Discovering Group Theory, Days 21-23

We spent three days discussing the conceptual framework of special relativity.

We reviewed the expressions for time dilation and length contraction (we didn’t derive the latter) and discussed what they tell us about the nature of space and time.  We introduced the Lorentz boosts as a replacement for the Galilean boosts, and formally introduced the Lorentz group, SO(1,3). New concepts and ideas included

• Spacetime events
• Spacetime diagrams and null cones
• Causally connected events 
• Relativity of simultaneity

The key takeaway was that Lorentz transformations leave the causal structure of spacetime the same, just like rotations of a polygon leave the shape and the orientation of the polygon the same.