Discovering Group Theory, Day 17

Realizing that space-time symmetries provide more intuitive introduction to the abstract notion of a symmetry used in physics,  on day 17 we switched gears by discussing Richard Feynman’s lecture “Symmetry in Physical Law,” which students watched outside the class.

Feynman introduces the notion of a symmetry of a physical law, which we disected in the context of Coulomb’s law.

• We defined a coordinate system and discussed the difference between passive and active transformations.
• We worked out the translational and rotational spatial symmetries in 2D and showed that translations form a group.
• We also introduced translations in time and showed how they leave the kinematic equations unchanged.

As a transition to the discussion of moving observers, we watched the first half of a wonderful video from the 60’s titled Frames of Reference.