JOINT UNCERTAINTIES IN “CANONICAL” QUANTITIES Measuring one quantity can blur another quantity Momentum and position: Determine position, probe imparts an uncertain motion. Determine speed, must observe travel over multiple positions. Energy and time: For short time window, energy hasn’t stabilized. For stable energy, must give it time to attain equilibrium.

ACTION  kilograms  (meters/second)  meters “ACTION” the most fundamental quantity is nature, is Momentum merged with Length: [ kilograms  meters/second ]  [ meters ] Energy merged with time: [ kilograms  (meters/second)2 ]  [ seconds ] ACTION  kilograms  (meters/second)  meters

The Principle of Least Action The laws of physics can be deduced from the fact that Nature chooses conditionsn that minimize action. Quantized Action All action is constructed from discrete blocks of a basic Unit (called Planck’s constant ħ )