Relativity and Modern Physics
Core concepts
Special relativity rests on two postulates: physics is the same in all inertial frames, and light speed is invariant. Consequences: time dilation Δt = γΔt₀, length contraction L = L₀/γ, and the Lorentz factor γ = 1/√(1 − v²/c²). Relativistic momentum p = γmv and energy E = γmc², with rest energy E₀ = mc² and E² = (pc)² + (mc²)². Mass–energy equivalence explains nuclear binding energy and fission/fusion deficits. General relativity reframes gravity as spacetime curvature, predicting gravitational lensing, time dilation in gravity wells, and black holes with Schwarzschild radius r_s = 2GM/c². Nuclear physics: alpha, beta, gamma decay, half-life N = N₀(1/2)^(t/T), and conservation laws in reactions.
Traps
Time dilation applies to the other frame's clock-the proper time is measured by the observer at rest with the event. Length contraction occurs only along the direction of motion. Rest mass is invariant; relativistic mass is an outdated concept-use total energy instead. Half-life problems often ask for remaining activity, not just nuclei. Binding energy per nucleon peaks near iron, so both fission of heavy and fusion of light nuclei release energy.
Worked example
A muon with proper lifetime 2.2 μs travels at 0.99c: γ ≈ 7.1, so lab-frame lifetime ≈ 15.6 μs and distance ≈ 4.6 km. Rule of thumb: at v = 0.6c, γ = 1.25; at 0.8c, γ = 1.67; at 0.99c, γ ≈ 7.1-worth memorizing for quick estimates.