Modern physics: relativity and quantum mechanics, and the strange truths that surfaced once we looked closely enough at very fast and very small things.
Modern Physics is what happens when the classical picture breaks down — at speeds close to light, and at scales close to a single atom. Relativity and quantum mechanics rebuild the fundamentals on stranger but deeper foundations.
| Relationship | Equation | What it tells you |
|---|---|---|
| Mass-energy equivalence | E = m·c² | Rest energy of a mass |
| Photon energy | E = h·f | Energy of a single quantum of light |
| De Broglie wavelength | λ = h / p | Wavelength of a moving particle |
| Lorentz factor | γ = 1 / sqrt(1 − v²/c²) | Time dilation and length contraction |
| Uncertainty principle | Δx · Δp ≥ h-bar / 2 | Position and momentum cannot both be sharp |
| Hydrogen energy levels | E = −13.6 / n² eV | Bohr model of the atom |
