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.

Quantum states of matter and metrology

Two characteristics of states of matter are associated with them being referred to as quantum. One characteristic is the importance of quantum statistics of particles, i.e., that the system is composed of particles that obey Fermi-Dirac or Bose-Einstein statistics. The second characteristic is that a macroscopic property is quantized with values determined by Planck’s constant. I now discuss each of these with respect to emergence.

Quantum statistics. 

For a system of non-interacting  fermions and bosons at high temperatures the properties of the system are those of a classical ideal gas. As the temperature decreases there is a smooth crossover to low-temperature properties that are qualitatively different for fermions, bosons, and classical particles. This crossover occurs around a temperature, known as the degeneracy temperature, that is dependent on the particle density and Planck’s constant. 

Many of the properties resulting from quantum statistics also occur in systems of strongly interacting particles and this is central to the concept of Landau’s Fermi liquid and viewing liquid 4He as a boson liquid. If liquid 3He and the electron liquid in elemental metals are viewed as a gas of non-interacting fermions, the degeneracy temperature is about 1 K and 1000 K, respectively. Thermodynamic properties are qualitatively different above and below the degeneracy temperature. Low-temperature properties can have values that differ by orders of magnitude from classical values and have a different temperature dependence. In contrast to a classical ideal gas, a fermion gas has a non-zero pressure at zero temperature and its magnitude is determined by Planck’s constant. This degeneracy pressure is responsible for the gravitational stability of white dwarf and neutron stars.  

These properties of systems of particles can be viewed as emergent properties, in the sense of novelty, as they are qualitatively different from high-temperature properties. However, they involve a crossover as a function of temperature and so are not associated with discontinuity. They also are not associated with unpredictability as they are straightforward to calculate from a knowledge of microscopic properties.

Quantised macroscopic properties.

These provide a more dramatic illustration of emergence. Here I consider four specific systems: superconducting cylinders, rotating superfluids, Josephson junctions, and the integer Quantum Hall effect. All of these systems have a macroscopic property that is observed to have the following features.

i. As an external parameter is varied the quantity varies in a step-like manner with discrete values on the steps. This is contrast to the smooth linear variation seen when the material is not condensed into the quantum state of matter.

ii. The value on the steps is an integer multiple of some specific parameter.

iii. This parameter (unit of quantisation) only depends on Planck’s constant h and other fundamental constants. 

iv. The unit of quantisation does not depend on details of the material, such as chemical composition, or details of the device, such as its geometrical dimensions.

v. The quantisation has been observed in diverse materials and devices.

vi. Explanation of the quantisation involves topology.

Superconducting cylinders. A hollow cylinder of a metal is placed in a magnetic field parallel to the axis of the cylinder. In the metallic state the magnetic flux enclosed by the cylinder increases linearly with the magnitude of the external magnetic field. In the superconducting state, the flux is quantized in units of the magnetic flux quantum, Φ0 = h/2e where e is the charge on an electron. It is also found that in a type II superconductor the vortices that occur in the presence of an external magnetic field enclose a magnetic flux equal to Φ0.  

Rotating superfluids. When a cylinder containing a normal fluid is rotated about an axis passing down the centre of the cylinder the fluid rotates with a circulation proportional to the speed of rotation and the diameter of the cylinder. In contrast, in a superfluid, as the speed of rotation is varied the circulation is quantised in units of h/M where M is the mass of one atom in the fluid. This quantity is also the circulation around a single vortex in the superfluid. 

Josephson junctions. In the metallic state the current passing through a junction increases linearly with the voltage applied across the junction. In the superconducting state the AC Josephson effect occurs. If a beam of microwaves of constant frequency is incident on the junction, jumps occur in the current when the voltage is an integer multiple of h/2e. The quantisation is observed to better than one part in a million (ppm).

Integer Quantum Hall effect. In a normal conductor the Hall resistance increases linearly with the external magnetic field for small magnetic fields. In contrast, in a two-dimensional conductor at high magnetic fields the Hall resistance is quantized in units of h/2e^2. The quantisation is observed to better than one part in ten million. Reflecting universality, the observed value of the Hall resistance for each of the plateaus is independent of many details, including the temperature, the amount of disorder in the material, the chemical composition of system (silicon versus gallium arsenide), or whether the charge carriers are electrons or holes.

Other examples of macroscopic quantum effects are seen in SQUIDs (Superconducting Quantum Interference Devices). They exhibit quantum interference phenomena analogous to the double-slit experiment. The electrical current passing through the SQUID has a periodicity defined by the ratio of the magnetic flux inside the current loop of the SQUID and the quantum of magnetic flux.

The precision of the quantisation provides a means to accurately determine fundamental constants. Indeed, the title of the paper announcing the discovery of the integer quantum Hall effect was, “New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance.” It is astonishing that a macroscopic measurement of a property of a macroscopic system, such as the electrical resistance, can determine fundamental constants that are normally associated with the microscale and properties of atomic systems. 

Laughlin and Pines claimed that the quantisation phenomena described above reflect organizing principles associated with emergent phenomena, and their universality supports their claim of the unpredictability of emergent properties. 

Quantum states of matter and metrology

The universality of these macroscopic quantum effects has practical applications in metrology, the study of measurement and the associated units and standards. In 1990 new international standards were defined for the units of voltage and electrical resistance, based on the quantum Hall effect and the AC Josephson effect, respectively.

Prior to 1990 the standard used to define one volt was based on a particular type of electrical battery, known as a Weston cell. The new standard using the AC Josephson effect allowed voltages to be defined with a precision of better than one part per billion. This change was motivated not only by improved precision, but also improved portability, reproducibility, and flexibility. The old voltage standard involved a specific material and device and required making duplicate copies of the standard Weston cell. In contrast, the Josephson voltage standard is independent of the specific materials used and the details of the device. 

Prior to 1990 the international standard for the ohm was defined by the electrical resistance of a column of liquid mercury with constant cross-sectional area, 106.3 cm long, a mass of 14.4521 grams and a temperature 0 °C. Like the Josephson voltage standard, the quantum Hall resistance standard has the advantage of precision, portability, reliability, reproducibility, and independence of platform. The independence of the new voltage and resistance standards from the platform used reflects the fact that the Josephson and quantum Hall effects have the universality characteristic of emergent phenomena.

This post is an adaptation of material in Condensed Matter Physics: A Very Short Introduction

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".

Emergence of the arrow of time

Time has a direction. Microscopic equations of motion in classical and quantum mechanics have time-reversible symmetry. But this symmetry is broken for many macroscopic phenomena. This observation is encoded in the second law of thermodynamics. We experience the flow of time and distinguish past, present, and future. The arrow of time is manifest in phenomena that occur at scales covering many orders of magnitude. Here are some of these different arrows of time, listed in order of increasing time scales. These are discussed by Tony Leggett in chapter 5 of The Problems of Physics.

Elementary particle physics. CP violation is observed in certain phenomena associated with the weak nuclear interaction, such as the decay of neutral kaons observed in 1964. The CPT symmetry theorem shows that any local quantum field theory that is invariant under the “proper” Lorentz transformations must also be invariant under combined CPT transformations. This means that CP violation means that time-reversal symmetry is broken. In 1989, the direction violation of T symmetry was observed.

Electromagnetism. When an electric charge is accelerated an electromagnetic wave propagates out from the charge towards infinity. Energy is transferred from the charge to its environment. We do not observe a wave that propagates from infinity into the accelerating charge, i.e., energy being transferred from the environment to the charge. Yet this possibility is allowed by the equations of motion for electromagnetism. There is an absence of the “advanced” solution to the equations of motion. 

Thermodynamics. Irreversibility happens in isolated systems. Heat never travels from a cold body to a hotter one. Fluids spontaneously mix. There is a time ordering of the thermodynamic states of isolated macroscopic systems. The thermodynamic entropy encodes this ordering.

Psychological experience. We remember the past and think we can affect the future. We don’t think we can affect the past or know the future.

Biological evolution. Over time species adapt to their environment and become more complex and more diverse.

Cosmology. There was a beginning to the universe. The universe is expanding not contracting. Density perturbations grow independent of cosmic time (Hawking and Laflamme).

It is debatable to what extent these arrows of time are related to one another. 

The problem of how statistical mechanics connects time-reversible microscopic dynamics with macroscopic irreversibility is subtle and contentious. Joel Lebowitz claimed this problem was solved by Boltzmann, provided the distinction between typical and average behaviour are accepted, along with the Past Hypothesis. This states that the universe was initially in a state of extremely low entropy. David Wallace discussed the need to accept the idea of probabilities in law of physics and that the competing interpretations of probability as frequency or ignorance matter. In contrast, David Deutsch claims that the second law of thermodynamics is an “emergent law”: it cannot be derived from microscopic laws, like the principle of testability.

I find the Past Hypothesis fascinating because it connects the arrow of time seen in the laboratory and everyday life (time scales of microseconds to years) to cosmology, covering timescales of the lifetime of the universe (10^10 years) and the “initial” state of the universe, perhaps at the end of the inflationary epoch (10^-33 seconds). This also raises questions about how to formulate the Second Law and the concept of entropy in the presence of gravity and on cosmological length and time scales. 

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.

Emergence and the stratification of physics into sub-fields

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

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

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

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

I welcome suggestions about entries that I could add.

Emergence in nuclear physics

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

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

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

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

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

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

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

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

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.

Amazing things about Chandrasekhar's white dwarf mass limit

This is ultra-condensed matter physics!

In 1931, Subrahmanyan Chandrasekhar published a seminal paper, for which he was awarded the Nobel Prize in 1983. He showed that a white dwarf star must have a mass less than 1.4 solar masses, otherwise it will collapse under gravity. White dwarfs are compact stars for which the nuclear fuel is spent and electron degeneracy pressure prevents gravitational collapse. 

The blog Galileo unbound has a nice post about the history and the essential physics behind the paper.

There are a several things I find quite amazing about Chandrasekhar's derivation  and the expression for the maximum possible mass. 

m_H is the mass of a proton. M_P is the Planck mass. The value of the mass limit is about 1.4 solar masses.

Relativity matters

If the electrons are treated non-relativistically then there is no mass limit. However, when the star becomes dense enough the Fermi velocity of the electrons approaches the speed of light. Then relativistic effects must be included.

A macroscopic quantum effect

Degeneracy pressure is a macroscopic quantum effect. The expression above involves Planck's constant.

Quantum gravity

The mass formula involves the Planck mass, M_P.  On the one hand, this phenomena does not involve quantum gravity because there is no quantisation of the gravitational field. On the other hand, the effect does involve the interplay of gravity and quantum physics.

A "natural" scale

Formula that involve Planck scales usually represent scales of length, energy, mass, time, and temperature that are "unreal", i.e., they are vastly different from terrestial and astrophysical phenomena. For example, the temperature of the Hawking radiation from a black hole of one solar mass is 60 nanoKelvin. 

In contrast, the limiting mass is on the same scale as that of our own sun!

It agrees with astronomical observations

Determinations of the masses of hundreds of white dwarfs show most have a mass of about 0.5 solar masses and the highest observed value is 1.3 solar masses.

Hollywood and a Physical Review paper

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

On Continued Gravitational Contraction

J. R. Oppenheimer and H. Snyder

A beautiful blog post just appeared on 3 Quarks Daily,

 

September 1, 1939: A Tale Of Two Papers

by Ashutosh Jogalekar

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

The Mechanism of Nuclear Fission

Niels Bohr and John Archibald Wheeler

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

Science and the universe are awesome

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

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

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

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

Science works! It is amazing what science can do.

We can understand the material world.

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

We can make precise measurements.

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

We can predict the outcome of new experiments.

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

We can use mathematics. 

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

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

We can manipulate and control nature.

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

We know so much but we know so little. 

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

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

The immense scales of the observable universe

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

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

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

Universal laws that are simple to state

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

Just a few building blocks

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

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

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

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

Emergence: simple rules produce complex behaviour

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

Nature appears to be fine-tuned for life

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

The intricate and subtle "machinery" of biomolecules

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

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

The green comet and quantum chemistry

The comet C/2022 E3 (ZTF) getting a lot of attention, pointed out to me by my friend Alexey. Why is it green? This basic question turns out to be scientifically rich and has only recently been answered.

The green glow comes from a triplet excited state of diatomic carbon, C2. This got my interest because a decade ago I blogged on debates by quantum chemists about whether C2 involves a quadruple bond. Back in 1995, Roald Hoffmann wrote an interesting column in The American Scientist (and reproduced in his beautiful book Same and Not the Same) about the molecule and how it is present in various organometallic compounds and inorganic crystals.

Recent advances in understanding the photophysics of C2 were reported in 2021 in this paper.

Photodissociation of dicarbon: How nature breaks an unusual multiple bond

Jasmin Borsovszky, Klaas Nauta, Jun Jiang, Christopher S. Hansen, Laura K. McKemmish, Robert W. Field, John F. Stanton, Scott H. Kable, and Timothy W. Schmidt 

Here is a summary of the significance and content of the paper from Chemistry World.

..as dicarbon streams out of the comet core, it is destroyed by sunlight – this is why the comet tail, unlike the coma, is colourless. However, the precise mechanism of this supposed photodissociation had remained unclear.

Researchers in Australia and the US have now for the first time observed diatomic carbon’s photodissociation in the lab. The team produced dicarbon by photolysing tetrachloroethylene, and then breaking it apart with laser pulses. This allowed them to determine its bond dissociation energy with the same precision as for oxygen and nitrogen. Previous measurements for dicarbon had uncertainties an order of magnitude higher than for other diatomic molecules.

To break its quadruple bond, the molecule must absorb two photons and undergo two ‘forbidden’ transitions, those that break spectroscopic rules. Cometary dicarbon, the researchers calculated, has a lifetime of around two days until sunlight breaks it apart – the reason why its colour is visible in the coma but not in the tail.

Eight amazing things physics has taught us

What are the most amazing things that we know about the physics of the universe? If you were to pick ten what would they be?

I recently read Fundamentals: Ten Keys to Reality (2021) a popular science book by Frank Wilczek. My interest in the book was piqued just to see what Wilczek's choices for his "ten" were. I got a copy from the public library and became entranced because I discovered what a gifted writer and expositor Wilczek is. I found I was learning some physics I did not know; or at least getting a deeper understanding of what I should know. I then bought my own copy so I could annotate it. I have previously enjoyed the insights in many of Wilczeks' Physics Today columns.

The book gives a popular presentation of some physics "basics" such as celestial mechanics, the Standard Model of elementary particles (which he renames the Core), and Big Bang cosmology.  I found it full of insights. I also appreciated that Wilczek does not have the hard reductionist or scientism edge found in the popular books of some distinguished theoretical physicists such as Weinberg and Hawking. However, a careful reading led me at times to be somewhat disappointed and irritated, for reasons that I discuss briefly below. In the end, this is because, not surprisingly, I have a much more emergentist perspective on reality, seeing it as stratified.

First, here are the ten things that Wilczek finds amazing, helpfully summarised in his chapter titles.

Part I. What There Is 

Chapter 1. There's Plenty of Space

Chapter 2. There's Plenty of Time

Chapter 3. There Are Very Few Ingredients

Chapter 4. There Are Very Few Laws

Chapter 5. There's Plenty of Matter and Energy

Part II. Beginnings and Ends 

Chapter 6. Cosmic History is an Open Book

Chapter 7. Complexity Emerges

Chapter 8. There's Plenty More to See

Chapter 9. Mysteries Remain

Chapter 10. Complementarity Is Mind-Expanding

Here are some of the ideas associated with each of the ten keys.

There's Plenty of Space

The scales of the universe are incredible. Beyond us, there is the vast numbers of stars and galaxies, and distances of more than ten billion light years. Within us, each of our bodies contains more atoms than there are stars in the universe. Our brains have as many neurons as there are stars in our galaxy. An atom is largely empty space.

There's Plenty of Time

Cosmic time is abundant. The quantity of time reaching back to the big bang dwarfs a human lifetime... [which] contains far more moments of consciousness than universal history contains human life spans. We are gifted with an abundance of inner time.

There Are Very Few Ingredients

Everything in the universe is made of just a few particles: leptons, quarks, and neutrinos. And forces and the associated bosons, such as photons, gravitons, and gluons. These particles have just a few properties: mass, charge, colour, and spin.

 "The most basic ingredients of physical reality are a few principles and properties. Four simple yet profound general principles govern how the world works.

1. The basic laws describe change.

2. The basic laws are universal.

3. The basic laws are local.

4. The basic laws are precise.

Newton realised locality was a problem. Fields rather than particles are the fundamenta building blocks of matter.

Quasiparticles are discussed. In high school, Wilczek was inspired by a visit to Bell Labs where he learnt that quanta of lattice vibrations are phonons. He describes how he introduced anyons in the early 1980s and how they were then identified with quasiparticles in fractional quantum Hall states.

There Are Very Few Laws

From forces we are led to fields, and from (quantum) fields, we are led to particles.

From particles we are led to (quantum) fields, and from fields, we are led to forces.

Thus, we come to understand that substance and force are two aspects of a common underlying reality.

The four fundamental forces (gravity, electromagnetism, weak nuclear, and strong nuclear) are described by just a few simple mathematical equations.

The art and science of spectroscopy is described as "Atoms sing songs that bare their souls, in light."

Wilczek's Ph.D. work on quark confinement and asymptotic freedom in Quantum Chromodynamics (QCD) was the beginning of QCD being accepted and used.

Newton's gravity theory presented the puzzle of the equivalence of inertial and gravitational mass. Einstein's gravity solved the puzzle and "fulfills Newton's aspiration for a theory of gravity based n local action". 

    "we can portray the majestic logic of general relativity in ten broad             strokes... "

    "John Wheeler, the poet of relativity, summed it up this way: "Space-time     tells matter how to move; matter tells space-time how to bend."

Wilczek makes the debatable and misleading claim that "The equations of QED, QCD, general relativity, and the weak force, ... have powered many advances, including lasers, transistors, nuclear reactors, MRIs, and GPS."

There's Plenty of Matter and Energy

The fact that the amount of solar energy falling on the surface of the earth is vastly greater than current human energy consumption.

The concept of "dynamical complexity" is introduced but not defined. "Music and ritual are purified expressions of dynamical complexity."

"The principle that the essence of human purposes is experienced through flows of information in dynamic complexity, rather than through details of chemistry and physiology, is both mind-expanding and liberating. It challenges us to imagine how minds could emerge elsewhere in the universe, and it prepares us to embrace those minds within our circle of empathy."

To me, this is "mumbo jumbo" and reflects the muddled thinking that occurs when Wilczek wildly extrapolates from "fundamental" physics to broader and deeper questions about humanity. The last chapter has similar weaknesses.

Cosmic History is an Open Book

A lucid short summary is presented of big bang cosmology. What we know and why we know it. The chapter ends with a brief reference to Augustine's prescient insights about time. It is what clocks measure and so time did not exist before the beginning of the universe.

Complexity Emerges

How did the featureless simple "soup" that existed a million years after the big bang develop into the complex universe seen today with structures such as stars, galaxies, planets, and biological life? This short chapter (only eight pages) mostly talks about the role of gravity. The chapter could have been much richer by discussing the emergence of complexity in biology, psychology, and sociology. Again, simple laws can produce complex properties.

There's Plenty More to See

The discovery of the Higgs particle and gravitational wave astronomy are both described. Some speculations are made to connect "Quantum Perception and Self-Perception."

Mysteries Remain

What triggered the big bang? Could it hapen again?

Are there meaningful patterns hidden in the apparent sprawl of fundamental particles and forces?

How, concretely, does min emerge from matter? (Or does it?)

Wilczek describes violation of time reversal invariance (T) in elementary particle physics and the Peccei-Quinn proposal for a new field to explain this. The corresponding particle was dubbed the axion by Wilczek, which fulfilled his high school dream to give a particle that name when he encountered a laundry detergent with that name. The axion "cleans up a problem" in elementary particle physics.

Axions are candidates for dark matter.

Complementarity Is Mind-Expanding

Bohr's concept of complementarity (embodied in wave-particle duality in quantum theory) is embraced. 

Complementarity is the concept that one single thing, when considered from different perspectives, can seem to have very different or even contradictory properties. Complementarity is an attitude toward experiences and problems that Ive found eye-opening an extremely helpful. It has literally changed my mind. Through it, I've become larger: more open to imagination, and more tolerant.

I am no fan of this perspective. I am all for having an open mind, considering a range of perspectives, and living with dialectic (intellectual tensions). However, I do not use quantum theory to justify that. There is a multitude of moral, philosophical, social, and political reasons that provide much more compelling justifications for humility. Bohr's perspective and extrapolations from the atomic world to politics has a long and dubious history that has systematically been debunked by Mara Beller, including in Physics Today.  Nevertheless, these ideas just won't go away, as seen why a recent volume of papers on Quantizing International Relations.

In summary, I love Wilczek's discussions of physics, and I think eight of the ten chapters describe amazing things about the physical world that we have learnt and should contemplate with awe and wonder.  But, two of the chapters make speculations about how the type of theoretical physics that Wilczek has made seminal contributions to is profoundly relevant to technological, social, economic, and political reality. I would much rather draw on the insights and debates from the humanities and social sciences to understand those realities and our place in them.

Famous last words

If you ever write a popular book about science I suggest you spend a lot of time honing your very last paragraph. If it is eloquent, grand, and hyperbolic it may be so widely quoted that many people will think that this is actually what the book is about or has proven. Here are a few examples that I often see.

Where then shall we find the source of truth and the moral inspiration for a really scientific socialist humanism? Only, we suggest, in the sources of science itself,..... it is the conclusion to which the search for authenticity necessarily leads. The ancient covenant is in pieces; man at last knows that he is alone in the unfeeling immmensity of the universe, out of which he emerged only by chance. Neither his destiny nor his duty have been written down. The kingdom above or the darkness below: it is for him to choose.''

Jacques Monod, Chance and Necessity: An Essay on the Natural Philosophy of Modem Biology, trans. Austryn Wainhouse (New York: Knopf, 1971), p. 167

But if there is no solace in the fruits of our research, there is at least some consolation in the research itself. Men and women are not content to comfort themselves with tales of gods and giants, or to confine their thoughts to the daily affairs of life; they also build telescopes and satellites and accelerators, and sit at their desks for endless hours working out the meaning of the data they gather. The effort to understand the universe is one of the very few things which lifts human life a little above the level of farce and gives it some of the grace of tragedy.

Steven Weinberg, The First Three Minutes (Basic Books, 1977), pages 154-155.

If we do discover a complete theory, it should in time be understandable in broad principle by everyone, .... Then we shall all ...[discuss] why it is that we and the universe exist. If we find the answer to that, it would be the ultimate triumph of human reason - for then we would truly know the mind of God.  

Stephen Hawking, A Brief History of Time

There is grandeur in this view of life, with its several powers, having been originally breathed by the Creator into a few forms or into one; and that, whilst this planet has gone circling on according to the fixed law of gravity, from so simple a beginning endless forms most beautiful and most wonderful have been, and are being evolved.

Charles Darwin, The Origin of Species

Can you think of any other examples of famous last paragraphs?

Many-worlds cannot explain fine tuning

There are several independent lines of argument that are used to support the idea of a multiverse: the many-worlds interpretation of quantum mechanics, the ``landscape problem'' in string theory, and the fine-tuning of fundamental physical constants. Previously, I wrote about four distinct responses to the fine-tuning of the cosmological constant.

I was recently trying to explain the above to a group of non-physicists. One of them [Joanna] had the following objection that I had not heard before. Schrodinger's cat can only exist in one universe within the multiverse. The multiverse involves zillions of universes. However, because of fine-tuning carbon-based life is so improbable that it can only exist in one (or maybe a handful?) of the universes, within the multiverse. Thus, when one observes whether the cat is dead or alive, and the universe ``branches" into two distinct universes, one with a dead cat and the other with a living cat, there is a problem. It is possible that many-worlds interpretation is still correct, but it does not seem possible to claim that many-worlds and the multiverse needed to ``explain'' fine-tuning are the same type of multiverse.

One response might be that Schrodinger's cat is just a silly extrapolation of entanglement to the macroscopic scale. However, the problem remains. Just consider radioactive decay of atoms. Each decay of a single atom should be associated with branching to two distinct universes. Both of those universes are identical, except for whether that single atom has decayed or not. Over history, zillions of radioactive decays have occurred. This means that there are zillions of universes almost identical to the one we live in right now. But, all these zillion universes are fine-tuned to be just like ours.

Is there a problem with this argument?

Addendum. (25 October, 2019).
Fine-tuning got a lot of attention after the 1979 Nature paper, The anthropic principle and the structure of the physical world, by Bernard Carr and Martin Rees.
The end of the article makes explicit the connection with the many-worlds interpretation of quantum theory.

...nature does exhibit remarkable coin- cidences and these do warrant some explanation.... the anthropic explanation is the only candidate and the discovery of every extra anthropic coincidence increases the post hoc evidence for it. The concept would be more palatable if it could be given a more physical foundation. Such a foundation may already exist in the Everett 'many worlds' interpretation of quantum mechanics, according to which, at each observation, the Universe branches into a number of parallel universes, each corresponding to a possible outcome of the observation. The Everett picture is entirely consistent with conventional quantum mechanics; it merely bestows on it a more philosophically satisfying interpretation. There may already be room for the anthropic principle in this picture. 

Wheeler envisages and infinite ensemble of universes all with different coupling constants and so on. Most are 'still-born', in that the prevailing physical laws do not allow anything interesting to happen in them; only those which start off with the right constants can ever become 'aware of themselves'. One would have achieved something if one could show that any cognisable universe had to possess some features in common witti our Universe. Such an ensemble of universes could exist in the same sort of space as the Everett picture invokes. Alternatively, an observer may be required to 'collapse' the wave function. These arguments go a little way towards giving the anthropic principle the status of a physical theory but only a little: it may never aspire to being much more than a philosophical curiosity...

In a review of a book based on a conference about the multiverse, Virginia Trimble states that:

There is also among the authors strong divergence of opinion on whether Hugh Everett's version of many worlds is (just) a quantum multiverse (Tegmark), almost certainly correct and meaningful (Page), or almost certainly wrong or meaningless (Carter). 

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

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

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

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