A mystery about science is that humans can do it

We are surrounded by scientific knowledge and have become so used to it that we often take science for granted. We may rarely reflect on the amazing revelations of science—and so miss the opportunity to recognize the awesome nature of the universe. Things that we know, learn, and do today in science would have been inconceivable decades, let alone centuries, ago. 

Einstein said, “The most incomprehensible thing about the universe is that it is comprehensible.”  For Einstein, the success of science was a wonderful mystery. As he wrote to his friend Maurice Solovine: 

. . . I consider the comprehensibility of the world (to the extent that we are authorized to speak of such a comprehensibility) as a miracle or as an eternal mystery. Well, a priori, one should expect a chaotic world, which cannot be grasped by the mind in any way . . . the kind of order created by Newton’s theory of gravitation, for example, is wholly different.  

There are several dimensions to the comprehensibility of the universe being mysterious. Einstein highlighted the first mystery, which is that there is order in the world, as reflected in scientific laws, such as Newton’s theory of gravity, and that this order can be succinctly stated in the language of mathematics. To the best of our knowledge, these laws hold for all time and everywhere in the universe. The existence of the orderly behaviour encoded in scientific laws is necessary for science to work, which leads to the second mystery. Why have we been able to discover these laws?

A second dimension that makes science possible is the intellectual abilities of humans. Humans not only have the rational ability to do science—to reason, to understand, to communicate—but also the ability to design instruments, such as telescopes and microscopes. There seems to be a connection between the rationality of the universe and human rationality. The idea that there may be harmony between the structures of the universe and those of the human mind has a long history.  In the Renaissance, it was encapsulated in the metaphor of the “music of the spheres”. In his book, Harmonies of the World (1619), Johannes Kepler connected music and his explanations of planetary orbits. Einstein said that “Mozart’s music is so pure and beautiful that I see it as a reflection of the inner beauty of the universe.” 

Humans might have been different. Suppose that the average human intelligence was lower than it is today, and the variation of human intelligence was smaller. Then, there might have been no Galileo, Isaac Newton, Robert Boyle, Charles Darwin, Albert Einstein, Richard Feynman, Phil Anderson, or Linus Pauling. Without these brilliant figures in scientific history, scientific progress would have been slow. 

The third dimension is that human language enables scientists to formulate, represent, and communicate ideas, theories, and the results of scientific experiments. This language sometimes involves mathematics, graphs, or tables of data. Scientists can understand one another. Even though there can be misunderstandings, these can be resolved. There is a scientific culture that transcends the diversity of cultures associated with different countries, linguistic groups, and ethnicities.

The fourth dimension is the physical dexterity of humans. I am a theoretical physicist not an experimental physicist. I am “all thumbs” and not particularly good in the lab. Consequently, I have done no laboratory work since I was a Ph.D. student. In contrast, some gifted scientists have an ability to do things in a laboratory that most people cannot. Their manual dexterity allows them to fabricate precision instruments, grow pure crystals, blow exquisite glassware, see faint images, and fine-tune electronic instruments in extraordinary ways. If some humans did not have such amazing abilities, scientific progress would have been much slower—or possibly non-existent.

A fifth dimension that makes science possible is the availability and processability of materials that have been central to scientific progress. Making instruments requires specific materials, such as metals, glass, rubber, insulators, plastics, and semiconductors. If we lived in a world where some of these materials were very rare or could not be processed to the purity or malleability required for scientific instruments, we would not have supercomputers, electron microscopes, or the James Webb Space Telescope today. We might be struggling to make even the simple telescopes used by Galileo.

These five dimensions are all required for humans to be able to do science. There are several additional mysteries of science.  These can be divided into two classes: what science can do and what we can learn about the universe from science. Science allows us to know certain things about reality (epistemology) and also to understand the nature of that reality (ontology). In other words, science helps us make maps of physical reality. The terrain represented by those maps is amazing. And the fact that we can make the maps is amazing.

From Leo Szilard to the Tasmanian wilderness

Richard Flanagan is an esteemed Australian writer. My son recently gave our family a copy of Flanagan's recent book, Question 7. It is a personal memoir that masterfully weaves together a dizzying array of topics, from nuclear physics to the Tasmanian wilderness. I mention it on this blog because of its endearing and fascinating portrayal of Leo Szilard, arguably one of the twentieth century's most creative, unconventional, and eccentric physicists.

The paragraph below gives an overview of the narrative that is used to weave together all the disparate topics.

“Without Rebecca West’s kiss H. G. Wells would not have run off to Switzerland to write a book in which everything burns, and without H. G. Wells’s book [The World Set Free] Leo Szilard would never have conceived of a nuclear chain reaction and without conceiving of a nuclear chain reaction he would never have grown terrified and without growing terrified Leo Szilard would never have persuaded Einstein to lobby Roosevelt and without Einstein lobbying Roosevelt there would have been no Manhattan Project and without the Manhattan Project there is no lever at 8.15 am on 6 August 1945 for Thomas Ferebee to release 31,000 feet over Hiroshima, there is no bomb on Hiroshima and no bomb on Nagasaki and 100,000 people or 160,000 people or 200,000 people live and my father dies. Poetry may make nothing happen, but a novel destroyed Hiroshima and without Hiroshima there is no me and these words erase themselves and me with them.”

You can read an extract here and a review in The Guardian here.

Physics on Netflix

The Netflix series, 3-body Problem, features physics and physicists throughout. I am not a big fan of science fiction, but watched the first episode, to try and get a sense of why the series is attracting so much attention. The opening scene (in the video above) is rooted in history. It depicts a "struggle session" during the Cultural Revolution, featuring the denunciation and killing of a physics professor, who is the father of the main character in the series.

For some more on the intellectual and political background see

Organized criticism of Einstein and relativity in China, 1949–1989, by Danian Hu

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.

Philosophers of science on which theories are fundamental

What is real? What is true? These big questions are central to philosophy and issues in the philosophy of science.

Emergent properties of complex systems raise similar philosophical questions such as  "What is fundamental?" and "Are quasiparticles real?".

Robert Batterman is a philosopher of science who is the author of the book,

The Devil in the Details: Asymptotic Reasoning in Explanation, Reduction, and Emergence

In 2017 Batterman wrote an article in an edition of the Journal of Statitiscal Physics that was in memory of Leo Kadanoff. 

Philosophical Implications of Kadanoff’s Work on the Renormalization Group

Below I reproduce some of the text as it provides a helpful (and disturbing) summary of how the philosophy of science has evolved.

There are very few natural philosophers anymore. The fields of philosophy and science parted company at the end of [the nineteenth] century. Philosophers more and more began to turn toward the disciplines of logic and the analysis of language, and their examination of the enterprise of science began to follow a different, less-engaged-with-scientific-detail, direction. They began to try to determine the logic and structure of scientific theorizing in a way that was much more arm-chair and much less concerned with details about individual theories. The aim was to construct or reconstruct the proper logical structures of scientific explanation, confirmation, and theory choice. The philosophical reconstructions were, by and large, designed to fit all empirical science. For example, an explanation in physics should share the same general (logical) form as explanations in biology, chemistry, or sociology. 

I find this problematic because how physicists and biologists do science and the knowledge that they produce is quite different. In fact, similar differences exist between elementary particle physics and condensed matter physics. That also applies to Batterman's next claim.

I think it is fair to say that from a philosophy of science point of view, physical theories are supposed to reflect our best attempts to understand nature. Philosophers are also enamored with the idea that theories have a certain logical structure—they can be written down in some kind of axiomatic form from which, given certain inputs, various features of physical systems (future states, e.g.) can be derived using logic and reasonably straightforward mathematics.

Furthermore, philosophers often distinguish fundamental from nonfundamental (or “phenomenological”) theories. This latter distinction presupposes the idea that fundamental theories are the ones that tell us really what nature is actually like at “bottom.” These presumably include, quantum theory, quantum field theory, maybe a theory of quantum gravity, etc.

In contrast, Bob Laughlin, argues that certain emergent properties are exact [such as quantisation of magnetic flux in a superconductor, hydrodynamics, sound waves] and so they are more fundamental than microscopic theories. [A Different Universe, pp. 36-40].

Batterman continues

Nonfundamental theories such as thermodynamics, continuum mechanics, and fluid dynamics, on the other hand, while pragmatically useful, are in a certain sense (exactly what sense is a matter of serious contention) superfluous. We could, in principle, solve problems involving the elastic bending of beams by starting from the fundamental atomic and subatomic theories of the constituents of the beam.

Nonfundamental theories don’t get nature right. Steel beams are not really the continua whose bending behaviors are described by the Navier–Cauchy equations. Gases are not continuous blobs of stuff. The important theories, according to many philosophers and, I believe, according to many physicists, are those that get the ontology right. In part, the (often unarticulated) reason for preferring fundamental theories over phenomenological theories is a realist presupposition that physical theories must accurately describe the world the way the world really is. 

 Perhaps the view that atoms are real but solids are not is reflected by Bertrand Russell in the opening paragraph of his book, The ABC of Atoms, published in 1923 and intended for popular audiences.

Phenomenological theories are often good for calculating, but they don’t accurately describe the world and so must, in a sense, play second fiddle to their fundamental partners.

This is also contentious. Thermodynamics, elasticity theory, and fluid dynamics are perfectly accurate and never wrong within their domain of validity. Many courses and texts on thermodynamics begin with the following quote from Einstein.

 A theory is the more impressive the greater the simplicity of its premises, the more different kinds of things it relates, and the more extended its area of applicability. Therefore the deep impression that classical thermodynamics made upon me. It is the only physical theory of universal content which I am convinced will never be overthrown, within the framework of applicability of its basic concepts.

I should stress that Batterman is not agreeing with or promoting the views I have questioned above. Rather, he is trying to characterise what many philosophers believe.

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.

Some amazing things about the universe that make science possible

 This post takes off from the following Einstein quotes.

"The most incomprehensible thing about the universe is that it is comprehensible"

from "Physics and Reality"(1936), in Ideas and Opinions, trans. Sonja Bargmann (New York: Bonanza, 1954), p292.

"...I consider the comprehensibility of the world (to the extent that we are authorized to speak of such a comprehensibility) as a miracle or as an eternal mystery. Well, a priori, one should expect a chaotic world, which cannot be grasped by the mind in any way .. the kind of order created by Newton's theory of gravitation, for example, is wholly different." 

Letters to Solovine, New York, Philosophical Library, 1987, p 131.

There are several dimensions to the comprehensibility of the universe. The dimension highlighted by Einstein is that there is order in the world, reflected in laws that can be succinctly stated and mathematically encoded. These laws seem to hold for all time and everywhere in the universe. Here I suggest there are three other dimensions that make science possible. 

A second amazing dimension is that humans have the rational ability to do science: to reason, to understand, to communicate, and to make instruments such as telescopes and microscopes. There seems to be somewhat of a match between the rationality of the universe and human rationality. This is written in the spirit of arguments about fine-tuning, where one imagines alternative universes.

Humans could have been different. Suppose that the amount and variation of human intelligence (at least that aspect of intelligence relevant to doing science) were different, and the mean and standard deviation were lower. Suppose that intelligence was lower so that there were no brilliant humans like Darwin, Einstein, Newton, Pauling, ... In fact, suppose that even the brightest people were as good at science as I am at music and dancing. Scientific progress would be rather limited.

But it is not just human intelligence that matters. A third amazing dimension is that of manual dexterity. I am "all thumbs" and not particularly good in the lab. There are some gifted experimentalists with an outstanding ability to do things most people cannot, even with training. Such abilities allow them to fabricate precision instruments, grow crystals, see faint images, ... If some humans did not have such abilities scientific progress would have been much slower, or possibly non-existent.

A fourth crucial dimension concerns the availability and processability of certain materials that are central to scientific progress. Making instruments requires particular materials such as metals, glass, and semiconductors. Suppose we lived in a world where some of these were very rare or just could not be processed to the purity or malleability required.

Einstein on big questions

The mere formulation of a problem is far more essential than its solution, which may be merely a matter of mathematical or experimental skills.

To raise new questions, new possibilities, to regard old problems from a new angle, requires creative imagination and marks real advance in science.

I am enough of an artist to draw freely upon my imagination. Imagination is more important than knowledge. Knowledge is limited. Imagination encircles the world.

Albert Einstein and Leopold Infeld (1938), The Evolution of Physics

I recently encountered this quotation in The Poetry and Music of Science: Comparing Creativity in Science and Art by Tom McLeish. I have heard many times the "Imagination is more important than knowledge" quote, sometimes as a dubious justification for dubious ideas. However, I did not know the context. 

My postdoctoral advisor, John Wilkins tried to drill into me, the idea in the first paragraph, that just coming up with a well-defined formulation of a problem could be a significant advance. This idea certainly had some impact on me, since I sometimes hear my non-scientist wife quote it!

On reflection, I am afraid that I too easily lose sight of this priority of defining problems, just like the method of multiple alternative hypotheses. Good science is hard.

Why am I reading this article? What question am I trying to answer?

Why am I writing this paper? What question am I trying to answer?

What is the problem I assigning a student to work on? Is it well-formulated?

Defining good research questions is hard work and requires discipline.

Management is not leadership

Being in a management position is neither a necessary nor a sufficient condition for academic leadership.

Senior managers at Australian universities sometimes wax lyrical about how they are in leadership. When it comes to promotion decisions, they also judge junior academics on whether they show "leadership".  This seems to be equated with the size of one's research group and the number of one's citations. The rise of this fixation on "leadership" in universities was highlighted by a commenter on a recent post.

This misunderstanding is another example of how university management does not actually consider what their own academics in the university may actually know. Leadership is a well-researched topic. If managers talked to faculty in business and history, they might be told something along the following lines.

                                                The cartoon is from here.

Real leadership is characterised by influence. It leads to change. Real leaders can motivate people to change their views and their lives. This is of substance, unlike "change management" which seems to me to be a euphemism for sacking people, changing lines of reporting, and renaming (rebranding) the names of departments and courses.

Real leadership is not about occupying a powerful position that you use to exert control over people. The authority that real leaders have is intellectual or moral authority, not legal authority.

Previously I posted about how humility and listening to others has been found to be a key ingredient of leadership, rather than self-promotion and defensiveness.

Consider Einstein working in the patent office, Douglas Hofstadter unemployed and living with his parents while writing Godel, Escher, Bach, the obscure virus club, Nelson Mandela in prison on Robben Island, and Gandhi on a hunger strike. None held formal positions of authority or commanded large salaries, budgets, or staff. But they were leaders. They influenced people.

Being in a management position or holding a political office does not mean you are a leader. Gorbachev and Brezhnev both held the same position (for 6 and 18 years respectively). Who was the real leader?

My postdoctoral mentor, the late John Wilkins, never held a management position, but he sure was a leader. He was influential for the good of others and for condensed matter physics.

I like the following text

Within minutes they were bickering over who of them would end up the greatest. But Jesus intervened: “Kings like to throw their weight around and people in authority like to give themselves fancy titles. It’s not going to be that way with you. Let the senior among you become like the junior; let the leader act the part of the servant."

Science begins and ends with humility

Science requires humility. Any scientific investigation starts with acknowledging ignorance. Scientific progress requires a willingness to admit mistakes and accept evidence, even when it goes against cherished and esteemed beliefs, theories, and colleagues.

As a scientist, I am fascinated by the science of covid-19, from the genetic code of the virus to the mathematical modeling of epidemics. I find it amazing how much we do know. It is also amazing how much we do not know.

The SARS-CoV2 virus is one of many coronaviruses; a name derived from the crown-like appearance of a virus particle in an electron microscope. The points on the crown are called spike proteins; they are attached to a spherical surface composed of other proteins. The diameter of the virus particle is about one-tenth of a micron. If you lined up ten thousand particles next to each other in a straight line they would be the size of a pinhead. The complete details of the atomic composition and geometrical arrangement of these spike proteins have been determined. This sphere (virus capsid) encapsulates the genetic information that is encoded in a single strand of an RNA molecule. The spike proteins allow a virus particle to attach itself to and enter a human respiratory cell. Inside the cell the virus particle bursts releasing the RNA molecule that then moves to the ribosome of the cell which then makes many copies of the RNA molecule. The information in each of these molecules is then used to manufacture the proteins that compose a virus particle. The copies of the RNA and proteins then reassemble into thousands more virus particles that then leave the host cell and move onto more cells.

It is amazing we know so much. Furthermore, we know the exact details of this genetic information. The RNA molecule in the SARS-CoV2 virus particle consists of a unique sequence of 33,000 letters (G, U, T, or C). In the laboratory, scientists can make a molecule with exactly this sequence and use these molecules to make artificial copies of the virus particles. We know so much. It is amazing. Aren’t we clever!

The flu epidemic of 1918-1920 killed more people than World War I. Back then we did not even know that RNA existed, the structure of any protein molecule, what the genetic code was, the mechanism of infection, how to mathematically model the spread of epidemics or the relative merits of different strategies for managing epidemics. We now know so much more. Today, this knowledge is saving thousands of lives.

Yet, we know so little. Although we know all the amazing details above, we cannot predict the structure of the virus particles. Furthermore, we don’t know the design of effective and safe drugs and vaccines to treat covid-19. A vaccine has never been developed for a coronavirus. This does not mean that it is not possible or even that it won’t happen in the next year. We also don’t really know how to balance the medical benefits and the economic and social costs of lockdowns.

Modeling, understanding, and describing social, political, and economic phenomena is even more difficult than physical, chemical, and biological phenomena. Scott E. Page is a Professor of Political Science, Complex Systems, and Economics at the University of Michigan. He teaches an online course, ``Model thinking’’ that has been taken by more than a million people. In his recent book, The Model Thinker, Page makes the case for using multiple models to describe human behavior.

We conclude with a plea for humility and empathy. In constructing models of people, a modeler must be humble. Given the challenges of diversity, social influence, cognitive errors, purpose, and adaptation, our models will inevitably be wrong, which is why we take a many-model approach.

Parenthetically, I note that this many-model approach is similar to the method of multiple hypotheses advocated by John Platt and that I have blogged about previously.

In 1932, Albert Einstein responded to a letter from Queen Elizabeth of Belgium, who complimented him on his lucid explanation to her of various topics in theoretical physics. Einstein wrote: 

It gave me great pleasure to tell you about the mysteries with which physics confronts us. As a human being, one has been endowed with just enough intelligence to be able to see clearly how utterly inadequate that intelligence is when confronted with what exists. If such humility could be conveyed to everybody, the world of human activities would be more appealing.

Quoted in Helen Dukas and Banesh Hoffman, Albert Einstein, The Human Side: Glimpses from His Archives. Princeton, NJ: Princeton University Press, 1979, 48.

The text above is an extract from a draft chapter that I have contributed to a forthcoming book produced with my friends in the "holy" scribblers group.

More to follow.

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...

Theoretical physics is much more than this

Via Peter Woit's blog I read an interesting article What Does Any of This Have To Do with Physics? Einstein and Feynman ushered me into grad school, reality ushered me out by Bob Henderson.
The facts it is quite long and that I read it all on a phone (something I virtually never do) on vacation shows how interesting I found it.

During his Ph.D Henderson worked on a theory of quantum gravity at the University of Rochester in the 1990s. He then left physics for Wall Street and is now a science writer.

Here are a few comments.

First, as often happens in discussions that come up related to Woit's blog, I take umbrage at the common assumption that "theoretical physics" is equated with  theories of elementary particles and string theory. The simplest argument against the narcissism of the proponents of this narrow view is that there are five Physical Review journals (A and E). Each contains (very roughly half) theory papers and only D is concerned with such topics.

Issues of emotional and mental health feature prominently; although, not as explicitly discussed as they could be.

Henderson struggles with working 15 hours a day, confirming my view that this is a big mistake.

The echo of “You can do whatever you want” still rang in my ears.

This is something that he learnt from his father and I consider is one of the three biggest lies that Western high school students are taught and need to recnounce as undergraduates.

The lack of direction and floundering in his research project on quantum gravity is unrepresentative of most Ph.D research in theoretical physics. It just suggests the field itself it at an impasse and is arguably unsuitable for Ph.D research.

A video worth showing non-scientists

Sometimes I give talks about science to high school students and to community groups, mostly churches. Recently I showed this one.



Besides the "wow factor" I think it is valuable because it demonstrates some very basic but profound and important points about science.

1. Common sense observation and experience can be misleading.

2. Consequently, nature appears sometimes to be counter intuitive.

3. The way to discover the way things really are is by doing experiments.

One can explain the historical significance of this experiment. Aristotle advocated basing science on common sense observations [heavy objects fall faster, objects that start their motion eventually slow down unless a force is applied to them, objects on earth move in a qualitatively different manner to those in the heavens, ....]. In contrast, Galileo went against this and did real experiments, dropping two balls of different mass [probably not from the leaning tower of Pisa].

This can also lead to a discussion of how scientific observations today confront us today with many counter-intuitive realities such as wave-particle duality, Schrodinger's cat, dark matter, ....

For high school or introductory college students who know Newton's laws of motion and gravitation one can explain how this illustrates the equality of inertial and gravitational mass.

Aside. Thanks to insights from my wife, I stop the video before the very end when Brian Cox starts talking about Einstein and the Principle of Equivalence. Non-scientists find this too confusing, get fixated on it since it is the last thing they hear, and then get distracted from the more basic stuff such as the above.

If your game, you could then discuss the problems with string theory....

The beauty and mysteries of imaginary time and temperature

Yesterday, at UQ Robert Mann gave a nice Quantum Science seminar, "Hot and Cold Accelerating Detectors".

It concerned the Unruh effect: suppose one observer is constantly accelerating relative to another. Then, what is a quantum vacuum (for a free boson or fermion field) to one observer is a thermally populated state to the other.

Specifically, if one considers a field with wave vector k and energy Ω k. Then the expectation of the number operator is,
$$\begin{array}{}\text{(5)}& ⟨<!--\; ⟨\; -->0|b_k^{†<!--\; †\; -->}{b}_k|0⟩<!--\; ⟩\; -->=(e^{2\mathrm{\pi <!--\; \pi \; -->}{\mathrm{\Omega <!--\; \Omega \; -->}}_k/g}-<!--\; -\; -->1{)}^{-<!--\; -\; -->1},\end{array}$$
which corresponds to a Bose distribution with a temperature given by
$$\begin{array}{}& T_{\mathrm{U}\mathrm{n}\mathrm{r}\mathrm{u}\mathrm{h}}=\frac{g}{2\mathrm{\pi <!--\; \pi \; -->}}=\frac{\mathrm{\hslash <!--\; \hslash \; -->}g}{2\mathrm{\pi <!--\; \pi \; -->}c{k}_B}\end{array}$$
where g is the constant acceleration. Note that this formula involves relativity (c), quantum physics (hbar), and statistical mechanics (kB).

I feel there is something rather profound going on here.
Without doing the calculation, it is perhaps not totally surprising that the accelerated observer sees a non-trivial occupation of excited states of the quantum field.
However, what is rather surprising to me is that the state occupation numbers has to be that associated with thermodynamic equilibrium.   Why not some other distribution? And that this holds for both fermions and bosons.
After all, you are starting purely with relativity [and the mathematics of Rindler co-ordinates] and quantum field theory and you are ending up with quantum statistical mechanics.
Is the thermal distribution just a "mathematical accident" because cosh functions are appearing in the Rindler co-ordinates, Bogoliubov transformation of the quantum field, and in thermal distribution?

The Scholarpedia page is helpful, stating this
``can also be understood as a manifestation of the general relationship between temperature and imaginary time in quantum statistical mechanics (KMS theory). When t and τ are extended as complex variables, iτ is revealed as an angular variable in the (it,z) plane. The periodicity determined by g, the acceleration, is the only one that makes functions of τ be analytic in t. That period corresponds, under the KMS theory, to the reciprocal of the Unruh temperature (Dowker, 1978; Christensen and Duff, 1978; Sewell, 1982; Bell et al., 1985; Fulling and Ruijsenaars, 1987).''

I welcome any further elucidations on this rich and subtle issue.

Stokes-Einstein relation between viscosity and diffusion in liquids

The Stokes-Einstein equation

relates the diffusion constant D of a macroscopic particle of radius r undergoing a Brownian motion to the viscosity eta of the fluid in which it is immersed.
It is a beautiful and simple example of a fluctuation-dissipation relation.

But suppose now we think about one of the individual atoms or molecules in the fluid. It also undergoes Brownian motion and one can define a self-diffusion constant.
It is amazing to me that the Stokes-Einstein relation still holds for a wide range of liquids, temperatures, and pressures with r being of the order of the molecular radius.

The figure and table below are taken from this paper.

Can this relation be derived from microscopic theory?
Zwanzig gave a heuristic justification here.
Rah and Eu gave a derivation from stat. mech. here.

The Stokes-Einstein relation does break down as one approaches the glass temperature in a supercooled liquid, as for example shown here. The origin of that breakdown is controversial, as is many phenomena involving glasses.

Seeing the effects of relativity with the naked eye

Our natural tendency is to think that to see the effects of Einstein's special theory of relativity you have to be travelling at some significant fraction of the speed of light. However, this is not the case. In solid state physics I am aware of three concrete phenomena that are purely due to relativistic effects.

1. Gold metal is the colour "gold".
According to Wikipedia, "non-relativistic gold would be white. The relativistic effects are raising the 5d orbital and lowering the 6s orbital.^[11]"

2. Mercury is a liquid at room temperature.
This is nicely discussed in a recent blog post by Henry Rzepa concerning a recent paper that shows that relativistic effects shift the melting temperature by about 100 K.

3. Magnetic anisotropy and hysteresis in ferromagnets.
This results from spin-orbit coupling which is a consequence of relativity.

Are scientific press conferences bad?

I fear that may be the case.
Previous cases of premature announcements include cold fusion, "life on mars" [really dead germs on meteorites from mars], neutrinos travelling faster than the speed of light, a Caltech theoretical chemist claiming he had solved high-Tc superconductivity,.....

In march BICEP2 scientists called a press conference to announce they had discovered evidence for cosmic inflation. This coincided with them placing a paper on the arXiv and Stanford releasing a Youtube video, that subsequently went viral, showing Andrei Linde being presented with the exciting news.

However, now questions are being asked. The chronology is described by Peter Woit on Not Even Wrong and there is a nice discussion of the science by Matt Strassler. The key issue seems to be the method used for subtracting the background signal due to galactic dust. It seems that BICEP2 scientists estimated this background signal by "scraping data" off the powerpoint slide from a talk given by their Planck competitors! But was this a robust estimate?

The issue has received coverage in the press including this Washington Post article.

I think there is a broader issue here of the role of rumours in the social media age. I am skeptical that one can have a forthright, robust, constructive, and thoughtful scientific discussion via tweets and blog rumours, when not all parties have access to the relevant information and there are a bunch of journalists watching. The problem is accentuated if people have already make strong public claims that have been further hyped up by the media and institutional press offices.

I thought that this issue of science via the media was a relatively new one. However, I learned this week that even Einstein was not immune from it! There is an interesting article in APS News, A Unified Theory of Journalistic Caution by science journalist Calla Cofield. She points out how Einstein went to the press to publicise his [now discredited] theory of distant parallelism. The New York Times covered it uncritically, since he was Einstein, after all.

Fulfilling Einstein's dream

Einstein considered that quantum mechanics must only be an approximate theory which was derivable from a "classical" theory which did not have the same philosophical problems. In a 1949 essay, Reply to Criticisms published in response to the essays in Albert Einstein: Philosopher-Scientist he wrote

...Within the framework of statistical quantum theory there is no such thing as a complete description of the individual system. ....The attempt to conceive the quantum-theoretical description as the complete description of the individual systems leads to unnatural theoretical interpretations, which become immediately unnecessary if one accepts the interpretation that the description refers to ensembles of systems and not to individual systems. .... For if the statistical quantum theory does not pretend to describe the individual system (and its development in time) completely, it appears unavoidable to look elsewhere for a complete description of the individual system; in doing so it would be clear from the very beginning that the elements of such a description are not contained within the conceptual scheme of the statistical quantum theory....this scheme could not serve as the basis of theoretical physics. Assuming the success of efforts to accomplish a complete physical description, the statistical quantum theory would, within the framework of future physics, take an approximately analogous position to the statistical mechanics within the framework of classical mechanics. I am rather firmly convinced that the development of theoretical physics will be of this type; but the path will be lengthy and difficult.

Stephen Adler has attempted to fulfill this mission in his book,  Quantum Theory as an Emergent Phenomena: Statistical Mechanics of Matrix Models as the Precursor of Quantum Field Theory
A review of the book by Philip Pearle gives a very helpful summary.  More comments on that later...