Steven S. Gubser: Thunder and Lightning from Neutron Star mergers

As of late 2015, we have a new way of probing the cosmos: gravitational radiation. Thanks to LIGO (the Laser Interferometer Gravitational-wave Observatory) and its new sibling Virgo (a similar interferometer in Italy), we can now “hear” the thumps and chirps of colliding massive objects in the universe. Not for nothing has this soundtrack been described by LIGO scientists as “the music of the cosmos.” This music is at a frequency easily discerned by human hearing, from somewhat under a hundred hertz to several hundred hertz. Moreover, gravitational radiation, like sound, is wholly different from light. It is possible for heavy dark objects like black holes to produce mighty gravitational thumps without at the same time emitting any significant amount of light. Indeed, the first observations of gravitational waves came from black hole merger events whose total power briefly exceeded the light from all stars in the known universe. But we didn’t observe any light from these events at all, because almost all their power went into gravitational radiation.

In August 2017, LIGO and Virgo observed a collision of neutron stars which did produce observable light, notably in the form of gamma rays. Think of it as cosmic thunder and lightning, where the thunder is the gravitational waves and the lightning is the gamma rays. When we see a flash of ordinary lightning, we can count a few seconds until we hear the thunder. Knowing that sound travels one mile in about five seconds, we can reckon how distant the event is. The reason this method works is that light travels much faster than sound, so we can think of the transmission of light as instantaneous for purposes of our estimate.

Things are very different for the neutron star collision, in that the event took place about 130 million light years away, but the thunder and lightning arrived on earth pretty much simultaneously. To be precise, the thunder was first: LIGO and Virgo heard a basso rumble rising to a characteristic “whoop,” and just 1.7 seconds later, the Fermi and INTEGRAL experiments observed gamma ray bursts from a source whose location was consistent with the LIGO and Virgo observations. The production of gamma rays from merging neutron stars is not a simple process, so it’s not clear to me whether we can pin that 1.7 seconds down as a delay precisely due to the astrophysical production mechanisms; but at least we can say with some confidence that the propagation time of light and gravity waves are the same to within a few seconds over 130 million light years. From a certain point of view, that amounts to one of the most precise measurements in physics: the ratio of the speed of light to the speed of gravity equals 1, correct to about 14 decimal places or better.

The whole story adds up much more easily when we remember that gravitational waves are not sound at all. In fact, they’re nothing like ordinary sound, which is a longitudinal wave in air, where individual air molecules are swept forward and backward just a little as the sound waves pass them by. Gravitational waves instead involve transverse disturbances of spacetime, where space is stretched in one direction and squeezed in another—but both of those stretch-squeeze directions are at right angles to the direction of the wave. Light has a similar transverse quality: It is made up of electric and magnetic fields, again in directions that are at right angles to the direction in which the light travels. It turns out that a deep principle underlying both Maxwell’s electromagnetism and Einstein’s general relativity forces light and gravitational waves to be transverse. This principle is called gauge symmetry, and it also guarantees that photons and gravitons are massless, which implies in turn that they travel at the same speed regardless of wavelength.

It’s possible to have transverse sound waves: For instance, shearing waves in crystals are a form of sound. They typically travel at a different speed from longitudinal sound waves. No principle of gauge symmetry forbids longitudinal sound waves, and indeed they can be directly observed, along with their transverse cousins, in ordinary materials like metals. The gauge symmetries that forbid longitudinal light waves and longitudinal gravity waves are abstract, but a useful first cut at the idea is that there is extra information in electromagnetism and in gravity, kind of like an error-correcting code. A much more modest form of symmetry is enough to characterize the behavior of ordinary sound waves: It suffices to note that air (at macroscopic scales) is a uniform medium, so that nothing changes in a volume of air if we displace all of it by a constant distance.

In short, Maxwell’s and Einstein’s theories have a feeling of being overbuilt to guarantee a constant speed of propagation. And they cannot coexist peacefully as theories unless these speeds are identical. As we continue Einstein’s hunt for a unified theory combining electromagnetism and gravity, this highly symmetrical, overbuilt quality is one of our biggest clues.

The transverse nature of gravitational waves is immediately relevant to the latest LIGO / Virgo detection. It is responsible for the existence of blind spots in each of the three detectors (LIGO Hanford, LIGO Livingston, and Virgo). It seems like blind spots would be bad, but they actually turned out to be pretty convenient: The signal at Virgo was relatively weak, indicating that the direction of the source was close to one of its blind spots. This helped localize the event, and localizing the event helped astronomers home in on it with telescopes. Gamma rays were just the first non-gravitational signal observed: the subsequent light-show from the death throes of the merging neutron stars promises to challenge and improve our understanding of the complex astrophysical processes involved. And the combination of gravitational and electromagnetic observations will surely be a driver of new discoveries in years and decades to come.

 

BlackSteven S. Gubser is professor of physics at Princeton University and the author of The Little Book of String TheoryFrans Pretorius is professor of physics at Princeton. They both live in Princeton, New Jersey. They are the authors of The Little Book of Black Holes.

Ian Hurd: Good medicine for bad politics? Rethinking the international rule of law

When an international crisis erupts it is common to hear experts say that the situation will be improved if all parties stick to international law. From the Syrian war to Burma’s massacres to Guantanamo torture, faithful compliance with the law of nations is often prescribed as the best way forward. I wrote this book because I was curious about the idea that international law is good medicine for bad policies, a kind of non-political, universal good. International law often appears like a magical machine that takes in hot disagreements about how things should unfold and produces cool solutions that serve the interests of everyone. The book examines this idea with a degree of skepticism, holds it up against some empirical cases, and suggests more realistic ways of thinking about the dynamics between international politics and international law.

The standard model of international law is built on two components, one more institutional and the other more normative. On the one hand, international law is seen as providing a framework for the coexistence for governments. Laws on diplomatic immunity, non-interference across borders, and the peaceful settlement of disputes, help organize inter-governmental relations and give a kind of civility to world politics. On this view, following the rules makes it possible for diplomacy and negotiation to happen. The second, normative strand adds substantive values such as a commitment to human rights, to the protection of refugees, and against nuclear proliferation. Here, following the rules is said to be important because it enhances human welfare and the other goals encoded by the law. The two strands agree that compliance with international rules is beneficial and that violations of the rules lead to international disorder at best—and violence and chaos at worst.

This represents what I see as a conventional view of the international rule of law. It is a commitment to the idea that governments should follow their legal obligations and that when they do the world is a better place. It is an ideology, in the sense noted by Shirley Scott.

My book explores the premise and the power of this ideology and its influence in global politics. I look at the presumptions that it rests on and the practices it makes possible. I see the power of international law on display in the ways that governments and others make use of legal resources and categories to understand, justify, and act in the world. This is a social power, built on the idea of the rule of law and employed by governments in the service of a wide array of goals.

The book does not aim to answer questions about why states comply with or flout the law. Instead, it asks what they do with the law – and why, and with what effects. As a methodology, this points toward looking for where international law appears in the strategies of governments. On substance, it suggests a close connection between international law and political power. International law has influence in certain situations, when powerful actors find it useful. For instance, the US gave legal arguments for why Russia’s annexation of Crimea was unlawful and therefore should not be accepted by other countries. In response, Russia gave legal arguments to sustain its behavior. Legal experts may well conclude that one side had the stronger legal argument; disagreements about interpretation and application are central to legal practices. But my curiosity comes from seeing both sides use legal arguments as political resources in defense of their preferred outcome.

The use of law to legitimize state policy is a central feature of contemporary international politics. And yet to some, the instrumental use of law is said to reveal the inappropriate politicization of law, contradicting their idea of the rule of law itself. I see it the other way around: the international rule of law is the instrumental use of law. The legalization of international politics gives legal rationalizations their political weight. Their political weight makes them important sites of contestation. In a legalized world, it makes sense for actors to contest their actions in the language of law. To borrow Helen Kinsella’s example, the line between civilian and combatant in a war zone distinguishes those who should be killed from those who should not; the line is defined by the Geneva Conventions and other legal instruments and it is brought to life (and death) as governments interpret it in relation to those whom they wish to kill. Legal categories have political valence and this makes them important resources of power and thus worth fighting over. How else to make sense of the energy that governments put into shaping rules that reflect their interests?

Recognizing the close connection between international and power politics opens a way to considering the political productivity of international law. Law is not only regulative and constraining; it is also empowering and permissive. By defining some acts as unlawful and others as lawful, it makes the former harder for governments to do (or more expensive) and the latter easier. The availability of a legal justification smoothes the way for action just as much as its unavailability impedes it. If we look at one side of this balance, we see for instance that the UN Charter outlaws the use of force by governments and limits their autonomy with respect to going to war. On the other side the Charter also authorizes them to go to war as needed for ‘self-defense’ against an armed attack. In ‘self-defense,’ the Charter creates a new legal resource with the capacity to differentiate between a lawful and an unlawful war. This is a powerful tool for governments, a means for legalizing their recourse to force, and they have used it with enthusiasm since 1945. The Charter produced something that previously didn’t exist and as a consequence changed how governments go to war, how they justify their wars, and how they think about their security in relation to external threats.

With the political productivity of international law in mind, the book shows that international law is inseparable from politics and thus from power. For powerful governments, international law puts an instrument in their tool-kit as they seek to influence what happens in the world, and for the less powerful it is a tool that they might also seek to take up when they can but may equally be a means of control whose influence they seek to escape.

There isn’t much evidence to back up the presumption that international law steers global affairs naturally toward better outcomes. How to Do Things With International Law is neither a celebration of international law nor an indictment. It offers instead a look into its practical politics, a messy world of power politics that is as full of interpretation, ambiguity, violence and contestation as any other corner of social life.

HurdIan Hurd is associate professor of political science at Northwestern University. He is the author of After Anarchy and How to Do Things with International Law.

Gary Saul Morson & Morton Schapiro: The Humanomics of Tax Reform

CentsThe Trump administration is now placing tax reform near the top of its legislative agenda. Perhaps they will garner the votes for tax reduction, but reform? Good luck.

It has been three decades since there has been meaningful tax reform in this country. In 1986, tax shelters were eliminated, the number of tax brackets went from 15 to 4, including a reduction of the highest marginal tax rate from 50% to 38.5% and the standard deduction was increased, simplifying tax preparation and resulting in zero tax liability for millions of low-income families. At the same time, a large-scale expansion of the alternative minimum tax affected substantial numbers of the more affluent.

President Reagan insisted that the overall effect be neutral with regard to tax revenues. That demand made it possible to set aside the issue of whether government should be larger or smaller and instead focus on inefficiencies or inequities in how taxes were assessed. Two powerful Democrats, Dick Gephardt in the House and Bill Bradley in the Senate, were co-sponsors.

Economists might evaluate the merits of this monumental piece of legislation in terms of the incentives and disincentives it created, its ultimate impact on labor force participation, capital investment and the like, but there is another metric to be evaluated – was it perceived to be fair? Accounts from that day imply that it was.

The notion of fairness is not generally in the wheelhouse of economics. But the humanities have much to say on that matter.

To begin with, literature teaches that fairness is one of those concepts that seem simple so long as one does not transcend one’s own habitual way of looking at things. As soon as one learns to see issues from other points of view, different conceptions of fairness become visible and simple questions become more complex. Great novels work by immersing the reader in one character’s perspective after another, so we learn to experience how different people – people as reasonable and decent as we ourselves are – might honestly come to see questions of fairness differently.

So, the first thing that literature would suggest is that, apart from the specific provisions of the 1986 tax reform, the fact that it was genuinely bipartisan was part of what made it fair. Bipartisanship meant the reform was not one side forcing its will on the other. Had the same reform been passed by one party, it would not have seemed so fair. Part of fairness is the perception of fairness, which suggests that the process, not just the result, was fair.

Fairness, of course, also pertains to the content of the reforms. What are the obligations of the rich to support needy families? Are there responsibilities of the poor to participate however they can in providing for their own transformation?

In Tolstoy’s novel Anna Karenina, two main characters, Levin and Stiva, go hunting with the young fop, Vasenka, and as they encounter hard-working peasants, they start discussing the justice of economic inequality. Only foolish Vasenka can discuss the question disinterestedly, because it is, believe it or not, entirely new to him: “`Yes, why is it we spend our time riding, drinking, shooting doing nothing, while they are forever at work?’ said Vasenka, obviously for the first time in his life reflecting on the question, and consequently considering it with perfect sincerity.” Can it really be that an educated person has reached adulthood with this question never having occurred to him at all?

And yet, isn’t that the position economists find themselves in when they ignore fairness? When they treat tax reform, or any other issue, entirely in economic terms? Levin recognizes that there is something unfair about his wealth, but also recognizes that there is no obvious solution: it would do the peasants no good if he were to just give away his property. Should he make things more equal by making everyone worse off? On the contrary, his ability to make farmland more productive benefits the peasants, too. So, what, he asks, should be done?

Levin also knows that inequality is not only economic. If one experiences oneself as a lesser person because of social status, as many of the peasants do, that is itself a form of inequality entirely apart from wealth. In our society, we refer to participants in government as “taxpayers.” Does that then mean that to exempt large numbers of people from any taxation entirely demeans them – not least of all, in their own eyes?  There may be no effective economic difference between a very small tax and none at all, but it may make a tremendous psychological difference. Isn’t the failure to take the psychological effect of tax rates seriously as disturbingly innocent as Vasenka’s question about inequality?

Combining a humanistic and an economic approach might not give us specific answers, but it does make questions of fairness, including symbolic effects, part of the question. And in a democracy, where popular acceptance of the rules as legitimate is crucial, that would be a step forward.

Gary Saul Morson is the Lawrence B. Dumas Professor of the Arts and Humanities and professor of Slavic languages and literatures at Northwestern University. His many books include Narrative and Freedom, “Anna Karenina” in Our Time, and The Words of Others: From Quotations to Culture. Morton Schapiro is the president of Northwestern University and a professor of economics. His many books include The Student Aid Game. Morson and Schapiro are also the editors of The Fabulous Future?: America and the World in 2040 and the authors of Cents and Sensibility: What Economics Can Learn from the Humanities.

Announcing the trailer for The Seduction of Curves by Allan McRobie

CurvesCurves are seductive. These smooth, organic lines and surfaces—like those of the human body—appeal to us in an instinctive, visceral way that straight lines or the perfect shapes of classical geometry never could. In this large-format book, lavishly illustrated in color throughout, Allan McRobie takes the reader on an alluring exploration of the beautiful curves that shape our world—from our bodies to Salvador Dalí’s paintings and the space-time fabric of the universe itself. A unique introduction to the language of beautiful curves, this book may change the way you see the world.

Allan McRobie is a Reader in the Engineering Department at the University of Cambridge, where he teaches stability theory and structural engineering. He previously worked as an engineer in Australia, designing bridges and towers.

Big Pacific: All About The Great White Shark

From page 14-17 of Big Pacific:

Peripatetic pilgrims of the Pacific, Great white sharks have one of the widest geographic ranges of any marine animal. Individuals migrate vast distances — even across entire ocean basins — and in the Pacific they can be found as far north as Alaska and as far south as New Zealand’s Sub-Antarctic Islands. Every year, however, a great many of these oceanic travelers congregate around La Isla Guadalupe (Guadalupe Island), 241 kilometers (150 miles) off the western coast of Mexico. First to arrive, in spring and summer, are males. The females — who generally dwarf the males — arrive in the fall. It’s thought mating occurs in the late fall, although no one has ever witnessed great whites in the act. Pregnant females spend a year or more at sea while as many as ten embryos develop inside their bodies. At birth the pups measure around a meter (3 to 4 feet). Like their parents, these youngsters disappear into the deep blue, perhaps using their remarkable ability to read the magnetic fields of the Earth’s crust to navigate their way across the ocean.

The Great White Shark. With little obvious differentiation other than the size disparity, it can be tricky to distinguish between male and female Great whites.

Unsurprisingly for such a highly evolved predator, Great white sharks are endowed with keen sensory organs. Their sense of smell — which enables them to detect a single drop of blood in 10 billion drops of water — is legendary and helps give rise to their fearsome reputation as hunters. But their vision is also good: the retina of a Great white’s eye is dually adapted for day vision and low light. Even more impressive is their ability to detect electrical currents through pores on their snouts which are filled with cells called the ampullae of Lorenzini.

Big Pacific: Passionate, Voracious, Mysterious, Violent
By Rebecca Tansley

The Pacific Ocean covers one-third of Earth’s surface—more than all of the planet’s landmasses combined. It contains half of the world’s water, hides its deepest places, and is home to some of the most dazzling creatures known to science. The companion book to the spectacular five-part series on PBS produced by Natural History New Zealand, Big Pacific breaks the boundaries between land and sea to present the Pacific Ocean and its inhabitants as you have never seen them before.

Illustrated in full color throughout, Big Pacific blends a wealth of stunning Ultra HD images with spellbinding storytelling to take you into a realm teeming with exotic life rarely witnessed up close—until now. The book is divided into four sections, each one focusing on an aspect of the Pacific. “Passionate Pacific” looks at the private lives of sea creatures, with topics ranging from the mating behaviors of great white sharks to the monogamy of wolf eels, while “Voracious Pacific” covers hunting and feeding. In “Mysterious Pacific,” you will be introduced to the Pacific’s more extraordinary creatures, like the pufferfish and firefly squid, and explore some of the region’s eerier locales, like the turtle tombs of Borneo and the skull caves of Papua New Guinea. “Violent Pacific” examines the effects of events like natural disasters on the development of the Pacific Ocean’s geography and the evolution of its marine life.

Providing an unparalleled look at a diverse range of species, locations, and natural phenomena, Big Pacific is truly an epic excursion to one of the world’s last great frontiers.

Learn more by watching Big Pacific, airing on select PBS affiliates this fall. Watch the trailer below:

Bird Fact Friday – Southern Carmine Bee-eater

From page 97 of Birds of Kruger National Park:

The Southern Carmine Bee-eater is a large, spectacular, long, slender, carmine-pink and teal-blue bee-eater with a long, pointed tail and black bill and facial mask. Immatures are duller than adults and lack long tail feathers. It is a common non-breeding summer migrant (December–April) to Kruger, where it can gather in large groups and often attends bush fires to feed on fleeing insects.

A mature Southern Carmine Bee-eater (Merops nubicoides). (Photo credit: Keith Barnes & Ken Behrens)

The “trik-trik-trik” or “ga-gaga” calls, sound more guttural than those of European Bee-eater. Although not a common behaviour, Southern Carmine Bee-eaters have been recorded sitting on the backs of antelopes or Kori Bustards, swooping out and catching insects that are flushed. It specializes in catching large flying insects, including termites, cicadas, dragonflies, butterflies and locusts and regurgitates pellets of indigestible insect remains.

 

Birds of Kruger National Park
Keith Barnes & Ken Behrens

South Africa’s Kruger National Park is one of the largest and most iconic conservation areas in Africa. Habitats range from wide-open savannah and rugged thornveld to broadleaved mopani woodland. This microhabitat variation gives Kruger a phenomenal diversity of some 520 bird species, half of which are resident. From Africa’s most extraordinary eagles, like the scarlet-faced Bateleur, to electric-colored glossy-starlings and jewel-like finches, Kruger offers an avian celebration of form and color. It is also a crucial conservation area, supporting South Africa’s largest viable populations of vultures, eagles, and large terrestrial birds.

This field guide offers a unique window into the world of Kruger’s birds. More than 500 stunning color photographs illustrate the 259 most frequently encountered species, and a habitat-based approach assists in identification. The authoritative text provides key information about identification, habitat, behavior, biology, and conservation. The guide contains information likely to be new to even the most experienced birders, but is written in a nontechnical style that makes it accessible to anyone.

  • An essential guide to Kruger’s birds
  • Perfect for new and experienced birders alike
  • Small, portable format ideal for field use
  • Unique attractive layout with more than 500 stunning color photographs
  • Covers the 259 most frequently seen species
  • Uses a habitat-based approach to aid identification
  • Authoritative and accessible text provides key information about identification, behavior, biology, and conservation

 

Steven S. Gubser & Frans Pretorius: The Little Book of Black Holes

Black holes, predicted by Albert Einstein’s general theory of relativity more than a century ago, have long intrigued scientists and the public with their bizarre and fantastical properties. Although Einstein understood that black holes were mathematical solutions to his equations, he never accepted their physical reality—a viewpoint many shared. This all changed in the 1960s and 1970s, when a deeper conceptual understanding of black holes developed just as new observations revealed the existence of quasars and X-ray binary star systems, whose mysterious properties could be explained by the presence of black holes. Black holes have since been the subject of intense research—and the physics governing how they behave and affect their surroundings is stranger and more mind-bending than any fiction. The Little Book of Black Holes by Steven S. Gubser and Frans Pretorius takes readers deep into the mysterious heart of the subject, offering rare clarity of insight into the physics that makes black holes simple yet destructive manifestations of geometric destiny. Read on to learn a bit more about black holes and what inspired the authors to write this book.

Your book tells the story of black holes from a physics perspective. What are black holes, really? What’s inside?

Black holes are regions of spacetime from which nothing can escape, not even light. In our book, we try to live up to our title by getting quickly to the heart of the subject, explaining in non-technical terms what black holes are and how we use Einstein’s theory of relativity to understand them. What’s inside black holes is a great mystery. Taken at face value, general relativity says spacetime inside a black hole collapses in on itself, so violently that singularities form. We need something more than Einstein’s theory of relativity to understand what these singularities mean. Hawking showed that quantum effects cause black holes to radiate very faintly. That radiation is linked with quantum fluctuations inside the black hole. But it’s a matter of ongoing debate whether these fluctuations are a key to resolving the puzzle of the singularity, or whether some more drastic theory is needed.

How sure are we that black holes exist?

A lot more certain than we were a few years ago. In September 2015, the LIGO experiment detected gravitational waves from the collision of two black holes, each one about thirty times the mass of the sun. Everything about that detection fit our expectations based on Einstein’s theories, so it’s hard to escape the conclusion that there really are black holes out there. In fact, before the LIGO detection we were already pretty sure that black holes exist. Matter swirling around gigantic black holes at the core of distant galaxies form the brightest objects in the Universe. They’re called quasars, and the only reason they’re dim in our sight is that they’re so far away, literally across the Universe. Similar effects around smaller black holes generate X-rays that we can detect relatively nearby, mere thousands of light years away from us. And we have good evidence that there is a large black hole at the center of the Milky Way.

Can you talk a bit about the formation of black holes?

Black holes with mass comparable to the sun can form when big stars run out of fuel and collapse in on themselves. Ordinarily, gravity is the weakest force, but when too much matter comes together, no force conceivable can hold it up against the pull of gravity. In a sense, even spacetime collapses when a black hole forms, and the result is a black hole geometry: an endless inward cascade of nothing into nothing. All the pyrotechnics that we see in distant quasars and some nearby X-ray sources comes from matter rubbing against itself as it follows this inward cascade.

How have black holes become so interesting to non-specialists? How have they been glorified in popular culture?

There’s so much poetry in black hole physics. Black hole horizons are where time stands still—literally! Black holes are the darkest things that exist in Nature, formed from the ultimate ashes of used-up stars. But they create brilliant light in the process of devouring yet more matter. The LIGO detection was based on a black hole collision that shook the Universe, with a peak power greater than all stars combined; yet we wouldn’t even have noticed it here on earth without the most exquisitely sensitive detector of spacetime distortions ever built. Strangest of all, when stripped of surrounding matter, black holes are nothing but empty space. Their emptiness is actually what makes them easy to understand mathematically. Only deep inside the horizon does the emptiness end in a terrible, singular core (we think). Horrendous as this sounds, black holes could also be doorways into wormholes connecting distant parts of the Universe. But before packing our bags for a trip from Deep Space Nine to the Gamma Quadrant, we’ve got to read the fine print: as far as we know, it’s impossible to make a traversable wormhole.

What inspired you to write this book? Was there a point in life where your interest in this topic was piqued?

We both feel extremely fortunate to have had great mentors, including Igor Klebanov, Curt Callan, Werner Israel, Matthew Choptuik, and Kip Thorne who gave us a lot of insight into black holes and general relativity. And we owe a big shout-out to our editor, Ingrid Gnerlich, who suggested that we write this book.

GubserSteven S. Gubser is professor of physics at Princeton University and the author of The Little Book of String Theory. Frans Pretorius is professor of physics at Princeton.

Kip Thorne & Roger Blandford on Modern Classical Physics

PhysicsThis first-year, graduate-level text and reference book covers the fundamental concepts and twenty-first-century applications of six major areas of classical physics that every masters- or PhD-level physicist should be exposed to, but often isn’t: statistical physics, optics (waves of all sorts), elastodynamics, fluid mechanics, plasma physics, and special and general relativity and cosmology. Growing out of a full-year course that the eminent researchers Kip S. Thorne, winner of the 2017 Nobel Prize in Physics, and Roger D. Blandford taught at Caltech for almost three decades, this book is designed to broaden the training of physicists. Its six main topical sections are also designed so they can be used in separate courses, and the book provides an invaluable reference for researchers.

This book emerged from a course you both began teaching nearly 4 decades ago. What drove you to create the course, and ultimately to write this book?

KST: We were unhappy with the narrowness of physics graduate education in the United States. We believed that every masters-level or PhD physicist should be familiar with the basic concepts of all the major branches of classical physics and should have some experience applying them to real world phenomena. But there was no obvious route to achieve this, so we created our course.

RDB: Of course we had much encouragement from colleagues who helped us teach it and students who gave us invaluable feedback on the content.

The title indicates that the book is a “modern” approach to classical physics (which emphasizes physical phenomena at macroscopic scales). What specifically is “modern” in your book’s approach to this subject?

KST: Classical-physics ideas and tools are used extensively today in research areas as diverse as astrophysics, high-precision experimental physics, optical physics, biophysics, controlled fusion, aerodynamics, computer simulations, etc. Our book draws applications from all these modern topics and many more. Also, these modern applications have led to powerful new viewpoints on the fundamental concepts of classical physics, viewpoints that we elucidate—for example, quantum mechanical viewpoints and language for purely classical mode-mode coupling in nonlinear optics and in nonlinear plasma physics.

Why do you feel that it is so important for readers to become more familiar with classical physics, beyond what they may have been introduced to already?

KST: In their undergraduate and graduate level education, most physicists have been exposed to classical mechanics, electromagnetic theory, elementary thermodynamics, and little classical physics beyond this. But in their subsequent careers, most physicists discover that they need an understanding of other areas of classical physics (and this book is a vehicle for that).

In many cases they may not even be aware of their need. They encounter problems in their research or in R&D where powerful solutions could be imported from other areas of classical physics, if only they were aware of those other areas. An example from my career: in the 1970s, when trying to understand recoil of a binary star as it emits gravitational waves, I, like many relativity physicists before me, got terribly confused. Then my graduate student, Bill Burke—who was more broadly educated than I—said “we can resolve the confusion by adopting techniques that are used to analyze boundary layers in fluid flows around bodies with complicated shapes.” Those techniques (matched asymptotic expansions), indeed, did the job, and through Bill, they were imported from fluid mechanics into relativity.

RDB: Yes. To give a second example, when I was thinking about ways to accelerate cosmic rays, I recalled graduate lectures on stellar dynamics and found just the tools I needed.

You also mention in the book that geometry is a deep theme and important connector of ideas. Could you explain your perspective, and how geometry is used thematically throughout the book?

KST: The essential point is that, although coordinates are a powerful, and sometimes essential, tool in many calculations, the fundamental laws of physics can be expressed without the aid of coordinates; and, indeed, their coordinate-free expressions are generally elegant and exceedingly powerful. By learning to think about the laws in coordinate-free (geometric) language, a physicist acquires great power. For example, when one searches for new physical laws, requiring that they be geometric (coordinate-free) constrains enormously the forms that they may take. And in many practical computations (for example, of the relativistic Doppler shift), a geometric route to the solution can be faster and much more insightful than one that uses coordinates. Our book is infused with this.

RDB: We are especially keen on presenting these fundamental laws in a manner which makes explicit the geometrically formulated conservation laws for mass, momentum, energy, etc. It turns out that this is often a good starting point when one wants to solve these equations numerically. But ultimately, a coordinate system must be introduced to execute the calculations and interpret the output.

One of the areas of application that you cover in the book is cosmology, an area of research that has undergone a revolution over the past few decades. What are some of the most transformative discoveries in the field’s recent history? How does classical physics serve to underpin our modern understanding of how the universe formed and is evolving? What are some of the mysteries that continue to challenge scientists in the field of cosmology?   

RDB: There have indeed been great strides in understanding the large scale structure and evolution of the universe, and there is good observational support for a comparatively simple description. Cosmologists have found that 26 percent of the energy density in the contemporary, smoothed-out universe is in the form of “dark matter,” which only seems to interact through its gravity. Meanwhile, 69 percent is associated with a “cosmological constant,” as first introduced by Einstein and which causes the universe to accelerate. The remaining five percent is the normal baryonic matter which we once thought accounted for essentially all of the universe. The actual structure that we observe appears to be derived from almost scale-free statistically simple, random fluctuations just as expected from an early time known as inflation. Fleshing out the details of this description is almost entirely an exercise in classical physics. Even if this description is validated by future observations, much remains to be understood, including the nature of dark matter and the cosmological constant, what fixes the normal matter density, and the great metaphysical question of what lies beyond the spacetime neighborhood that we can observe directly.

KST: Remarkably, in fleshing out the details in the last chapter of our book, we utilize classical-physics concepts and results from every one of the other chapters. ALL of classical physics feeds into cosmology!

The revolution in cosmology that you describe depends upon many very detailed observations using telescopes operating throughout the entire electromagnetic spectrum and beyond. How do you deal with this in the book?

RDB: We make no attempt to describe the rich observational and experimental evidence, referring the reader to many excellent texts on cosmology that describe these in detail. However, we do describe some of the principles that underlie the design and operation of the radio and optical telescopes that bring us cosmological data.

There is has also been a lot of excitement regarding the recent observation by LIGO of gravitational waves caused by merging black holes. How is this subject covered in the book, and how, briefly, are some of the concepts of classical physics elucidated in your description of this cutting-edge research area?   

KST: LIGO’s gravitational wave detectors rely on an amazingly wide range of classical physics concepts and tools, so time and again we draw on LIGO for illustrations. The theory of random processes, spectral densities, the fluctuation-dissipation theorem, the Fokker-Planck equation; shot noise, thermal noise, thermoelastic noise, optimal filters for extracting weak signals from noise; paraxial optics, Gaussian beams, the theory of coherence, squeezed light, interferometry, laser physics; the interaction of gravitational waves with light and with matter; the subtle issue of the conservation or non conservation of energy in general relativity—all these and more are illustrated by LIGO in our book.

What are some of the classical physics phenomena in every day life that you are surprised more people do not fully understand—whether they are lay people, students, or scientists?

KST: Does water going down a drain really have a strong preference for clockwise in the northern hemisphere and counterclockwise in the south? How strong? What happens as you cross the equator? How are ocean waves produced? Why do stars twinkle in the night sky, and why doesn’t Jupiter twinkle? How does a hologram work? How much can solid objects be stretched before they break, and why are there such huge differences from one type of solid (for example thin wire) to another (a rubber band)?

RDB: I agree and have to add that I am regularly humbled by some every day phenomenon that I cannot explain or for which I have carried around for years a fallacious explanation. There is, rightly, a lot of focus right now on climate change, energy, hurricanes, earthquakes, and so on. We hear about them every day. We physicists need to shore up our understanding and do a better job of communicating this.

Do you believe that some of your intended readers might be surprised to discover the deep relevance of classical physics to certain subject areas?

KST: In subjects that physicists think of as purely quantum, classical ideas and classical computational techniques can often be powerful. Condensed matter physics is an excellent example—and accordingly, our book includes a huge number of condensed-matter topics. Examples are Bose-Einstein condensates, the van der Waals gas, and the Ising model for ferromagnetism.

RDB: Conversely, quantum mechanical techniques are often used to simplify purely classical problems, for example in optics.

Writing a book is always an intellectual journey. In the preparation of this tremendously wide-ranging book, what were some of the most interesting things you learned along the way?

KST: How very rich and fascinating is the world of classical physics—far more so than we thought in 1980 when we embarked on this venture. And then there are the new inventions, discoveries, and phenomena that did not exist in 1980 but were so important or mind-boggling that we could not resist including them in our book. For example, optical-frequency combs and the phase-locked lasers that underlie them, Bose-Einstein condensates, the collapse of the World Trade Center buildings on 9/11/01, the discovery of gravitational waves and the techniques that made it possible, laser fusion, and our view of the universe at large.

Kip S. Thorne is the Feynman Professor Emeritus of Theoretical Physics at Caltech. His books include Gravitation and Black Holes and Time Warps. Roger D. Blandford is the Luke Blossom Professor of Physics and the founding director of the Kavli Institute of Particle Astrophysics and Cosmology at Stanford University. Both are members of the National Academy of Sciences.

 

Global Math Week: The Universal Language

by Oscar Fernandez

FernandezFill in the blank: Some people speak English, some speak French, and some speak ____. I doubt you said “math.” Yet, as I will argue, the thought should have crossed your mind. And moreover, the fact that mathematics being a language likely never has, speaks volumes about how we think of math, and why we should start thinking of it—and teaching it—as a language.

To make my point, consider the following fundamental characteristics shared by most languages:

  •  A set of words or symbols (the language’s vocabulary)
  •  A set of rules for how to use these words or symbols (the language’s rules of grammar)
  •  A set of rules for combining these words or symbols to make statements (the language’s syntax)

Now think back to the math classes you have taken. I bet you will soon remember each of these characteristics present throughout your courses. (For instance, when you learned that 𝑎2 means 𝑎 × 𝑎, you were learning how to combine some of the symbols used in mathematics to make a statement—that the square of a number is the number multiplied by itself.) Indeed, viewed this way, every mathematics lesson can be thought of as a language lesson: new vocabulary, rules of grammar, or syntax is introduced; everyone then practices the new content; and the cycle repeats. By extension, every mathematics course can be thought of as a language course.

Now that I have you thinking of mathematics as a language, let me point out the many benefits of this new viewpoint. For one, this viewpoint helps dispel many myths about the subject. For instance, travel to any country and you will find a diverse set of people speaking that country’s language. Some are smarter than others; some are men and some women; perhaps some are Latino and some Asian. Group them as you wish, they will all share the capacity to speak the same language. The same is true of mathematics. It is not a subject accessible only to people of certain intelligence, sex, or races; we all have the capacity to speak mathematics. And once we start thinking of the subject as a language, we will recognize that learning mathematics is like learning any other language: all you need are good teachers, and lots of practice. And while mastering a language is often the endpoint of the learning process, mastering the language that is mathematics will yield much larger dividends, including the ability to express yourself precisely, and the capacity to understand the Universe. As Alfred Adler put it: “

Mathematics is pure language – the language of science. It is unique among languages in its ability to provide precise expression for every thought or concept that can be formulated in its terms.” Galileo—widely regarded the father of modern science—once wrote that Nature is a great book “written in the language of mathematics” (The Assayer, 1623). Centuries later, Einstein, after having discovered the equation for gravity using mathematics, echoed Galileo’s sentiment, writing: “pure mathematics is, in its way, the poetry of logical ideas” (Obituary for Emmy Noether, 1935). Most of us today wouldn’t use words like “language” and “poetry” to describe mathematics. Yet, as I will argue, we should. And moreover, we should start thinking of—and teaching—math as a language.

Oscar E. Fernandez is assistant professor of mathematics at Wellesley College and the author of The Calculus of Happiness: How a Mathematical Approach to Life Adds Up to Health, Wealth, and Love. He also writes about mathematics for the Huffington Post and on his website, surroundedbymath.com.

Kieran Setiya on Midlife: A Philosophical Guide

How can you reconcile yourself with the lives you will never lead, with possibilities foreclosed, and with nostalgia for lost youth? How can you accept the failings of the past, the sense of futility in the tasks that consume the present, and the prospect of death that blights the future? In Midlife, a self-help book with a difference, Kieran Setiya confronts the inevitable challenges of adulthood and middle age, showing how philosophy can help you thrive. Ranging from Aristotle, Schopenhauer, and John Stuart Mill to Virginia Woolf and Simone de Beauvoir, as well as drawing on Setiya’s own experience, Midlife combines imaginative ideas, surprising insights, and practical advice. Writing with wisdom and wit, Setiya makes a wry but passionate case for philosophy as a guide to life. Read on to learn more about the process of writing the book, the pervasiveness of the midlife crisis, and how philosophy can help.

How did you come to write this book?

You can probably guess! I think academic life is perfectly structured to induce a midlife crisis: decades of relentless striving in conditions of uncertainty, culminating either in failure or in a form of success that you leaves you wondering how you got here and what comes next. That’s how it was for me, anyway. Through a combination of luck and hard work, I had a tenured position in a good department and I found myself off-script for the first time in fifteen years. I recognized how fortunate I was, comparatively speaking: what I felt was not pointlessness, but nostalgia for lost alternatives, something like regret, a sense of emptiness in the relentless grind, and a visceral awareness of how short life is. It occurred to me that philosophy should have something to say about these challenges, which turn on the temporal structure of human life and the projects that occupy it—but that it hadn’t been said. The idea was to use my problem to solve itself: writing about the midlife crisis would be my answer to the midlife crisis. Midlife is the product.

How widespread is the midlife crisis?

That is a contentious question. The phrase comes from a 1965 essay by psychoanalyst Elliott Jaques, whose patients were experiencing their malaise in the midst of relative success. The idea caught on in the 1970s, with the publication of Gail Sheehy’s Passages: Predictable Crises of Adult Life. But the first serious attempts to test the prevalence of the midlife crisis were decidedly mixed. The MacArthur Network on Midlife Development conducted a huge survey in the 1990s and found that credible reports of a midlife crisis were not widespread. Social scientists rushed to declare the midlife crisis a myth. But the idea has been revived. According to influential research by economists David Blanchflower and Andrew Oswald, levels of life-satisfaction around the world take the shape of a gently curving U, starting high in youth, reaching their nadir in midlife, before recovering in old age. Not a crisis, necessarily, but a predictable dip in life-satisfaction that occupies middle age. Controversy continues to rage. Every six to twelve months, newspapers report a study that claims to prove the reality of the midlife crisis or debunk it as a myth. For what it is worth, my money is on the U-curve. But even if midlife is no more difficult than childhood or old age, it brings distinctive challenges: intense demands on one’s time, the legacy of an imperfect past, a limited but substantial future, and the repetition of projects that fill one’s days. These are the problems I confront in the book.

Can philosophy really help?

I think so. The idea of moral philosophy as a literature of self-improvement or self-help has a distinguished history: it is the divorce between these aims that is the novelty. What is distinctive of my approach is that, unlike other philosophers who have written self-help books, I don’t look primarily to the past. I am not trying to revive or rediscover the lost wisdom of the Stoics, for example, but to apply philosophy to the problems of midlife in original ways. There was no guarantee that the results of doing this would be consoling, but as it happens, I believe they are. There are philosophical ideas and arguments that help to address the feelings of regret, of missing out, of finitude, of emptiness and repetition, that we associate with middle age. I want to share these insights.

What sort of guidance do you offer? Can you give us an example?

I won’t give away all my secrets here, but I will introduce one.  It comes from an unexpected source: nineteenth-century pessimist and philosopher, Arthur Schopenhauer. Interpreting his argument about the futility of desire, I draw a crucial distinction between two sorts of activities: ones that aim at an end-point, projects like earning a promotion, getting married or writing a book, and ones that don’t, like going for a walk or spending time with friends. A characteristic defect of midlife – certainly, of mine – is excessive investment in projects. But projects are inherently self-subversive: to engage with them successfully is to complete them and so to expel them from your life. The solution is not to deny that projects matter but to invest more fully in the process, to value what I call “atelic” activities (from the Greek “telos” or end). For every project, there is a process of engagement: as well as finishing this book, there is the activity of reading and writing about philosophy; as well as making dinner for your kids or putting them to bed, there is the activity of parenting. Unlike projects, atelic activities do not aim at end-points at which they are completed; to engage with them is not to exhaust them; the satisfaction they provide is not deferred to the future but realized here and now. The final chapter of the book explains how to fill the void in the pursuit of projects by valuing the process, drawing comparisons with the appeal to mindfulness in Buddhism and clinical psychology. It is not an easy transition to make, but it can change your life.

What was it like to move from writing for colleagues to addressing a wider audience?

What I realized in working on Midlife is that the editorial voice in my head when I write for other philosophers is frustratingly argumentative. The nagging questions are “Do you mean X or Y?” and “What about this objection?” The result of listening to that voice is often a tiresome clarity. Not much fun to read. The voice in my head when I wrote Midlife was just as critical, but the refrain was very different. I think about an anecdote I heard from a friend whose family became impatient with stories recounted at the dinner table. When they got bored, they would chant in unison: “Faster! Funnier!” I can’t say how fast or funny I managed to be, but that is more or less the voice I had in mind. Making arguments and distinctions is unavoidable in a work of philosophy, but I tried to keep complexity to a minimum, to make things personal, and to write with my tongue ever so slightly in my cheek. There is a delicate synthesis of sincerity and irony in attempting to write a self-help book without pretending to have it all figured out. For the most part, I enjoyed the balancing act.

Is your book only for the middle-aged?

I hope not. While I had my midlife crisis right on cue at thirty-five, friends have told me that they had theirs earlier or that it is yet to come. You can face up to regret and missing out, to mortality and the tyranny of projects, at almost any age. I think these challenges are especially pressing around midlife, when you are likely to have made serious mistakes and irreversible decisions, when you have achieved success in your ambitions or must finally give them up, when you face the death of parents and loved ones, and when your own death is no longer an abstraction. But they do not go away, and you are welcome to confront them in advance! A case I dwell on in the book is that of Victorian activist and philosopher, John Stuart Mill, who had his crisis at the age of twenty. Not midlife, I know, but Mill was precocious. His attempt to philosophize his nervous breakdown was a major inspiration for my book.

 

setiyaKieran Setiya is professor of philosophy at the Massachusetts Institute of Technology. He is the author of Reasons without Rationalism and Knowing Right from Wrong. He lives in Brookline, Massachusetts with his wife and son.