A.5 Galilean and special relativity

Objective notes

15 learning objectives

—A.5.1 (HL)—Reference frames

• Reference frames.

—A.5.2 (HL)—Galilean relativity

• Galilean relativity: Newton’s laws are identical in all inertial frames.

—A.5.3 (HL)—Galilean transformations

• Galilean transformations: x′=x-vt and t′=t.

—A.5.4 (HL)—Galilean velocity addition

• Galilean velocity addition: u′=u-v.

—A.5.5 (HL)—Two postulates of special relativity

• Two postulates of special relativity.

—A.5.6 (HL)—Lorentz transformations

• Lorentz transformations relate event coordinates between inertial frames.

• Use γ and the two inertial-frame coordinates x, t and x′, t′.

—A.5.7 (HL)—Relativistic velocity addition

• Relativistic velocity addition: u′=(u-v)/(1-uv/c^2).

—A.5.8 (HL)—Space-time interval

• Space-time interval is invariant: (Δs)^2=(cΔt)^2-(Δx)^2.

—A.5.9 (HL)—Proper time interval and proper length

• Proper time interval and proper length.

—A.5.10 (HL)—Time dilation

• Time dilation: Δt = γΔt0.

—A.5.11 (HL)—Length contraction

• Length contraction: L = L0/γ.

—A.5.12 (HL)—Relativity of simultaneity

• Relativity of simultaneity.

—A.5.13 (HL)—Space-time diagrams

• Space-time diagrams.

—A.5.14 (HL)—World lines and speed

• On space-time diagrams, world-line angle relates to speed: tan θ = v/c.

—A.5.15 (HL)—Muon decay evidence

• Muon decay is experimental evidence for time dilation and length contraction.