Thursday, September 26, 2019

Symmetry is the origin of all interactions

In Phil Anderson's review of Lucifer's Legacy: The Meaning of Asymmetry by Frank Close, Anderson makes the following profound and cryptic comment.
In a book focusing, as this does, on symmetry, it seems misleading not to explain the fundamental principle that all interaction follows from symmetry: the gauge principle of London and Weyl, modelled on and foreshadowed by Einstein's derivation of gravity from general relativity (Einstein seems to be at the root of everything). The beautiful idea that every continuous symmetry implies a conservation law, and an accompanying interaction between the conserved charges, determines the structure of all of the interactions of physics. It is not appropriate to try to approach advanced topics such as electroweak unification and supersymmetry without this foundation block.
To see how this plays out in electrodynamics see here.


  1. I can't help but wonder if this idea is backwards. Is it more that as physicists we can *only* make sense of interactions in terms of symmetry? It doesn't seem that symmetry plays nearly such a decisive role in biological interactions for example.

    1. Good point. This perspective is a ``fundamental'' one. Van der Waals interactions arise from quantum fluctuations in the Coulomb interaction. The latter arises from the U(1) gauge invariance of electromagnetism.

  2. Hi Ross, I am sure you have thought about this, and come farther than I. I don't "understand" how symmetry breaking leads to interacting theories. Sure, I have applied the gauge transformations, and saw how the couplings emerged in the Lagrangian. Unfortunately, that does not give me any feel of what is happening. The situation is different for VdW forces, where you can understand the force emerging from fluctuating charges. Are we even talking about the same sort of emerging? Cheers,--stijn

  3. Seems odd for Anderson not to mention Noether in there. Her eponymous theorem certainly predated London's work, and I think also Weyl's.