Posts Tagged ‘physics’

Susskind & Friedman: Quantum Mechanics

February 22, 2018

Quantum Mechanics
The Theoretical Minimum
Leonard Susskind and Art Friedman
(Basic, 2014)
xx + 364 p.

Books on quantum mechanics tend to come to two main varieties: introductions for non-scientists, which normally focus on the conceptual underpinnings of the subject and avoid mathematics, and technical books written for advanced undergraduates or higher. This book, however, doesn’t quite fall in either camp. It spends a good deal of time carefully exploring the conceptual foundations, but it also does contain enough mathematics — all of it fairly gentle, but pertinent — so that the reader is not only told, but also is able to see, how certain of the most famous predictions of quantum mechanics follow from those conceptual foundations.

Susskind and Friedman begin with a simple quantum system, a single quantum spin, and use it to lay out the unusual logic of quantum states, emphasizing how it differs from the logic of classical physics. They discuss both time independent and time dependent quantum mechanics, emphasizing the value of the former for deducing the energy states of a system and of the latter for deducing how the system evolves in time. About one-third of the book is devoted to an exploration of entanglement, traditionally one of the strangest aspects of the quantum world, but they take some pains to argue that entanglement does not imply any sort of non-locality, as is sometimes claimed. Later sections of the book transition to the topic of wavefunctions and particles, and creep right up to the edge of quantum field theory, so as to peer over for a moment. At the end, they give a nice treatment of the quantum mechanical harmonic oscillator, which is one of the simplest but most important quantum systems.

Susskind is one of the best-known physicists of his generation. It is not all that common, I think, for such an eminent scientist to have a passion for teaching his subject to beginners, so I very much admire what he is doing here. The development of the subject is clear, with intermediate steps worked, and the significance of conclusions are emphasized. The book has a welcoming tone, and the enthusiasm of the authors is evident. They do not refrain from an occasional joke. The book is, apparently, derived from an online course which Susskind has given at Stanford. (Friedman is one of his students, and it is unclear to me exactly what his role has been in writing the book.) The book has been typeset with LaTeX, as is right and just.

It’s a little hard to say who the target audience is. It would be accessible, certainly, to an interested reader who had been trained in, for instance, engineering. The mathematics required doesn’t extend much beyond complex numbers, basic calculus, and linear algebra, and even these are given quick explanations in the text. I could see it being a very good read for an ambitious high school student or beginning undergraduate who has an interest in the subject. Or, for that matter, the target might be me: a trained physicist who has been out of academia for a while and would enjoy a trip down memory lane.

The book is part of a series, in fact, that goes under the title “The Theoretical Minimum”. It was preceded by a book on classical mechanics (to which this volume makes occasional reference), and has now been succeeded by a recent book on special relativity and classical field theory. I’ve not read either of those, but I had enough fun with this one that I might.

Meanwhile, elsewhere

October 26, 2017

A few recent items that might be of wider interest:

  • The next volume in Bob Dylan’s “Bootleg Series” is scheduled for a November issue. Trouble No More, the thirteenth volume in the series, will treat Dylan’s “Gospel period” of the late 1970s and early 1980s. The Gospel records are not among my favourites, but there is likely to be some good, previously unreleased material in this set. In fact, we know there is, because we can listen to “Making a Liar Out of Me”, which is pretty fabulous by just about any measure.
  • David Bentley Hart has had, I think, 4 books published in the past year. There were three collections of essays on various subjects, and his translation of the New Testament appeared this week. I am indifferent to the Bible translation; I’m sure it will be interesting, and controversial (on account of the “pitilessly literal” course he set himself), but another Bible translation is likely to just sink beneath the flood of Bible translations. I’d prefer to have fewer translations than more, and this project strikes me as an unfortunate distraction for a man whose talents are so prodigious. Anyway, all that aside, there was a nice essay by Brad East at the LA Review of Books about his recent essay collections, and I highly recommend it. Hart also delivered a good lecture at Fordham on the topic “Orthodoxy in America and America’s Orthodoxies”, very much worth hearing.
  • At City Journal, Heather Mac Donald takes a critical look at the idea of “unconscious bias”. A good and instructive read.
  • Following up on the Nobel Prize in Physics for 2017, which was for the discovery, a few years ago, of a black hole collision using gravitational waves, the same technique has now been used to discover a collision of neutron stars. Physicists were able to identify the direction from which the space-time ripples were coming with sufficient precision for optical telescopes to turn and see the electromagnetic radiation from the collision as well. Amazing. This happened in August, but I was on holiday and missed it.
  • Everybody knows that Stradivarius made the best violins, right? Right? A group of French and American researchers asked several renowned violin soloists to blind-test modern violins against old Italian instruments, including a few by Stradivarius. The result: they could not reliably distinguish the old from the new, and they generally preferred the sound of the new.  Adding insult to injury, a follow-up study of audience perceptions found that they, too, could not reliably tell the difference between old and new, but generally preferred the newer instruments. How to fittingly bid farewell to the beloved myth of the Stradivari? Here is the Tokyo String Quartet, all playing Stradivari instruments, performing Barber’s sad Adagio:

Rovelli: Seven Brief Lessons on Physics

September 6, 2016

Seven Brief Lessons on Physics
Carlo Rovelli
(Riverhead, 2016)
96 p.

These short “lessons” were originally serialized in the Italian press, and are here collected and rendered into elegant English. Rovelli is an eminent physicist who gives us a series of meditations on developments in physics since 1900.

They are arranged in order of increasing speculation: he begins with general relativity and quantum mechanics, presenting in non-technical language the main points — space and time are dynamic and responsive, and are filled with a restless boil of quantum fields. He proceeds to give brief — and I do mean brief — overviews of modern cosmology and the Standard Model of elementary particles. All of this is solid science; questions linger, of course, and he draws attention to those loose threads and nagging problems, but basically he is describing successful theories.

In the last three sections of the book he moves to topics of greater uncertainty. The outstanding problem of how to reconcile general relativity with quantum mechanics he broaches with a very interesting discussion of theories of loop quantum gravity, the basic postulate of which is that space-time is quantized. (Rovelli is himself one of the architects of this theory.) Amazingly, and rather gratifyingly, he doesn’t even mention the other principal effort to solve this problem: string theory. This is unquestionably the book’s finest witticism, one that I imagine has raised a few consternated eyebrows in faculty lounges.

The last section specifically about physics tackles the vexing puzzles that arise at the intersection of gravity, quantum mechanics, and thermodynamics. Laying great stress on the time-irreversibility of thermodynamic processes, he argues that thermodynamics has something crucial to tell us about the uni-directionality of time itself. This is a common trope in physics circles, but, correlation not being causation, it seems to me suggestive at best. But then he reminds us of Hawking radiation, in which quantum effects near black holes actually cause them to radiate heat, and one feels a chill of delight running up the spine.

Alas, the same cannot be said of the book’s final chapter, in which Rovelli takes a step back to ponder the implications of all this for human self-understanding. He emphasizes that modern physics has revealed the world to be radically different from the way we intuitively think of it, which is fair enough, and then argues that more such intuitions — those pertaining to human freedom, for instance, or consciousness — are due to be superseded by counter-intuitive scientific explanations. There appears to be nothing more to his argument than the power of analogy. He tries to declare a peace between his commitment to the power of physics to completely describe the world, on one hand, and his commitment to the legitimacy of humanistic values, on the other, but it is far from convincing. And he is rather dispiritingly emphatic in his devotion to immanence:

“Immersed in this nature that made us and that directs us, we are not homeless beings suspended between two worlds, parts of but only partly belonging to nature, with a longing for something else. No: we are home.”

Nothing new here, of course, and this view does have about it a certain poetry — he even cites Lucretius, the patron poet of materialism — but there are such a host of issues being passed over in silence that such poetry as it possesses sounds rather hollow.

The book is written in a lyrical tone, and would be accessible, I imagine, to anyone who has an interest in the subject matter. There is only one equation — Einstein’s field equation for general relativity, which he describes as “the most beautiful of theories,” and I’ll not argue with that.

Books briefly noted

August 16, 2016

Usually I try to post these short notes in thematically-related groups, but I can’t spot the theme in this batch.


lyrical-balladsLyrical Ballads
William Wordsworth and Samuel Taylor Coleridge
(Penguin, 2007) [1798]
128 p.

This slim volume is, by reputation, one of the heavyweights in the history of English poetry, being generally acknowledged as having overturned the then-prevailing poetic conventions and inaugurated the Romantic period of English verse.

Wordsworth and Coleridge challenged the idea that poetry should attend only to lofty subjects, writing poems instead on humble, but far from trivial, matters: a lost boy, a woman dying alone, a peasant family. Many, though not all, of the poems are narrative, and the poetic forms matched their subjects: simple forms, with clear and musical rhyming schemes, such as those characteristic of folk songs.

That, at least, describes a considerable number of these poems, but there is another type too: metrical verse on personal themes, in which we are taken inside the mind of the poet as he ponders something. If you’ve any experience with Wordsworth, you’ll be content to describe these as “Wordsworthian”, and wonderful they are. They made me realize how much I’ve missed him; it has been years since I read his long poem “The Prelude”, which I loved at the time, and perhaps I am due to revisit it, or his poetry more generally.

Although authorship of the individual poems is not attributed within the book, Wikipedia says that only a handful of the twenty-odd poems are by Coleridge. The two most famous poems in the collection are Coleridge’s “The Rime of the Ancyent Marinere” and Wordsworth’s “Tintern Abbey”, being, respectively, outstanding examples of the two poetic models I just described.


classical-mechanicsClassical Mechanics Illustrated by Modern Physics
42 Problems and Solutions
David Guéry-Odelin and Thierry Lahaye
(Imperial College, 2010)
268 p.

Most symmetric potentials will be quadratic to a first approximation, which is why the simple harmonic oscillator is such a useful model in so many areas of physics, and if there were ever a book to illustrate that wide usefulness it might well be this one, in which concepts usually associated with classical mechanics — including an abundance of simple harmonic oscillators — are applied to problems in modern physics. The range of topics is quite wide: gravitation, friction, fluids, electromagnetics, astrophysics, atomic physics, relativity, and more. One of the most interesting sections to me was on experimental methods for cooling clouds of atoms: Zeeman cooling (my favourite), doppler cooling, and evaporative cooling. The problems are each marked with a level of difficulty, and the solutions are worked in detail sufficient for relatively easy comprehension. The book as a whole is very clearly written, and I thoroughly enjoyed reading it.


guarendi-disciplineDiscipline That Lasts a Lifetime
The Best Gift You Can Give Your Kids
Ray Guarendi
(Servant, 2003)
306 p.

A few months ago we went to hear Ray Guarendi speak on parenting and discipline. His talk turned out to be a comedy routine that was light on substance (and rather light on laughs too, I’m afraid), so I figured I’d better read one of his books if I wanted to learn something. This particular book is epistolary: he answers questions from parents, real or imagined. It’s still comedic, but the humour works better for me on the page. What I like about Guarendi is that he gives no-nonsense advice. Discipline is necessary, both for parental sanity and for kids’ formation. If you discipline, everyone will be happier in the end. He has some good ideas about techniques: blackouts, house rules, chore charts, and so on. We’re going to try a few of them. Our kids are savages.

Gravitational waves

February 11, 2016

There’s a very exciting announcement today from the LIGO experiment: they are reporting the first ever direct observation of gravitational waves. Read all about it.

The existence of gravitational waves — which are “ripples” in spacetime produced by catastrophic astrophysical events like black hole collisions or supernovae — are one of the most important predictions of general relativity. Today’s discovery will go into every future textbook on the subject, and the scientists involved go straight to the Nobel shortlist.

The LIGO experiment (LIGO = Laser Interferometer Gravitational-Wave Observatory), if you haven’t heard of it, is one of the most amazing physics experiments ever conceived. Gravitational waves travelling through the detector change its size by a small amount, and so the experiment consists of making continual, very precise measurements of distance. The sensitivity is exquisite: they can detect a change in length of a fraction of the radius of a proton.

The particular observation reported today is of a collision of two black holes at an estimated distance of 1.3 billion light years. Here is the technical paper describing the discovery.

What a great day!

Happy birthday, General Relativity

November 25, 2015


One hundred years ago today, on 25 November 1915, Einstein first presented the field equations for General Relativity during a lecture in Gottingen. GR is regarded, with justice, as among the most beautiful and creative achievements in the history of science. I know of none greater, and I am thankful to have had the opportunity to spend many happy hours working with the field equations — and some unhappy ones too, of course, because they are fiendishly difficult to solve!

On the same date, 25 November 1915, Einstein’s paper on the perihelion advance of Mercury was published in Königlich Preußische Akademie der Wissenschaften. This was the first, and is still one of the most important, experimental tests of General Relativity.


Much ado about nothing

March 15, 2012

A few interesting articles about science or philosophy of science:

  • William Carroll criticizes several recent statements about nothing by prominent physicists. That might sound like an odd thing to do, or like an awfully easy thing to do, but it is neither — well, maybe it is fairly easy. I recall that Stephen Hawking, in his most recent book, made a statement that deserved some kind of award from the Association for Short Term Memory Loss, for by the time he reached the end of the sentence he appeared to have forgotten how he started it. To wit: “Because there is a law such as gravity, the Universe can and will create itself from nothing.” One is tempted to ask, “What part of nothing don’t you understand?” Clearly, there is some conceptual confusion here, and Carroll is doing his part to try to clear it up.
  • Edward Feser gives a nice summary of Karl Popper’s arguments against the computational theory of mind. If you’ve ever passed an unpleasant afternoon reading contemporary philosophy of mind, you’ll have run into the idea: the mind is a computer program and the brain is a biological computer. Popper’s argument, which is essentially an argument against any causal theory of intentionality — where ‘causal’ means the kind of spatio-temporal causation relevant to physical science — is quite fascinating, and even thrilling. It has given rise, in the hands of folks like John Searle and others, to a suite of related arguments, all of which hinge, more or less, on the materialist’s own ‘interaction problem’, namely, the fact that there is a difference between physical causation and logical causation. Good stuff, and Feser’s writing is clear and accessible.
  • Finally, I am delighted to inform you that the Super Mario Bros. video game has been proved NP-hard. The march of knowledge is truly relentless.

Antarctic science: IceCube

February 26, 2011

When Antarctica was first explored it was quickly obvious that it did not have much potential for commercial or industrial activity. It was simply too remote, too barren, and too cold. Consequently most Antarctic activity has had a scientific focus; this was true of early expeditions like Scott’s, and it is certainly true today.

Today there are a handful of permanent Antarctic research stations, some located near the coast and others, such as the Amundsen-Scott Research Station, which is at the South Pole itself, well inland. Scientists are interested in the biology, geology, vulcanology, and meteorology of the place. Its pure ice cores provide a good way to study the history of earth’s climate. Its high altitude and clear atmosphere make it appealing for astronomical observation (as at the South Pole Telescope).

But there is one modern Antarctic experiment that surpasses all others in the vastness of its scale and the beauty of its conception, and it is that experiment that I would like to highlight today: IceCube, the South Pole Neutrino Detector.

Schematic of the IceCube 'apparatus'. The Eiffel Tower is shown to give an idea of scale. (Source: IceCube)

IceCube is a new project; its five-year construction period was completed only in December 2010. Its principal goal is to study ultra-high energy neutrinos originating from astrophysical sources. In that sense it can be thought of as a neutrino telescope. (A neutrino, if your physics is rusty, is a subatomic particle similar in some respects to an electron but without electric charge that interacts very weakly with other matter.) Neutrinos are produced in radioactive sources. The vast majority of the neutrinos around us — and there are billions of them passing through our bodies every second — come from the sun, but there are also some from other astrophysical objects. For some time now there has been a mystery about a class of neutrinos that have been measured to have very high energies, far higher than we would have thought likely, or even possible. Where do they come from? What kind of physical process produces them? IceCube is going to try to detect these high energy neutrinos and identify the direction from which they come. If they seem to be coming from a few specific points in the sky, we can then take a closer look at those points using more conventional telescopes.

Why build the detector at the South Pole? The reason is that the only way to detect a neutrino is to pile a whole lot of stuff in front of it and hope that the neutrino will hit the stuff. If it does (and if certain conditions are satisfied) a brief flash of light, called Cherenkov radiation, will be produced, and this light can be detected.

One way to make Cherenkov radiation from a neutrino. (Source: Carleton University)

The brilliant idea behind IceCube is to use Antarctica itself — and, more particularly, its immensely thick ice layer — as the stuff. Accordingly, scientists have drilled 2-1/2 km down into the ice and sunk strings of sensitive light detectors down the shafts. The detectors simply sit there, waiting, until a neutrino interacts with an atom somewhere in the ice, and then they measure the flash of light that is produced.

This sort of experimental design is not new; detectors such as Japan’s Super-Kamiokande and Canada’s Sudbury Neutrino Observatory (SNO) are built on the same principles. What is special about IceCube is its incredible scale: the ice shafts are distributed over an area of roughly one square kilometer, and the strings of detectors are roughly one kilometer long. In this way, the scientists have instrumented an ice volume of about one cubic kilometer. IceCube is about 20 000 times larger than Super-Kamiokande, and over a million times larger than SNO. Even with this massive volume, however, the detector is expected to detect only one neutrino every 20 minutes or so; all of the other gajillions of neutrinos passing through the ice every second simply coast on through without hitting anything. As I said, neutrinos interact very weakly with matter.

One of IceCube ice shafts, 2-1/2 km deep. (Source: IceCube)

There are not many scientific results from IceCube yet — the 400 papers already published are mostly, it appears, about its construction, testing, and potential — but it is definitely a project to watch. Wikipedia lists a number of its experimental objectives in plain language, and a more technical overview is available from the IceCube collaboration itself. For me the most amazing things about IceCube are the sheer audacity of the concept, and the fact that it has actually been built. It is all quite wonderful.

Moffat: Einstein Wrote Back

November 26, 2010

Einstein Wrote Back
My Life in Physics
John W. Moffat (Thomas Allen, 2010)
244 p.

When I was a graduate student at the University of Toronto, my office was adjacent to an office occupied by John Moffat. He would pop in occasionally to chat, and once or twice to ask us to work out a tricky integral, but I never had the opportunity to work closely with him. By reputation he was something of a maverick, working on ideas one or two steps outside the mainstream, always with an interest in whether the data could be accounted for by means different from the conventional explanation.

From time to time I picked up hints that his education and entry into physics had been rather unorthodox. It was rumoured that as a young man he had lived in Paris and pursued the art of painting before turning to the sciences. Indeed, I once saw a book of photographs of his paintings. Yet I never had — or, at any rate, never took — the opportunity to talk with him about this at any length.

I was delighted, therefore, to see that he has published a memoir. It is principally an account of his early life, and in particular of the way in which he came to study physics, which turns out to have been even more unconventional than I had suspected. In addition to his interesting biography, a chief pleasure of the book lies in Moffat’s hilarious, and often touching, first-hand stories about his encounters with many of the great physicists of the twentieth century.

As a child his schooling had been somewhat desultory, and he showed no special aptitude for mathematics or science. He took up painting as a young man, and moved to Paris to study with Serge Poliakoff. After some time, however, it became clear that it was not easy to earn a living at that noble art, and he returned home to Denmark, pondering his future. It so happened that he stumbled upon some of the popular cosmology writing of Sir Arthur Eddington, and these books changed his life, permanently. Moffat puts it this way:

After reading the books, I began having strange visions of the structure of the universe and the fabric of space-time as revealed by Albert Einstein. In these daydreams, I tried to comprehend how the universe was structured. These daydreams were intuitive forms rising from my subconscious rather than conscious attempts to understand the universe. The visions seemed to indicate some primal urge developing in me to connect with the stars and galaxies of the universe.

Under the sway of this powerful experience, he resolved to pursue theoretical physics, and in particular to study Einstein’s general relativity. With no training whatsoever in mathematics or physics, he began frequenting a local library and reading everything he could find on the subject. Incredibly, within a year he had taught himself enough mathematics and physics to compose an original paper on an aspect of general relativity. Even more incredibly, a family friend arranged for him to meet with one of the great physicists of the century, and certainly the greatest physicist in Denmark, Niels Bohr.

This meeting provided Moffat with the entry point he needed, and it was just the first in a series of remarkable meetings with the luminaries of modern physics. Bohr sent him to Erwin Schrödinger, and Schrödinger wrote him a letter of reference to Cambridge. (Moffat was a British citizen, and had a better chance of pursuing graduate studies there.) Surprisingly, Cambridge agreed to accept him into the doctoral program, despite his lacking an undergraduate degree of any kind, and he began formal studies under the supervision of Fred Hoyle.

During this transition period, Moffat wrote to Einstein, who was then at Princeton, and, to his surprise and delight, he received several thoughtful and encouraging letters in return. These letters gave him the confidence to imagine that he could succeed as a physicist, and it makes good sense that he has structured his memoir around them.

As a graduate student, post-doc, and young professor, Moffat crossed paths, and sometimes swords, with an amazing number of famous physicists: Paul Dirac, Wolfgang Pauli, Abdus Salam, Murray Gell-Mann, and others. His stories about these meetings are tremendously entertaining. It is said that genius is to madness near allied, and these stories provide evidence to that effect.  More than once I had to set the book down for laughter and astonishment. He relates all these tales with a good-natured affection, as well he might.

Moffat went on to have a very successful career. He is now Professor Emeritus at the University of Toronto, and is on staff at the Perimeter Institute for Theoretical Physics, where he pursues an active research program. This memoir, which makes a nice pendant to his earlier book Reinventing Gravity, is well worth the attention of anyone with an interest in the human side of the sciences.


I did not know that books could have trailers, but apparently they can. Here is the trailer for “Einstein Wrote Back”:


Related reading: John W. Moffat – Reinventing Gravity