Physics 5 — Modern Physics

Special relativity — γ

continues from lesson 3 — values defined earlier in the course stay live here

ELI5: nothing outruns light, and the universe enforces it with the Lorentz factor γ = 1/√(1 − v²/c²). At human speeds γ ≈ 1 and you notice nothing; approach light-speed and γ explodes — moving clocks run slow, moving lengths shrink.

c_{l} = 299800000

speed of light (m/s)

v_{fast} = 0.9 \cdot c_{l}

2.6982 \times 10^{8}

90% of c

\gamma_{r} = \frac{1}{\sqrt{1 - \left(\frac{v_{fast}}{c_{l}}\right)^{2}}}

2.2942

γ ≈ 2.29 — onboard clocks tick at 44% of ours

1 / sqrt(1 - x^2)

γ vs speed (as a fraction of c) — flat, then a wall at 1

Real-world hook: GPS depends on this. Satellite clocks drift ~38 µs/day relative to yours; left uncorrected, your map position would wander ~10 km per day.

Try it yourself: what is the Lorentz factor γ at 60% of c (v/c = 0.6)? (γ = 1/√(1 − (v/c)²).)

\gamma_{you} = \frac{1}{\sqrt{1 - 0.6^{2}}}

1.2500

✏️ Your turn: compute 1/√(1 − 0.6²). (It works out to 1.25.)

✓ pass

\mathrm{abs}\left(\gamma_{you} - \frac{1}{\sqrt{1 - 0.6^{2}}}\right) < 0.000001

green when your Lorentz factor is correct