Question 1

What is the Lorentz factor γ?

Accepted Answer

The Lorentz factor γ = 1/√(1−β²) where β = v/c is the ratio of object velocity to the speed of light. At rest γ=1; as v→c, γ→∞. Time dilation, length contraction, and relativistic mass all scale with γ. At v=0.99c, γ≈7.09, which explains why cosmic-ray muons survive the trip to Earth's surface despite their short half-life.

Question 2

What is the twin paradox?

Accepted Answer

In the twin paradox, one twin travels at high speed on a rocket and returns younger than the twin who stayed home. Time dilation Δt′=γΔt₀ means the traveler's proper time is shorter. This is not a paradox: the traveler undergoes acceleration/deceleration, breaking the symmetry. Special relativity fully resolves it — the traveling twin is genuinely younger upon return.

Question 3

How does relativistic velocity addition work?

Accepted Answer

In classical mechanics velocities add directly, which can exceed c. The relativistic addition formula u′=(u−v)/(1−uv/c²) guarantees the result is always less than c. For example, if a rocket moves at v=0.9c and fires a projectile at u=0.9c, the ground-frame speed is only ≈0.994c, not 1.8c.

Question 4

How is relativistic kinetic energy different from classical KE?

Accepted Answer

Classical KE=½mv² diverges to infinity at finite energy, incorrectly implying particles can be accelerated beyond c. Relativistic KE=(γ−1)m₀c² correctly shows that accelerating a particle to near-c requires ever-increasing energy. For particle accelerators, this formula (often expressed in MeV) is essential for beam energy calculations.

Special Relativity Simulator

Key Formulas