Sunday, August 3, 2014

Quick Review: Elementary Particles and the Laws of Physics

Or, The First Annual Paul Dirac Fan Club!
P Dirac

This is actually a pair of lectures from physicists Richard Feynman and Steven Weinberg entitled "The Reason for Antiparticles" and "Towards the Final Laws of Physics". They were on topics inspired by the great English physicist Paul Dirac, one of the people who codified Quantum Mechanics and one of the first to deal with quantum mechanics and relativity. The excellent biography The Strangest Man is about his life and work, so ... go read that too. Dirac is widely believed to have suffered from Asperger's Syndrome, so people with an interest in that topic might find it interesting to read about one person's life.

R Feynman

Feynman's work is pedagogical, it explains the modern view on antiparticle that evolved out of Feynman's elucidation of Dirac's work on relativistic quantum mechanics. This is a really good lecture, very well presented. Many of the most important laws of physics, such as the Pauli Exclusion theorem and the  spin-statistics theorem (and therefore, virtually all of chemistry...), are direct consequences of relativistic quantum mechanics. Feynman talks about Dirac's style, which he describes as trusting his equations. There's been some interesting history of science work on Dirac's attachment to projective geometry, which was essential to his understanding of relativity. H S M Coxeter wrote several articles on this idea for classical (that is, non-Quantum) relativity, such as "A Geometrical Background for de Sitter's World" and elsewhere. Feynman aims his lecture at a fairly high level, knowledge of basic quantum mechanics and relativity, but this is fairly well presented. Familiarity with Bra-Ket notation and space-time diagrams should be enough when it comes to physical theory. More important is the level of mathematical imagination it requires. Feynman puts the interpretation into easy to understand levels, a process he compares to Maxwell's mechanical models of electrodynamics, but it will really help if you're already used to this kind of discussion. This is too bad, since this is a very important topic, especially for chemists, and could use better popularization. Of course, it would take at least three times as much time and space... If you're capable of doing math at an advanced undergraduate level, I highly recommend this talk for a deep understanding of the parts of this theory most relevant to non-specialists. I'd particularly recommend it to chemists for the proofs of the Pauli Exclusion Principle and the Spin-Statistics Theorem. Particularly excellent is his discussion of the proof (first arrived at by Dirac) that if there is one magnetic monopole then magnetism is quantized everywhere, essentially as a consequences of path independence of a particular integral that comes up naturally in the theory.

S Weinberg

Steven Weinberg's lecture is more philosophical. He describes the symmetries and physical intuitions that lead to QED and then later theories, and takes care to be critical of insecure notions. Weinberg is careful to note the actual consequences of knowing the ultimate laws of physics and disclaims overblown Laplacian conclusions, distancing himself from what Daniel Dennett would call "greedy reductionists". This part has less diagrams, less physical intuition (it is after all, being compared to Feynman) and more speculation, but Weinberg also covers a much more ambitious topic. Feynman doesn't discuss, for instance, Dirac's model of anti-particles, the Dirac Sea, just constructs the modern version. This is a good discussion, but still a textbook topic. Weinberg explains why the Dirac Sea was abandoned for the modern theory in a footnote (it only works for spin-1/2 particles), and moves on to more speculative theories. Weinberg doesn't cover any topics not of interest to specialists, but it is good for young people wondering if they want to become specialists. This area, the idea of final laws of physics, is an area of interest to Weinberg and is better covered in Weinberg's book Dreams of a Final Theory. Weinberg's connection to Dirac is mostly from Dirac's Platonism, Dirac's suggestion that the final laws of physics will be mathematically beautiful. Weinberg points out that much of our skepticism of proposed roads to final theories - such as String Theory - comes from their mathematical inelegance, such as renormalization difficulties or lacking non-perturbative forms. This is a nice observation and obviously true, but I don't know what to make of it philosophically.


  1. Does he mean to say that said skepticism is irrational due to a preference for mathematical elegance? Or does he just note it as a fact?

  2. William Smith,

    He meant it as a fact. Elegant theories are preferred to inelegant theories for several reasons other than general aesthetics. An inelegant theory can be inelegant because it is, in fact, incoherent. This happened to many early ideas in statistical mechanics. Inelegance can come from unclear foundations, meaning a theory has hidden assumptions. Finally, inelegance can mean unmeasurable parameters, which mean that a theory must be tuned rather than tested.

  3. That makes sense. So inelegance is a technical term. Might it be used to describe Berkeley's criticism of the calculus? His critique that derivatives uinfinitesimals or fluxions were incoherent but only worked because two errors managed to "cancel each other out" makes a great deal of sense without a rigorous definition of the derivative based upon limits (which came much later).

    1. William Smith,

      Yes, Bishop Berkeley's criticism was that calculus and physics of his own time was inelegant. We would say now that they lacked rigorous algebraic ideas of limits, infinitesimals and even functions. Mathematically, Berkeley was correct and even innovative - he was the first person to realize there was something wrong with division by zero. Previous thinkers were still bound by thinking geometrically and didn't notice that their careful geometric limiting arguments were not matched by careful algebraic translations. In fact, they couldn't be without significantly many more innovations that took place after Berkeley's death. Whether Berkeley's philosophical conclusions follow from these premises is - of course - a different matter.

  4. Right. Is the whole world "just" thought? Any theist might have good grounds to think so, but having good grounds for a belief and being correct are different matters.
    Btw, I'm Geoff from class.

    I had never taken the time to study elegance in a technical sense. Thank you for the primer.