(HL) Galilean and special relativity

Learning objectives

(HL) Define an inertial reference frame, apply the Galilean transformation equations for position and velocity, and explain why Newton's laws take the same form in every inertial frame

(HL) State the two postulates of special relativity and explain why Galilean velocity addition cannot be correct for a beam of light

(HL) Apply the Lorentz transformation equations and the Lorentz factor γ = 1/√(1 − v²/c²), together with the relativistic velocity addition equation, to relate measurements made in two inertial frames

(HL) Calculate time dilation and length contraction from a proper time interval and a proper length, and explain why two events that are simultaneous in one frame are not simultaneous in another

(HL) Explain how the number of muons detected at the Earth's surface provides experimental evidence for time dilation in the Earth frame and for length contraction in the muon frame

(HL) Draw and interpret spacetime diagrams, plotting worldlines and the tilted axes of a moving frame, and use the invariance of the spacetime interval (ct)² − x²