The lecture Feynman really wanted to give to undergraduates

For Condensed Matter Physics: A Very Short Introduction, I have started writing a chapter on "Quantum matter". It is a challenge to decide what to include, particularly given how the content needs to be accessible to a general audience. The question, "What is quantum matter?" is an interesting one. Currently, I have decided to focus on how superconductors and superfluids can exhibit macroscopic quantum effects. More on that later. 

In the process, I was reminded of the last lecture in the celebrated Feynman Lectures on Physics. These are now available online, including photos.

The Schrödinger Equation in a Classical Context: A Seminar on Superconductivity

Here is Feynman's introduction to the lecture, given on June 4, 1964. This was the last lecture in a two-year ``introductory" physics course for Caltech undergraduates.

This lecture is only for entertainment. I would like to give the lecture in a somewhat different style—just to see how it works out. It’s not a part of the course—in the sense that it is not supposed to be a last minute effort to teach you something new. But, rather, I imagine that I’m giving a seminar or research report on the subject to a more advanced audience, to people who have already been educated in quantum mechanics.

All that aside, this is a subject I want to talk about. It is recent and modern and would be a perfectly legitimate talk to give at a research seminar. My subject is the Schrödinger equation in a classical setting—the case of superconductivity.

The lecture includes a description of the quantisation of magnetic flux, the Josephson effect, Shapiro steps, and a SQUID. All of these phenomena had only been discovered in the two years before the lecture. It is striking that Feynman clearly appreciated the significance of these recent discoveries, not just for condensed matter but also for quantum theory. He concludes the lecture as follows.

These then are some illustrations of things that are happening in modern times—the transistor, the laser, and now these junctions, whose ultimate practical applications are still not known. The quantum mechanics which was discovered in 1926 has had nearly 40 years of development, and rather suddenly it has begun to be exploited in many practical and real ways. We are really getting control of nature on a very delicate and beautiful level.

I am sorry to say, gentlemen, that to participate in this adventure it is absolutely imperative that you learn quantum mechanics as soon as possible. It was our hope that in this course we would find a way to make comprehensible to you at the earliest possible moment the mysteries of this part of physics.

 

Entering the strange world of Kurt Godel

The picture below is of Godel's rotating universe. It represents an exact solution to Einstein's gravitational field equations and has the strange property of closed timelike curves (i.e. one can travel into the past!). This mathematical solution was found by Kurt Godel while he was employed by the Institute for Advanced Study at Princeton.

I think I first encountered this picture in my final undergraduate year in the classic book, The Large Scale Structure of Space-Time by Hawking and Ellis, while working on a research project in general relativity.

Godel's universe is just one example of the fascinating science and stories recounted in the book
Who Got Einstein's Office? Eccentricity and Genius at the Institute for Advanced Study by Ed Regis, first published 30 years ago.

I only read the book this past week and loved it. It is a captivating blend of science, mathematics, personalities, history, philosophy, humorous anecdotes, gossip, eccentricities ...
I was so captivated that I read it during two situations I would not normally read something so "heavy": during a long flight [normally I watch reruns of The Big Bang Theory or Upper Middle Bogan [need to laugh!] or recently a Warren Buffett documentary... sorry better not mention that again...], and during "down time" in the evening after a busy day.

Regis nicely describes the continuum hypothesis, Einstein-Podolsky-Rosen (EPR) "paradox" in quantum theory, von Neumann machines, cellular automata, the Bourbaki seminar, parity violation, the solar neutrino problem, fractals, the stability of matter, ...

The personalities covered include Godel, Einstein, Herman Weyl, John von Neumann, J. Robert Oppenheimer, Freeman Dyson, T.D. Lee,  C.N. Yang, Andre Weil, John Bahcall, Stephen Wolfram, Ed Witten, .....

It is amazing how much Regis packs into less than 300 pages (in a paperback).

The tragic mental health problems of Godel are described in a sensitive manner.

One pathetic story concerns the endless quibbles of T.D. Lee and C.N. Yang.
(Aside: They actually did their Nobel Prize winning work on parity violation at the IAS. This is in contrast to the countless Nobel laureates who at one time have been affiliated with the IAS but did not do their prize work there.)
Lee and Yang (or is it Yang and Lee?) argued constantly about the order in which their names should be listed, not just as co-authors, and at the Nobel ceremony, but even in newspaper and magazine articles about them. Furthermore, it is crazy to read the wildly different and self-serving accounts of certain concrete events. Great scientists are all too human ......

Some people consider the book is a bit of a "hatchet" job and has a mocking tone that paints the IAS in a poor light and questions its value and existence. I would not agree. I think it does show that the IAS has produced a lot of important scholarship. Regis does raise some important questions I mention below. But, I did think that he did refer to the IAS as "the One True Platonic Heaven" too many times.

Regis is implicitly critical of the fact that there is very little interaction between different research groups and disciplines within IAS. However, there is one important story he missed: when Freeman Dyson and the number theorist Hugh Montgomery were introduced at tea at the IAS and they made a connection between random matrix theory (quantum physics) and zeros of the Riemann zeta function.

Some questions the book raises for me include:

Can you really "manage" genius?

How do you create an institutional environment that increases the likelihood of truly great discoveries and scholarship?

What is the best way to hire "great" people?

What is a good mix of young and old staff?

What is a good mix of permanent faculty, postdocs, and short term senior visitors?

When is the absence of students in a research institute good or bad?

When is the absence of experimentalists in an institution bad/good for theoretical physics?

How do you foster a healthy synergy between pure mathematics and theoretical physics?

How might you foster some constructive interaction between distinct disciplines: philosophy, mathematics, theoretical physics, economics, history, ....?

Here is Feynman's perspective (partly quoted in the book):

I don't believe I can really do without teaching. The reason is, I have to have something so that when I don't have any ideas and I'm not getting anywhere I can say to myself, "At least I'm living; at least I'm doing something; I am making some contribution" -- it's just psychological. 

When I was at Princeton in the 1940s I could see what happened to those great minds at the Institute for Advanced Study, who had been specially selected for their tremendous brains and were now given this opportunity to sit in this lovely house by the woods there, with no classes to teach, with no obligations whatsoever. These poor bastards could now sit and think clearly all by themselves, OK? So they don't get any ideas for a while: They have every opportunity to do something, and they are not getting any ideas. I believe that in a situation like this a kind of guilt or depression worms inside of you, and you begin to worry about not getting any ideas. And nothing happens. Still no ideas come. 

Nothing happens because there's not enough real activity and challenge: You're not in contact with the experimental guys. You don't have to think how to answer questions from the students. Nothing!

Governments have less and less interest in "research for its own sake" and "without constraints" [hallmarks of the IAS]. However, there is an increasing number of generous and wealthy philanthropic organisations who are very interested. These are important questions for them.

Although I lived in Princeton for four years around the time the book was being written I only recall going inside "the Brain Farm" [as a friend called it] once, and that was for a music concert. Nevertheless, I spent many pleasant hours walking, jogging, bird watching, and skiing in the beautiful woods located behind the IAS.

I thank Ben Powell for a conversation about the IAS, stimulating me to remember I had inherited a copy of the book from my parents.

I welcome thoughts on any of the questions and any good IAS stories...

Should Hollywood make a Linus Pauling biopic?

The past few years has seen Hollywood make movies about famous scientists and mathematicians, including A Beautiful Mind (John Nash), The Theory of Everything (Stephen Hawking), The Imitation Game (Alan Turing), and now The Man Who Knew Infinity (Ramanujan).
The latter is to be released April 29 in the USA and May 5 in Australia.


Are there others?

This post is not about the important issue whether this is a good thing, particularly when you consider all the creative license taken, and whether the movies capture the science in an appropriate way.

First, what kind of scientist is an appropriate candidate for such a movie?
I think their life must have some significant components of romance, scandal, tragedy, and redemption. The list above does include substantial ingredients of most of these. Pure scientific heroism and brilliance just does not cut it.

Second, who might be some candidates from condensed matter physics or theoretical chemistry?

Feynman was one that came to mind, particularly because of the tragic death of his first wife and his involvement in the Challenger inquiry. However, I see that back in 1998 there was Infinity, starring Matthew Broderick and Patricia Arquette. It looks like it was box office flop. Has anyone seen it?
Interestingly, about 15 years ago, Alan Alda commissioned and was the lead actor in a play QED about Feynman. No signs of a movie.

So who might be other candidates? Greats like John Bardeen, Phil Anderson, Walter Kohn, are just too boring ....
But, what about Linus Pauling? There is the romance and partnership with his wife, amazing lecturing skills, the political activism and persecution, and the controversy of his views about vitamin C.

Perhaps William Shockley might make the cut, because of his role in starting Silicon Valley, conflict with everyone, and racist views, ...

Any other ideas?

A basic but important research skill, 6: skepticism

Feynman said "The first principle is that you must not fool yourself and you are the easiest person to fool."

Walter Kauzmann emphasised that people will often believe what they want to believe rather than what the evidence before them suggests they should believe.

Students need to learn skepticism. Furthermore, it needs to be modelled to them by their advisors.
In particular, students should not just believe something because

- their advisor/supervisor believes it or tells them it is true
- it has been published, especially if it is in a luxury journal
- someone famous [or a group of famous people] claims it is true
- it is an exciting idea.

Basic but important questions to ask are:

What is the evidence? How reliable is the evidence?
Is there an alternative explanation, particularly a simpler one?

Maybe I am just becoming a grumpy old man, but I think I do increasingly encounter students and young researchers who lack this basic skill.
I fear that this is because of the seductive power of "sexy" explanations and topics. Furthermore, some of the students mentors and role models don't model or practise skepticism, particularly if their career success and funding [or hope thereof] depends on the exotica favoured by the luxury journals.

Good science is just plain hard work and not as exciting or clear cut as we might wish.

What are the ten most remarkable scientific ideas?

Feynman said the most important idea is that all things are made from atoms. On the weekend I listened to a short and fascinating talk by Bill Bryson The four most remarkable things I know.
So, I wondered what do I think? What are the ten most remarkable scientific ideas?

I have used the following rough criteria. The idea

• is far from obvious
• is often not thought about because we have become so used to it that we take it for granted 
• may evoke not just an intellectual response but also a somewhat emotional one of wonder and awe
• is profound but can be simply stated
• is a specific law, principle, or property, rather than a general scientific idea such as that laws can be encoded mathematically, experiments must be repeated, the same laws apply everywhere in the universe.

Here is my first rough attempt at a list of the top ten, in no particular order. I hope it will generate some discussion.

1. The universe had a beginning.

2. Time has a direction.

3. The fundamental constants of nature are fine-tuned for life.

4. All elementary particles are identical.

5. Energy is quantised.

6. Particles are fields and fields are particles.

7. All of life has a common molecular template (DNA and proteins).

8. Everything is made from atoms. The periodic table of chemistry.

9. Evolution: many small genetic variations can produce biological diversity.

10. Emergence and reductionism. Complexity can emerge from simplicity.

Here are some runners up. Some are more specific versions of those above.

A. The genetic code. DNA prescribes protein synthesis.

B. Genetic information is encoded in DNA.

C. Water is a unique liquid with remarkable properties with important implications for biomolecular function.

D. Diffraction of waves [x-rays, electrons, neutrons] can be used to determine the atomic structure of materials.

E. The geometry of molecules and chemical reactivity is determined by quantum mechanics [and can be described by potential energy surfaces].

F. The second law of thermodynamics: entropy is a state function. Free energy determines stability of open systems.

G. Symmetry constrains physical laws; spontaneously broken symmetry leads to different physical interactions and states of matter.

H. Macroscopic properties are determined by microscopic properties.

I. Protein folding. Amino acid sequence uniquely determines protein structure which determines function.

I am missing anything about earth science due to my ignorance.

Presumably, others have compiled such lists and taught courses based on them. Please let me know. One example is a course by Robert Hazen and James Trefil. Each chapter is centred around a great idea.

What do you think?
How would you change the above lists?

What motivated Feynman?

There is nice book of essays by Richard Feynman, The Pleasure of Finding Things Out, that is worth reading. The title piece is the transcript of an interview with the BBC in 1981. Here is an extract:

 I won't have anything to do with the Nobel Prize... it's a pain in the... I don't like honours. I appreciate it for the work that I did, and for people who appreciate it, and I know there's a lot of physicists who use my work, I don't need anything else. I don't see that it makes any point that someone in the Swedish Academy decides that this work is noble enough to receive a prize - I've already got the prize. The prize is the pleasure of finding the thing out, the kick in the discovery, the observation that other people use it - those are the real things, the honours are unreal to me. I don't believe in honours, it bothers me, honours bother, honours is epaulettes, honours is uniforms, my papa brought me up this way. I can't stand it, it hurts me.

Feynman dreams of a final theory

In 1957 Reviews of Modern Physics published a conference talk by Feynman, Superfluidity and Superconductivity. The last paragraph is fascinating where he laments the problem of finding a theory of superconductivity.
[Click to make it larger]

This highlights just how brilliant BCS were!
Coincidentally, BCS published their theory the same year.

Gell-Mann and Feynman in 1957 

Feynman on path integrals for cheap

The book Quantum mechanics and path integrals by Feynman and Hibbs is a classic that was out of print and an old hardback edition is currently going for $799! The good news is the book has been reprinted by Dover and you can now buy a copy on Amazon for only US$12. My copy arrived today.

The easiest person to fool is yourself

Key moderating principles I try to keep in mind as I struggle to understand complex molecular materials

-correlation does not imply causality

-extraordinary claims require extraordinary evidence

-Kauzmann's maxim: people will tend to believe what they want to believe rather than believing what the evidence before them suggests they should believe

-use the method of multiple alternative hypothesis

-be mindful of the dangers of curve fitting

-in systems with many degrees of freedom it is very hard to find control variables, because most variables are not independent of one another

-Feynman's warning: the easiest person to fool is yourself

A great way to start learning (and understanding) quantum physics?

At UQ the Faculty of Science has an Advanced Study Program, which gets gifted (and hopefully highly motivated!) undergraduates involved in research early. I have a second year student, Michael Horn, who is doing a project with me on optically excited states of biomolecules. However, he hasn't taken any courses in quantum physics yet.

So what should he read? Volume III of The Feynman lectures turns out to be ideal. I never cease to be amazed at Feynman's originality and profound insight. He certainly does not treat topics in the conventional order! Just using a Hamiltonian matrix he describes the ammonia maser, the hydrogen molecule, benzene, dyes, the neutral K-meson, semiconductor devices, ... Only after all this in chapter (lecture) 16 does he introduce the Schrodinger equation (i.e., the differential equation) and the hydrogen atom. Michael only needs to read 12 lectures to learn what he needs to know to understand the essential quantum physics associated with a lot of the photochemical properties of organic molecules.