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delta_x * delta_p >= h/(4pi). Equivalently: delta_x * m * delta_v >= h/(4pi). This is fundamental — not a measurement limitation but an intrinsic property of quantum mechanics. For an electron confined to atomic dimensions (~10^-10 m): delta_v ~ 10^6 m/s (comparable to actual velocity). For a 1 g object confined to 1 mm: delta_v ~ 10^-28 m/s (completely negligible). Consequences: (1) Electron "orbits" are meaningless — replaced by probability distributions (orbitals). (2) The concept of trajectory doesn't apply to atomic particles. (3) Position and momentum are complementary variables — knowing one precisely makes the other completely uncertain. delta_E * delta_t >= h/(4*pi) is the energy-time uncertainty relation (for excited state lifetimes). The uncertainty principle explains why electrons don't spiral into the nucleus: confining the electron to a smaller space increases its kinetic energy (higher momentum uncertainty), creating a balance.