Summary of "Six Not-So-Easy Pieces"

Core Idea

Physics laws remain identical under symmetry transformations (rotations, translations, time shifts) — this principle alone generates all conservation laws
Space and time are unified, and gravity isn't a force but curved space-time geometry — objects follow paths maximizing their proper time, which appears as gravitational motion
Intuition fails at extremes (high speeds, strong gravity); rely on mathematics and experiments, not mental pictures

One symmetry → one conservation law (mirror image):
- Translation in space → momentum conserved
- Rotation → angular momentum conserved
- Time translation → energy conserved
Test symmetries experimentally — weak forces violate mirror symmetry; cobalt atoms emit electrons preferentially in one direction, breaking left-right equivalence
Matter and antimatter restore symmetry — right-handed matter pairs with left-handed antimatter

Light speed (186,000 mi/sec) is an absolute limit, not negotiable — nothing can exceed it
Moving clocks run slow and objects contract — time and length are relative to reference frame (proven: muons from cosmic rays survive longer in Earth's reference frame than their "lifespan" suggests)
Simultaneity is relative — events "at the same time" to you occur at different times to moving observers
Energy = mass × c² — interchangeable: 1 gram of fuel → energy of 20,000 tons of TNT

Combine 3 spatial + 1 time coordinate into four-vectors — energy and momentum transform together as one entity across all reference frames
Unified description replaces separate laws — energy-momentum conservation becomes one four-vector law; electric and magnetic forces merge into one field

Massive objects curve space-time like a bowling ball denting rubber — measure curvature by testing if circumference ÷ 2π ≠ radius
Clocks run at different rates depending on gravitational field — time literally passes faster at higher altitudes (proven with Mössbauer effect)
"Falling" is following the maximum proper-time path through curved space-time — what feels like free fall is actually the straightest path in warped geometry

Prioritize symmetry arguments before solving equations — ask what must stay constant; conservation laws follow automatically
Use vectors to write laws that survive rotation and translation — reveals which principles are universal
Accept that intuition fails; trust mathematics and experiments — test predictions directly, don't rely on mental models at extremes
Build understanding sequentially: vectors → special relativity → space-time curvature → curved gravity
Unify paired concepts (space+time, energy+momentum, electricity+magnetism) — they're aspects of one entity, not separate phenomena