Category Archives: Quantum Mechanics

The pleasures of reading Feynman on Physics — III

The more I read volume III of the Feynman Lectures on Physics about Quantum Mechanics the better I like it.  Even having taken two courses in it 60 and 10 years ago, Feynman takes a completely different tack, plunging directly into what makes quantum mechanics different than anything else.

He starts by saying “Traditionally, all courses in quantum mechanics have begun in the same way, retracing the path followed in the historical development of the subject.  One first learns a great deal about classical mechanics so that he will be able to understand how to solve the Schrodinger equation.  Then he spends a long time working out various solutions.  Only after a detailed study of this equation does he get to the advanced subject of the electron’s spin.”

Not to worry, he gets to the Hamiltonian on p. 85 and  the Schrodinger equation p. 224.   But he is blunt about it “We do not intend to have you think we have derived the Schrodinger equation but only wish to show you one way of thinking abut it.  When Schrodinger first wrote it down, he gave a kind of derivation based on some heuristic arguments and some brilliant intuitive guesses.  Some of the arguments he used were even false, but that does not matter. “

When he gives the law correct of physics for a particle moving freely in space with no forces, no disturbances (basically the Hamiltonian), he says “Where did we get that from”  Nowhere. It’s not possible to derive it from anything you know.  It came out of the mind of Schrodinger, invented in his struggle to find an understanding of the experimental observations of the real world.”  How can you not love a book written like this?

Among the gems are the way the conservation laws of physics arise in a very deep sense from symmetry (although he doesn’t mention Noether’s name).   He shows that atoms radiate photons because of entropy (p. 69).

Then there is his blazing honesty “when philosophical ideas associated with science are dragged into another field, they are usually completely distorted.”  

He spends a lot of time on the Stern Gerlach experiment and its various modifications and how they put you face to face with the bizarrities of quantum mechanics.

He doesn’t shy away from dealing with ‘spooky action at a distance’ although he calls it the Einstein Podolsky Rosen paradox.  He shows why if you accept the way quantum mechanics works, it isn’t a paradox at all (this takes a lot of convincing).

He ends up with “Do you think that it is not a paradox, but that it is still very peculiar?  On that we can all agree. It is what makes physics fascinating”

There are tons more but I hope this whets your appetite

The pleasures of reading Feynman on Physics – II

If you’re tired of hearing and thinking about COVID-19 24/7 even when you don’t want to, do what I did when I was a neurology resident 50+ years ago making clever diagnoses and then standing helplessly by while patients died.  Back then I read topology and the intense concentration required to absorb and digest the terms and relationships, took me miles and miles away.  The husband of one of my interns was a mathematician, and she said he would dream about mathematics.

Presumably some of the readership are chemists with graduate degrees, meaning that part of their acculturation as such was a course in quantum mechanics.  Back in the day it was pretty much required of chemistry grad students — homage a Prof. Marty Gouterman who taught the course to us 3 years out from his PhD in 1961.  Definitely a great teacher.  Here he is now, a continent away — http://faculty.washington.edu/goutermn/.

So for those happy souls I strongly recommend volume III of The Feynman Lectures on Physics.  Equally strongly do I recommend getting the Millennium Edition which has been purged of the 1,100 or so errors found in the 3 volumes over the years.

“Traditionally, all courses in quantum mechanics have begun in the same way, retracing the path followed in the historical development of the subject.  One first learns a great deal about classical mechanics so that he will be able to understand how to solve the Schrodinger equation.  Then he spends a long time working out various solutions.  Only after a detailed study of this equation does he get to the advanced subject of the electron’s spin.”

The first half of volume III is about spin

Feynman doesn’t even get to the Hamiltonian until p. 88.  I’m almost half through volume III and there has been no sighting of the Schrodinger equation so far.  But what you will find are clear explanations of Bosons and Fermions and why they are different, how masers and lasers operate (they are two state spin systems), how one electron holds two protons together, and a great explanation of covalent bonding.  Then there is great stuff beyond the ken of most chemists (at least this one) such as the Yukawa explanation of the strong nuclear force, and why neutrons and protons are really the same.  If you’ve read about Bell’s theorem proving that ‘spooky action at a distance must exist’, you’ll see where the numbers come from quantum mechanically that are simply impossible on a classical basis.  Zeilinger’s book “The Dance of the Photons” goes into this using .75 (which Feynman shows is just cos(30)^2.

Although Feynman doesn’t make much of a point about it, the essentiality of ‘imaginary’ numbers (complex numbers) to the entire project of quantum mechanics impressed me.  Without them,  wave interference is impossible.

I’m far from sure a neophyte could actually learn QM from Feynman, but having mucked about using and being exposed to QM and its extensions for 60 years, Feynman’s development of the subject is simply a joy to read.

So get the 3 volumes and plunge in.  You’ll forget all about the pandemic (for a while anyway)

 

The pleasures of reading Feynman on Physics

“Traditionally, all courses in quantum mechanics have begun in the same way, retracing the path followed in the historical development of the subject.  One first learns a great deal about classical mechanics so that he will be able to understand how to solve the Schrodinger equation.  Then he spends a long time working out various solutions.  Only after a detailed study of this equation does he get to the advanced subject of the electron’s spin.”

From vol. III of the Feynman lectures on physics  p. 3 – 1.

Certainly that’s the way I was taught QM as a budding chemist in 1961. Nothing wrong with that.  For a chemist it is very useful to see how all those orbitals pop out of series solutions to the Schrodinger equation for the hydrogen atom.

“We have come to the conclusion that what are usually called the advanced parts of quantum mechanics are in fact, quite simple. The mathematics that is involved is particularly simple, involving simple algebraic operations and no differential equations or at most only very simple ones.”

Quite true, but when, 50 years or so later,  I audited a QM course at an elite woman’s college, the underlying linear algebra wasn’t taught — so I wrote a series of posts giving the basics of the linear algebra used in QM — start at https://luysii.wordpress.com/2010/01/04/linear-algebra-survival-guide-for-quantum-mechanics-i/ and follow the links (there are 8 more posts).

Even more interesting was the way Mathematica had changed the way quantum mechanics was taught — see https://luysii.wordpress.com/2009/09/22/what-hath-mathematica-wrought/

But back to Feynman:  I’m far from sure a neophyte could actually learn QM this way, but having mucked about using and being exposed to QM and its extensions for 60 years, Feynman’s development of the subject is simply a joy to read. Feynman starts out as a good physicist should with the experiments.  Nothing fancy, bullets are shot at a screen through a slit, then electrons then two slits, and the various conundrums arising when one slit is closed.

Onward and upward through the Stern Gerlach experiments and how matrices are involved (although Feynman doesn’t call them that).  The only flaw in what I’ve found so far is his treatment of phase factors (p. 4 -1 ).  They aren’t really defined, but they are crucial as phase factors are what breaks the objects of physics into fermions and bosons.

If you’ve taken any course in QM and have some time (who doesn’t now that we’re all essentially inmates in our own homes/apartments) than have a look.   You’ll love it.  As Bill Gates said about the books “It is good to sit at the feet of the master”.

One piece of advice — get the new Millennium edition — it has removed some 1,100 errors and misprints found over the decades, so if you’re studying it by yourself, you won’t be tripped up by a misprint in the text when you don’t understand something.

Want to understand Quantum Computing — buy this book

As quantum mechanics enters its second century, quantum computing has been hot stuff for the last third of it, beginning with Feynman’s lectures on computation in 84 – 86.  Articles on quantum computing  appear all the time in Nature, Science and even the mainstream press.

Perhaps you tried to understand it 20 years ago by reading Nielsen and Chuang’s massive tome Quantum Computation and Quantum information.  I did, and gave up.  At 648 pages and nearly half a million words, it’s something only for people entering the field.  Yet quantum computers are impossible to ignore.

That’s where a new book “Quantum Computing for Everyone” by Chris Bernhardt comes in.  You need little more than high school trigonometry and determination to get through it.  It is blazingly clear.  No term is used before it is defined and there are plenty of diagrams.   Of course Bernhardt simplifies things a bit.  Amazingly, he’s able to avoid the complex number system. At 189 pages and under 100,000 words it is not impossible to get through.

Not being an expert, I can’t speak for its completeness, but all the stuff I’ve read about in Nature, Science is there — no cloning, entanglement, Ed Frenkin (and his gate), Grover’s algorithm,  Shor’s algorithm, the RSA algorithm.  As a bonus there is a clear explanation of Bell’s theorem.

You don’t need a course in quantum mechanics to get through it, but it would make things easier.  Most chemists (for whom this blog is basically written) have had one.  This plus a background in linear algebra would certainly make the first 70 or so pages a breeze.

Just as a book on language doesn’t get into the fonts it can be written in, the book doesn’t get into how such a computer can be physically instantiated.  What it does do is tell you how the basic guts of the quantum computer work. Amazingly, they are just matrices (explained in the book) which change one basis for representing qubits (explained) into another.  These are the quantum gates —  ‘just operations that can be described by orthogonal matrices” p. 117.  The computation comes in by sending qubits through the gates (operating on vectors by matrices).

Be prepared to work.  The concepts (although clearly explained) come thick and fast.

Linear algebra is basic to quantum mechanics.  Superposition of quantum states is nothing more than a linear combination of vectors.  When I audited a course on QM 10 years ago to see what had changed in 50 years, I was amazed at how little linear algebra was emphasized.  You could do worse that read a series of posts on my blog titled “Linear Algebra Survival Guide for Quantum Mechanics” — There are 9 — start here and follow the links — you may find it helpful — https://luysii.wordpress.com/2010/01/04/linear-algebra-survival-guide-for-quantum-mechanics-i/

From a mathematical point of view entanglement (discussed extensively in the book) is fairly simple -philosophically it’s anything but – and the following was described by a math prof as concise and clear– https://luysii.wordpress.com/2014/12/28/how-formal-tensor-mathematics-and-the-postulates-of-quantum-mechanics-give-rise-to-entanglement/

The book is a masterpiece — kudos to Bernhardt

Feynman and Darwin

What do Richard Feynman and Charles Darwin have in common?  Both have written books which show a brilliant mind at work.  I’ve started reading the New Millennium Edition of Feynman’s Lectures on Physics (which is the edition you should get as all 1165 errata found over the years have been corrected), and like Darwin his thought processes and their power are laid out for all to see.  Feynman’s books are far from F = ma.  They are basically polished versions of lectures, so it reads as if Feynman is directly talking to you.  Example: “We have already discussed the difference between knowing the rules of the game of chess and being able to play.”  Another: talking about Zeno  “The Greeks were somewhat confused by such problems, being helped, of course, by some very confusing Greeks.”

He’s always thinking about the larger implications of what we know.  Example: “Newton’s law has the peculiar property that if it is right on a certain small scale, then it will be right on a larger scale”

He then takes this idea and runs with it.  “Newton’s laws are the ‘tail end’ of the atomic laws extrapolated to a very large size”  The fact that they are extrapolatable and the fact that way down below are the atoms producing them means, that extrapolatable laws are the only type of physical law which could be discovered by us (until we could get down to the atomic level).  Marvelous.  Then he notes that the fundamental atomic laws (e.g. quantum mechanics) are NOTHING like what we see in the large scale environment in which we live.

If you like this sort of thing, you’ll love the books.  I don’t think they would be a good way to learn physics for the first time however.  No problems, etc. etc.  But once you’ve had exposure to some physics “it is good to sit at the feet of the master” — Bill Gates.

Most of the readership is probably fully engaged with work, family career and doesn’t have time to actually read “The Origin of Species”. In retirement, I did,and the power of Darwin’s mind is simply staggering. He did so much with what little information he had. There was no clear idea of how heredity worked and at several points he’s a Lamarckian — inheritance of acquired characteristics. If you do have the time I suggest that you read the 1859 book chapter by chapter along with a very interesting book — Darwin’s Ghost by Steve Jones (published in 1999) which update’s Darwin’s book to contemporary thinking chapter by chapter.  Despite the advances in knowledge in 140 years, Darwin’s thinking beats Jones hands down chapter by chapter.

Book recommendation

Tired of reading books about physics?  Want the real McCoy”?  Well written and informal?  Contains stuff whose names you know but don’t understand — Jones Polynomial, Loop Quantum Gravity, Quantum field theory, Gauge groups and transformations —  etc. etc.

Up to date?  Well no, it’s 25 years old but still very much worth a read, so very unlike molecular biology, chemistry, computer science etc. etc.

Probably you should know as much physics and math as a beginning chemistry grad student. If you studied electromagnetism through Maxwell’s equations it would be a plus.  I stopped at Coulomb’s Law, and picked up enough to understand NMR.

This will give you a sample of the way it is written

“Much odder is that we are saying the vector field v is the linear combination of . .  partial derivatives.  What we are doing might be regarded as rather sloppy, since we are identifying two different although related things: the vector  field and the operator v^i * d-/dx^i which takes a directional derivative in the direction of v.”

“Now let us define vector fields on a manifold M. .. . these will be entities whose sole ambition in life is to differentiate functions”

The book is “Gauge FIelds, Knots and Gravity” by John Baez and Javier P. Muniain.

The writing, although clear has a certain humility.  “Unfortunately understanding these new ideas depends on a through mastery of quantum field theory, general relativity, geometry, topology and algebra.  Indeed, it is almost certain that nobody is sufficiently prepared to understand these ideas fully.”

I’m going to take it with me to the amateur chamber music festival.  As usual, at least 2 math full professors will be there to help me out.  Buy it and enjoy

 

 

Book Review — The Universe Speaks in Numbers

Let’s say that back in the day, as a budding grad student in chemistry you had to take quantum mechanics to see where those atomic orbitals came from.   Say further, that as the years passed you knew enough to read News and Views in Nature and Perspectives in Science concerning physics as they appeared. So you’ve heard various terms like J/Psi, Virasoro algebra, Yang Mills gauge symmetry, Twisters, gluons, the Standard Model, instantons, string theory, the Atiyah Singer theorem etc. etc.  But you have no coherent framework in which to place them.

Then “The Universe Speaks in Numbers” by Graham Farmelo is the book for you.  It will provide a clear and chronological narrative of fundamental physics up to the present.  That isn’t the main point of the book, which is an argument about the role of beauty and mathematics in physics, something quite contentious presently.  Farmelo writes well and has a PhD in particle physics (1977) giving him a ringside seat for the twists and turns of  the physics he describes.  People disagree with his thesis (http://www.math.columbia.edu/~woit/wordpress/?p=11012) , but nowhere have I seen anyone infer that any of Farmelo’s treatment of the physics described in the book is incorrect.

40 years ago, something called the Standard Model of Particle physics was developed.  Physicists don’t like it because it seems like a kludge with 19 arbitrary fixed parameters.  But it works, and no experiment and no accelerator of any size has found anything inconsistent with it.  Even the recent discovery of the Higgs, was just part of the model.

You won’t find much of the debate about what physics should go from here in the book.  Farmelo says just study more math.  Others strongly disagree — Google Peter Woit, Sabine Hossenfelder.

The phenomena String theory predicts would require an accelerator the size of the Milky Way or larger to produce particles energetic enough to probe it.  So it’s theory divorced from any experiment possible today, and some claim that String Theory has become another form of theology.

It’s sad to see this.  The smartest people I know are physicists.  Contrast the life sciences, where experiments are easily done, and new data to explain arrives weekly.

 

 

Good to see Charlie’s still at it

Good to see Charlie Perrin is still pumping out papers, and interesting ones to boot.  I knew him in grad school.  He’s got to be over 80.

This one —J. Am. Chem. Soc. 141, 4103 (2019) –is about something that any undergraduate organic chemist can understand (if not the techniques he used) — keto/enol tautomerism, in which the hydrogen bounces between two oxygens, so that, given N molecules in solution, N/2  have the hydrogen bound to one oxygen and N/2 have it bound to the other.

No so in what Charlie found — a compound where the hydrogen is smack dab in the middle.  Some fancy NMR techniques were used to show this.

Hydrogen bonds are extremely subtle (which is why we don’t understand water as well as we might).  Due to the small mass of the proton it isn’t appropriate to treat the proton in hydrogen bonded systems as a classical particle.  When quantum mechanics enters, aspects such as zero point motion, quantum delocalization and tunneling come into play.  These are called quantum nuclear effects (aka Ubbelohde effects).

Book recommendation

“It’s complicated”.  No this isn’t about the movie with Meryl Streep but the response I got from several Harvard PhD physicists five years ago at Graduate Alumni Day in April 2014.  A month earlier the BICEP2 experiment claimed to have seen B-mode polarization in the cosmic background radiation, which would have been observational proof of cosmic inflation.  Nobel prize material for sure.  Unfortunately the signal turned out to be from dust in our galaxy, the milky way

You can read all about it in “Losing the Nobel Prize” by Brian Keating, who developed the instrumentation for BICEP2.  I recommend the book for several reasons.  The main reason is the discussion of cosmology and its various theories starting with Galileo (p. 28) getting up to  the B-Modes that BICEPs thought it saw by p. 138.  The discussion is incredibly clear, with discussions (to name a few) of how Galileo knew Ptolemy was wrong (the way the moons of Jupiter moved around it in time), refracting vs.reflecting telescopes, Hubble and cepheid variables, Vera Rubin and why she didn’t get a Nobel — she died too soon, how polaroid glasses work, and why bouncing of water is enough to polarize unpolarized light.  Want more? Fred Hoyle and steady state cosmology, the problems with the big bang (smoothness problem, horizon problem, flatness problem) solved by Alan Guth and inflation, false vacuum, and finally what B-modes actually are.

If you’ve a typical reader of blogs scientific but not a pro in physics, astronomy, cosmology, you’ve probably heard all these terms. Keating explains them clearly.

Even better, he writes well and is funny.  Here is the opening paragraph of the book.

“Each year, on December tenth, thousands of worshippers convene in Scandinavia to commemorate the passing of an arms dealer known as the merchant of death.  The eschatological ritual features all the rites and incantations befitting a pharaoh’s funeral.  Haunting dirges play as the worshippers, bedecked in mandatory regalia, mourn the merchant.  He is eerily present; his visage looms over the congregants as they feast on exotic game, surrounded by fresh-cut flowers imported from the merchant’s mausoleum.  The event culminates with the presentation of gilded, graven images bearing his likeness.”

Anything dealing with the creation of the universe has theological overtones, and we can regard the book as a history of various scientific creation myths, the difference being that they are abandoned when evidence is found which contradicts them.  Georges’ Lemaitre, a catholic priest and relativist puts in more than an appearance (p. 56) as he predicted what is probably the first big bang theory — the primeval atom with its subsequent expansion.

The book isn’t all science, and the author whose Jewish father abandoned them was raised by a catholic step-father describes being an altar boy for a time.   Then there are adventure stories of journeys to the south pole for the BICEP experiment.

There’s a lot more in the book, which is definitely worth a read.

Finally a few personal notes.  The man who brought BICEP2 down to earth David Spergel appears.  He’s a good guy.  At my 50th reunion there my wife and I  were standing in our reunion suits outside our hotel across route 1 waiting for a bus to take us across.  Some guy (Spergel) sees us an offers a ride to campus. On the ride over I asked what he did, and he says astronomy and physics.  So I asked how come the universe is said to be homogenous when all we see is clumpy galaxies and stars — you asked the right guy saith Spergel, and he launches into an explanation (which I’ve forgotten).  I mention that Jim Hartle is a class member.  “He’s very smart” saith David.  Later I tell Hartle the same story.  “He’s very smart” saith Jim.

Another good person is Meryl Streep.  A cousin is in movies both acting in the past and now directing and knows her.  Her father was a great admirer, so Meryl took the trouble to hike over to New Jersey and say hello.  She didn’t have to do that.  Unfortunately in the movie mentioned first, Meryl had to play a porn star with her aged scrawny body (probably Harvey Weinstein put her up to it).  I couldn’t stand it and walked out at that point.

Book recommendation

“Losing the Nobel Prize”  by Brian Keating is a book you should read if you have any interest in l. physics. 2. astronomy 3. cosmology 4. the sociology of the scientific enterprise (physics division) 5. The Nobel prize 6. The BICEPs and BICEP2 experiments.

It contains extremely clear explanations of the following

l. The spiderweb bolometer detector used to measure the curvature of the universe

2. How Galileo’s telescope works and what he saw

3. How refracting and reflecting telescopes work

4. The Hubble expansion of the universe and the problems it caused

5. The history of the big bang, its inherent problems, how Guth solved some of them but created more

6. How bouncing off water (or dust) polarizes light

7. The smoothness problem, the flatness problem and the horizon problem.

8. The difference between B modes and E modes and why one would be evidence of gravitational waves which would be evidence for inflation.

9. Cosmic background radiation

The list could be much longer.  The writing style is clear and very informal.   Example: he calls the dust found all over the universe — cosmic schmutz.   Then there are the stories about explorers trying to reach the south pole, and what it’s like getting there (and existing there).

As you probably know BICEP2 found galactic dust and not the polarization pattern produced by gravitational waves.  The initial results were announced 17 March 2014 to much excitement.  It was the subject of a talk given the following month at Harvard Graduate Alumni Day, an always interesting set of talks.  I didn’t go to the talk but there were plenty of physicists around to ask about the results (which were nowhere nearly as clearly explained as this book).  All of them responded to my questions the same way — “It’s complicated.”

The author Brian Keating has a lot to say about Nobels and their pursuit and how distorting it is, but that’s the subject of another post, as purely through chance I’ve known 9 Nobelists before they received their prize.

It will also lead to another post about the general unhappiness of a group of physicists.

Buy and read the book