for their tremendous brains and were now given this opportunity to sit in this lovely house by the woods there, with no classes to teach, with no obligations whatsoever. These poor bastards could now sit and think clearly all by themselves, OK? So they don't get any ideas for a while: They have every opportunity to do something, and they are not getting any ideas. I believe that in a situation like this a kind of guilt or depression worms inside of you, and you begin to worry about not getting any ideas. And nothing happens. Still no ideas come. 

Nothing happens because there's not enough real activity and challenge: You're not in contact with the experimental guys. You don't have to think how to answer questions from the students. Nothing!

Governments have less and less interest in "research for its own sake" and "without constraints" [hallmarks of the IAS]. However, there is an increasing number of generous and wealthy philanthropic organisations who are very interested. These are important questions for them.

Although I lived in Princeton for four years around the time the book was being written I only recall going inside "the Brain Farm" [as a friend called it] once, and that was for a music concert. Nevertheless, I spent many pleasant hours walking, jogging, bird watching, and skiing in the beautiful woods located behind the IAS.

I thank Ben Powell for a conversation about the IAS, stimulating me to remember I had inherited a copy of the book from my parents.

I welcome thoughts on any of the questions and any good IAS stories...