Quantum Uncertainty

In this chapter, we show how uncertainty relations arise naturally from quantum theory for position and momentum, time and energy, and so on. We explore the meaning of these relations and apply them to the quantum mechanical description of the pendulum. We then use our new-found knowledge of the pendulum to construct Schrödinger cat-like states in opto-mechanical systems. Finally, we show how we can use entanglement to enhance the precision of measurements.