Relativity and quantum ideas

Special relativity starts from one experimental fact: every inertial observer measures the same speed of light, c = 2.998 × 10⁸ m/s. The consequences are kinematic. Clocks that move relative to you tick slowly, lengths contract along the direction of motion, and simultaneity depends on the observer. The factor that appears everywhere is γ = 1/√(1 − v²/c²), which is about 1 at everyday speeds and grows without bound as v approaches c. Nothing with mass reaches c, because γ, and therefore the energy, would have to become infinite.

Energy and momentum combine into E² = (pc)² + (mc²)². At rest, p = 0 and E = mc². That rest energy is not a metaphor; it is the energy available if the mass disappears, as in matter–antimatter annihilation, and the deficit that appears as binding energy when a nucleus is lighter than its parts. For slow motion the total energy is mc² + ½mv² plus higher orders, so Newtonian kinetic energy is the first correction.

Quantum theory starts from a different fact: the energy of light of frequency f comes in amounts hf, where h is Planck’s constant, 6.626 × 10⁻³⁴ J·s. The photoelectric effect ejects electrons only when hf exceeds a work function φ, and extra frequency becomes kinetic energy, not a waiting time. De Broglie assigned a wavelength h/p to any particle. The Heisenberg relation Δx Δp ≥ ℏ/2 says a state sharply localized in position is broad in momentum. The Schrödinger equation is the dynamical law whose standing waves are the orbitals of chemistry.