Mini-Lesson

Special Relativity

This HL-only mini-lesson covers Theme A.5 — Galilean & special relativity: inertial reference frames, Einstein's two postulates, the Lorentz factor γ, time dilation and length contraction, and mass–energy.

Work through each screen, answer the questions as you go (some are reasoning, some are calculations) and collect ⭐ stars. Watch for the HL flag on higher-level extensions. Press Start when you're ready.

A.5 · postulates

Frames and the two postulates

Galilean relativity works well at everyday speeds: velocities simply add. But it fails near the speed of light. Einstein's special relativity rests on two postulates:

The laws of physics are the same in all inertial (non-accelerating) frames.
The speed of light in vacuum, c, is the same for all inertial observers, whatever the source's motion.

The constancy of c forces space and time themselves to be relative — leading to time dilation and length contraction.

Quick check

?You fly towards a star at 0.5c and measure the speed of its light reaching you. What value do you get?

A.5 · Lorentz

The Lorentz factor

The Lorentz factor γ quantifies relativistic effects. It is always ≥ 1 and grows without limit as v → c:

γ = 1 ÷ √(1 − v²/c²)at v = 0.6c, γ = 1/√(1−0.36) = 1/0.8 = 1.25

At everyday speeds v ≪ c, γ ≈ 1 and relativity reduces to ordinary Galilean physics — which is why we never notice it.

Calculate

#Find the Lorentz factor γ for a speed of 0.60c.

Hint: γ = 1 ÷ √(1 − 0.6²) = 1 ÷ √0.64 = 1 ÷ 0.8.

Calculate

#Find the Lorentz factor γ for a speed of 0.80c.

Hint: γ = 1 ÷ √(1 − 0.8²) = 1 ÷ √0.36 = 1 ÷ 0.6.

A.5 · dilation & contraction

Time dilation & length contraction

To a stationary observer, a moving clock runs slow and a moving object is shorter along its motion:

Δt = γΔt₀ · L = L₀ ÷ γΔt₀ = proper time (in the object's own frame); L₀ = proper length

Worked example — a fast rocket at 0.6c (γ = 1.25)

Its 2.0 s onboard interval is measured on Earth as Δt = 1.25 × 2.0 = 2.5 s.

Its 100 m proper length is measured as L = 100 ÷ 1.25 = 80 m.

Calculate

#A clock on a rocket moving at 0.60c (γ = 1.25) ticks off 2.0 s of its own (proper) time. How long is this measured to last on Earth?

s

Hint: Δt = γΔt₀ = 1.25 × 2.0.

Calculate

#A rocket is 100 m long in its own frame and moves at 0.60c (γ = 1.25). Find its length measured from Earth.

m

Hint: L = L₀ ÷ γ = 100 ÷ 1.25.

Sort it

From a stationary observer's view…

Tap an item, then tap the group it belongs to.

⬆️ Larger / dilated

⬇️ Smaller / contracted

🟰 Invariant (same for all)

Calculate

#Find the rest energy of an electron, in MeV. Use mₑ = 9.11 × 10⁻³¹ kg, c = 3.0 × 10⁸ m s⁻¹, e = 1.60 × 10⁻¹⁹ C.

MeV

Hint: E₀ = mc² = 9.11e-31 × (3.0e8)² = 8.2e-14 J; ÷1.6e-19 → eV; ÷1e6 → MeV.

Match it

Match the expression to its name

Tap a statement on the left, then its match on the right.

Statement

Answer

Recap

The big ideas to know

Postulates: laws of physics same in all inertial frames; c is invariant

Lorentz factor: γ = 1/√(1−v²/c²) ≥ 1, → ∞ as v → c

Time dilation: moving clocks run slow: Δt = γΔt₀

Length contraction: moving lengths shrink along motion: L = L₀/γ

Mass–energy: rest energy E₀ = mc²; total energy E = γmc²

That completes Special Relativity for IB Diploma Physics HL. Press Finish to see your score.

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