## Thursday, April 18, 2013

### Dirac's 1975 lectures

Spiros found this remarkable 1-hour talk by Paul Dirac in New Zealand in 1975:

Recall that Dirac was born in 1902 and died 1984; so he was 73 in the video above. He is a serious man but there's a lot of room for his memories as well as some jokes.

There are actually four talks. The first one above is on quantum mechanics; the second one is on quantum electrodynamics; the third is on the magnetic monopoles; and the fourth one is on his largely incorrect large number hypothesis (variation of universal constants).

Even if you focus on the first lecture on quantum mechanics, there's a lot of interesting stuff to listen to. He was impressed by the successes of the old Bohr model of the atom. He identified the key property of Heisenberg's quantum mechanics to be the non-commutation of the observables. He thinks that Heisenberg himself was afraid of this feature – much like almost every originator of a great idea is afraid of the key revolutionary relationship because it could also very well spell the doom for his pet idea. But Dirac himself wasn't afraid. He took it seriously.

At the end, he also mentions that he doesn't believe renormalization unless the quantities are renormalized by small amounts. He explains the success of the renormalized quantum field theories by comparing them with the successful old Bohr model of the atom which was fundamentally wrong, too. Well, Dirac was both right and wrong in his counter-revolutionary attitude. He was wrong because the success of renormalization is no accident, of course. He was right because it's possible to reorganize the field theory in such a way – a way using counterterms – that the renormalization is small, indeed. However, you must still accept that there are counterterms that cancel the loop divergences. I am not sure whether Dirac understood the Renormalization Group and similar insights of the 1970. He may have already been too old for that.

1. Dirac seems older than his years. I will soon be 77 but I act and feel younger than Dirac looks in these lectures.

2. Dear Lubos,

I agree that this video is a jewel.

The ending is also remarkable. Dirac makes some very strong statements that quantum mechanics is not the final word and determism might come back later although not as a step backwards but as a step forward at the espense of other things which we take for granted now. We can say that Einstein, Dirac and 't Hooft really team up as the proponents of determinism.

Let me add that of course I know that in physics it is not about the names of the people but only about whether their ideas are any good.

Getting at least a rough idea what 't Hooft is doing with his cellular automats is still on my todo list though.

3. Diracs remarks about renormalization are best simply ignored I guess.

4. Dirac apparently had very bad social skills, and so his weak lecturing style probably has more to do with his personality rather than his age here.

5. "The Strangest Man" by Farmelo talks about Dirac refusal to accept renormalization in his last decade. It supports that by the mid 70's he had lost some of the capacity and much of the interest needed to understand that the ills he perceived with renormalization had been cured.
I enjoyed the book but do not by that approve all. His choice to include from crackpot attackers of ST in the last pages of the book irritated me.

6. Those videos are indeed remarkable, I had previously only seen Dirac in brief video footage recorded at the 1927 Solvay conference. I have watched the first two lectures, the first on Quantum Mechanics is fascinating. Most of the general details are known, but to hear the finer points from the man himself who was part of the stunning historical events of the mid 1920s is compelling. He very clearly explained how Heisenberg constructed his "matrices" without having any knowledge of matrices (this is surprising to some people, because you might think that a decade after General Relativity, that matrices and tensors might be common knowledge to physicisits), and also makes it very clear how Schrodinger derived his wave equation by essentially just adding an external potential to de Broglie's equation I detect a slight attempt by Dirac to emphasise the superiority of Heisenberg's discovery here, but he does acknowledge that both Heisenberg and Schrodinger could have separately discovered QM independently. (It's also nice to be reminded of the correct pronunciation of "de Broglie" :-) )

I had not known of his thoughts on the future of QM, at least not to the extent that he thought determinism might return at the expense of some even more radical pardigm shift - perhaps this is an effect of nostalgia for Einstein, or perhaps he was cryptically referring to a many-worlds interpretation :-)

His answers to question section is difficult to follow as the questions can't be heard, but the reply to the renormalisation question seems a little short-tempered - maybe he was becoming impatient. In any case, he was only agreeing with Feynman who pointed out that the procedure, as introduced in QED was a "game" , "hocus-pocus", "a dippy process" (see his QED book). As we now know, the renormalisation process was given a firmer mathematical footing in the 1970s with ideas from statistical physics with the renormalisation group, but that does not mean that the original model could not be improved so as to not require the heavy duty mathematical justifications.

The second lecture on field theory lacks the passion and interesting historical anecdotes of the first lecture. I will watch the one on magnetic monopoles later, and the one on large numbers if I get time over the weekend. Such a pity he didn't speak about his most brilliant discovery of his celebrated equation.

7. Vladimir KalitvianskiApr 19, 2013, 9:22:00 AM

Lubosh wrote: "...the success of renormalization is no accident, of course." Lubosh, is there a theorem that proves your words? Is there a theorem that shows the uniqueness of renormalization way of doing physics? If there is not, you are an advocate of non existent theorem.

8. Oh yep, I will watch these as soon as I'm back home (currently traveling) :-)

9. I am sure Dirac was right about renormalization. He new what it was and understood it very well. He just did not share the enthusiasm of renormalization practitioners and he was aimed first of all at the theory reformulation rather than at "doctoring numbers". The success of renormalization is a fluke, see http://arxiv.org/abs/1110.3702

10. It’s more than his lecturing style, John. His clinging to determinism, without any justification, indicates cognitive deterioration along with the more obvious physical symptoms. Bohr and Heisenberg got it but, sadly, Dirac lost it in his senescence.
I do not wish to detract in any way from his accomplishments. His book on quantum mechanics stands out as the most remarkable textbook I have ever read. He was simply amazing.

11. The other great thing about this lecture is Dirac demonstrates that you also have to be very lucky in making a major discovery. Innate talent isn't enough. In Dirac's case, he was fortunate to have worked on the Sommerfield model which required him to read up on Hamiltonian mechanics and the Poisson bracket, and also having Fowler as an adviser who showed him Heisenberg's paper. First time round he admitted he dismissed it.

Just because we get older shouldn't stop us from learning a new areas of physics and mathematics, even if it takes longer as we get older.

12. Him clinging onto determinism doesn't have anything to do with him getting older. Young people today cling on to it, with some even producing papers that question the foundations of quantum mechanics. Quantum mechanics is very difficult to understand for most people.

13. Wrong. When a man of Dirac’s astonishing intellect and physics intuition fails to grasp the very essence of QM he has completely gone bonkers. Loss of cognition can have causes other than age, of course, but the evidence strongly implicates senility in Dirac’s case.
There’s nothing wrong, necessarily, with questioning the foundations of QM or anything else but when one asserts that QM is wrong or incomplete it is proof that one is a crackpot.

14. Is it not just a matter of merely accepting the perfect match between the results of laboratory experiments (practical probes of basic Reality) and its QM-logical (mathematical) descriptions WHILE BEING ABLE TO WITHSTAND the from deep inside emanating surge of one's primitive/instinctive inclination to impose common sense?
(At least I think I've gathered this much - even without actually being able to juggle the maths.)

15. I think that is too simplified. Dirac went from recluse to family man. He learned other things that in that last decade landed him gently in comparison many of the shooting stars of math and physics. QM has withstood much after his death and ST provides also a mathematically reasoned solution to infinities ... Or so I am told. Sure age dulls the brain but one gains some wisdom too, right?

16. It is unfair to criticize Dirac for being too old to understand the Renormalization Group work, because his criticisms of the mathematical nonrigorousness of Quantum Electrodynamics remain valid -- even today, nearly 40 years later, "effective quantum field theory" has not succeeded in providing correct well-defined convergent algorithms to map experimental inputs to experimental output probability distributions. The "ills" of renormalization have not been "cured", although renormalization has been shown to improve the situation in many more cases than previously known.

Dirac's preference for deterministic theories is less justifiable, but at least he absorbed the lesson of Bell that we would have to give up principles previously taken for granted in order to have determinism.

17. Dear Joe, we have rigorous ways to define quantum field theories such as QCD by putting them on the lattice. We may prove the continuum limit is the "right thing" and the lattice QCD isn't the helpful way to determine most of the interesting things we want to know about QCD - and there's no reason why it should be because the continuous resulting theory may be discussed in lots of ways that avoid the auxiliary discrete formulation.

QED and other theories have a Landau pole so they're inconsistent at short enough distances, can't be put on lattice, and their consistency works at most to all orders of the perturbative expansion. At any rate, we know how to answer this "consistency question for a given QFT" completely.

It's surely untrue that "ills of renormalization haven't been cured". On the contrary, they have been fully legitimized and the validity of the procedure - the reasons for why it works - has been made transparent.

Your comment makes it 100% obvious that you can't understand what Renormalization Group actually means, and you shouldn't use concepts that you don't understand at all.

18. Returning to your statement "...the success of renormalization is no accident, of course", I would say : "...the failure of renormalization in non renormalizable theories is no accident, of course."

19. Lubos, you misunderstand my point. Renormalization works sometimes, but for other situations such as QED it does not work, as you just admitted. We hope that eventually we will have a theory that applies everywhere that makes everything calculable, but why should Dirac in 1975 be faulted for not thinking that the work done up to that point showed that one need not worry about effectivity? I completely agree with you that some QFTs can be rigorously shown to be consistent, and for THOSE theories the ills of renonormalization have indeed been cured, but I referred specifically to curing the ills of QED in order to defend Dirac against the charge of senility.

20. Vladimir KalitvianskiApr 23, 2013, 8:05:00 AM

Lubosh, but Dirac new all those things, "insights" and remedies! He considered them as a temporary working rules and as a hint that the solution could be close. He dreamed of physical and mathematical reformulation rather than of finding more convincing pretexts to deal with physically wrong constructions.

Apart from UV problems, there are IR problems that show immediately that our initial approximation is wrong. Theory needs reformulation to become a routine scheme of calculating Taylor series terms. Renormalization+IR diagram summation = Reformulation in terms of better initial approximation.

21. Please, stop with this infrared crackpottery of yours, otherwise I will permanently ban you. I have explained to you what the infrared divergences mean and don't mean about 50 times already. If you're still not getting it, your IQ must be below a puppy's, and puppies aren't posting here themselves so I don't know why you should have the privilege.

22. Vladimir KalitvianskiApr 23, 2013, 9:02:00 AM

I thank you, Lubosh, for explaining me IR problem, but I would like you to hear my point of view substantiated with proofs and demonstrations. Depending on our initial approximation, we may have or we may not have those IR problems. So do not insist they are inevitable. They only are inevitable in the present scheme you stick to.

23. "... renormalizability is not some deep property of nature, but rather an inevitable consequence of doing physics well below the next scale where interesting new phenomena occur.
> - A. N. Schellekens -"
Best.

24. Nicely and succintly put, Robert!

25. These lectures were written up and published long ago. Thanks for the live video.