Theories of Everything with Curt Jaimungal Janna Levin: The Unreasonable Effectiveness of the Klein Bottle
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May 11, 2026 
Janna Levin, Claire Tow Professor of Physics and Astronomy and author exploring cosmology and topology. She describes the Klein bottle as a hidden-shape that could explain matter’s dominance. She talks about spin and pin structures, extra dimensions, topology-driven CP breaking, and how geometry might link to dark energy and black hole puzzles.
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Glass Klein Bottle Demonstration Reveals Projection Distortions
- Levin shows a glass Klein bottle physically and notes embeddings into 3D distort its true 2D symmetry.
- She points out forcing it into 3D changes local geometry (shorter inside, longer outside) unlike the true 2D form.
Pin Structures Allow Fermions On Nonorientable Spaces
- Pin structures (pin+ and pin–) let fermions exist on non-orientable manifolds, so non-orientability doesn't block fermions outright.
- The distinction is whether a fermion returns to itself or minus itself after one loop, which affects allowed boundary conditions.
Geometry Can Generate CP Violation And Baryon Asymmetry
- Topology can break fundamental symmetries: a Klein bottle extra-dimension can break parity and charge symmetries, enabling CP violation geometrically.
- Levin and collaborators found geometry can preferentially favor matter over antimatter without inserting parameters by hand.
