Special Relativity — Flashcards & Quiz

Q1: State the two postulates of Einstein's special relativity.

1) The laws of physics are the same in all inertial frames. 2) The speed of light in vacuum (c) is the same for all observers, regardless of their motion or the motion of the source. These lead to time dilation, length contraction, and E = mc².

Q2: What is time dilation and what is the formula?

Moving clocks run slower relative to a stationary observer: t = t₀γ, where γ = 1/√(1 − v²/c²) (Lorentz factor). t₀ is proper time (measured in the moving frame), t is dilated time (measured by stationary observer). At low speeds (v << c), γ ≈ 1 (no dilation).

Q3: What is length contraction?

Objects moving at high speed are contracted along the direction of motion: L = L₀/γ, where L₀ is proper length (rest length) and γ = 1/√(1 − v²/c²). Only the dimension parallel to motion contracts; perpendicular dimensions are unchanged.

Q4: What does E = mc² mean and when does it apply?

Mass and energy are equivalent: E = mc², where E is rest mass energy (J), m is rest mass (kg), and c is the speed of light. Even stationary objects possess enormous energy. In nuclear reactions, mass converts to energy or vice versa.

Q5: Why can nothing travel faster than the speed of light?

As v approaches c, the Lorentz factor γ approaches infinity. Accelerating to c would require infinite energy. Time dilation and length contraction also become infinite at v = c. Photons travel at c because they have zero rest mass.

Q1: The speed of light is the same for all observers regardless of their relative motion.

Answer: TRUE

This is Einstein's second postulate. The constancy of c is fundamental to special relativity and leads to time dilation and length contraction.

Q2: A clock moving at high speed runs faster than a stationary clock.

Answer: FALSE

Moving clocks run SLOWER (time dilation): t = t₀γ, where γ > 1 for v > 0. The moving clock measures less elapsed time.

Q3: Length contraction occurs only in the direction of motion.

Answer: TRUE

An object moving at relativistic speed contracts along the direction of motion: L = L₀/γ. Perpendicular dimensions remain unchanged.