Physicists use the term “symmetry” for what mathematicians would call an invariance in the equations that describe the energy in a system (Hamiltonian T+V, or Lagrangian T-V). I will discuss the important consequences of such symmetries in physics. The “good Idea” I will talk about is a solution to a problem in particle theory –namely how can it be that, in a theory that describes both weak and strong interactions, the strong interactions appear (with very high precision) to maintain a symmetry that is not maintained in weak interactions –namely CP symmetry –a mirror symmetry between the laws of physics for matter and those for antimatter.
The solution that Roberto Peccei and I found involves adding yet another symmetry, now called PQ-symmetry. Our mistakes included, first an completely wrong answer, then fixing that by adding the new symmetry but not recognizing that this as what we had done, and hence not noticing a very important consequence of the new symmetry –the particle called the axion that is currently being searched for as a candidate to explain dark mattrer.
My point is not the technical details of this particular case but rather (1) a more general observation about the important role of wrong ideas in the process of discovery and (2) the importance of examining inconsistencies that appear when two previously separate areas of inquiry begin to overlap.
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