Tuesday, June 26, 2012

Feynman's 1986 Dirac Memorial Lecture

He talked about antiparticles, CPT, spin, and statistics

You may watch those 70 minutes. Feynman starts by saying that Dirac has been his hero so he was honored to give a Dirac lecture. Dirac was a magician because he could guess the right equation, a new strategy to do science.

However, Feynman also says that Dirac also invented Zitterbewegung which wasn't terribly useful. Well, not only that: Zitterbewegung is completely unphysical. However, it wasn't invented by Dirac but by Schrödinger as the German name of the non-effect indicates. ;-) Dirac wouldn't make such an elementary mistake when it came to basic quantum mechanics.

However, Feynman quickly returns to the marriage of special relativity and quantum mechanics: antiparticles are essential for the union. He was going to focus on antiparticles and the Pauli exclusion principle.

Without particle-antiparticle production, the antisymmetry of the wave function would boil down to the initial state – God knows why it's the way it is – and the antisymmetry would just be preserved by the evolution. However, it gets more interesting because new particles may be produced and the wave function is still antisymmetric in them.

Feynman began to talk about amplitudes for processes with particles and antiparticles. Unfortunately, the transparencies are not too readable. Can you find a better quality video somewhere? Well, the camerawoman didn't look at the slides most of the time, anyway.

At any rate, he says that the Fourier transform composed of positive-frequency modes only is inevitably non-vanishing in each interval. You need negative frequencies as well if you want things to vanish in the past or outside light cones which is needed for causality. The negative-energy objects have to be a part of physics in some way.

Virtual particles have to exist and one man's virtual particle is another man's virtual antiparticle, not to mention women's antiparticles :-), simply because the sign of energy of spacelike energy-momentum vectors depends on the reference frame. So the antiparticles' properties are actually fully determined by particles' properties because of relativity.

Feynman mentioned that he had never pronounced "probability" correctly because he didn't have the patience. LOL.

He explains why the fermions cancel diagrams to impose the Pauli exclusion principle, something that doesn't hold for bosons such as spin \(j=0\) particles (Feynman confusingly talks about photons with \(j=1\) just seconds earlier).

The Bose-Einstein statistics isn't hard to understand whenever we talk about oscillations. The Fermi-Dirac statistics may be more counterintuitive so of course some special attention is invested into explanations of the minus signs for fermions.

A segment of the lecture in which the (invisible) math formulae are important is dedicated to clarifying the Feynman propagator – why it's the right way to combine the retarded and advanced propagators' features. Unfortunately, he's too modest to call it "Feynman propagator" so you may have a problem to determine what he's really talking about here. ;-)

The CPT-theorem is explained in the same way I am doing it (independently). The CPT-operation is really just a rotation of spacetime. In the Minkowski space, there's also the mysterious nowhere land, the spacelike region, but with continuations to the Euclidean space, the CPT-operation simply is just a rotation by 180 degrees. So the world has to be invariant under it. (The C, charge conjugation, is an internal operation that is automatically included in the operation because if a particle goes backwards in time, as seen on the arrow of the 4-vector \(j^\mu\), and it does go backwards if we perform the T, the time reversal, then e.g. the charge \(\int\dd^3 x\,j^0\) reverts the sign.)

Around 29:00, the fermions change the sign of the wave function with rotations under 360 degrees: \(\exp(im\phi)\) just gives you that. Intuition wouldn't be enough. At 30:00, he reviews the Dirac's belt trick, a physical exercise showing that a rotation by 720 degrees is like doing nothing while a 360-degree rotation twists your arm. A huge applause follows.

The rest of the lecture is about a careful tracing whether you did the rotation or not. Without clearly readable transparencies, the technical stuff may be a bit hard to follow. He calculates \(T^2\) which has to change the state at most by a phase but the phase may be nontrivial. There are differences for bosons and fermions...

At 57:50, Feynman discusses a permuted connection between two loops – attributed to a Mr Finkelstein – that could be instantly used as an explanation of your humble correspondent's matrix string theory. ;-)


  1. I have been studying the Dirac equation and its solutions a lot lately, and I of course came across the Zitterbewegung. I don't feel qualified enough to have an oppinion about its reality, but I found some papers by David Hestenes about this topic. He is one of the pioneers of the geometric algebra in physics (Clifford algebra) and he interprets the Zitterbewegung differently from the Schrödinger interpretation.

  2. I`d like to watch the video, but it his to wait until I`m back home due to the lame internet connection here :-/

  3. I do truly find this interesting in terms of the geometric and dynamics going on.

    In terms of your Disqus development.....how would one create a bar above your comment section in order to allow you to use HTML language to make bold, italicize, or use quotes by selecting a button.

    Would this not be better then having to know HTML to make comment more dynamical?

  4. Dear Plato, I think that Feynman himself has often been "the best picture is an equation" kind of guy. Certain things simply shouldn't be visualized in terms of any everyday life things because such a visualization is bound to be wrong.

    Analogously, the DISQUS comments can't be styled via general CSS. It's deliberately forbidden by DISQUS, as I mentioned in an article today, to prevent users from screwing the comment sections. The DISQUS block appears in a separate iframe - essentially an independent page within the larger page - and it manually picks some properties of the parent page that are explicitly listed and allowed by DISQUS. No styling of the "authoring textarea" is allowed and in the same way, things like Mathjax or replacement of smileys by images are deliberately forbidden, too.

    If you disagree with any of these policies, you must tell it to the DISQUS guys but believe me, what you're proposing - and what Dilaton is proposing - isn't a detailed change. It goes against the very philosophy of DISQUS 2012.

  5. Hi Lubos,

    I think that Feynman himself has often been "the best picture is an
    equation" kind of guy. Certain things simply shouldn't be visualized in
    terms of any everyday life things because such a visualization is bound
    to be wrong.

    Mos definitely the best picture is equation, but imagining can be done in concert.

    The waiter jacket and and belt rotations are a case in point.

    Testing HTML within Disqus comment area.


  6. Thank you for posting link to this lecture . Feynman's lectures have been always something special .
    Interestingly, he was always careful when talking about retarded and advanced waves , Feynmans propagators and their role in QED. Many others ,in popular books,were not and did more damage than good.Example which comes to mind is Abdus Salam who wrote book dedicated to Dirac:
    "Unification of fundamental forces "

  7. I agree with PlatoHagel, I would tend to think that even a "primitive" geometry has to come naturally as the algebraic equation progresses. Isn't it key for the "elegance" of the equation ?

  8. Hmm, seems my yesterday post didn't make it. Probably new DISQUS feature on the TRF.