Physics 5 — Modern Physics

Special relativity — γ

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

Nothing outruns light, and the universe enforces it with the Lorentz factor: γ = 1/√(1 − v²/c²). At everyday speeds γ ≈ 1 and nothing seems amiss; near c it explodes — time dilates, lengths contract:

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 run at 44%

1 / sqrt(1 - x^2)

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

GPS lives on this: satellite clocks tick ~38 µs/day differently than yours. Uncorrected, your position would drift ~10 km per day.