Heisenberg Uncertainty Principle
A fundamental quantum limit stating that canonical conjugate physical variables (such as position and momentum, or energy and time) cannot be simultaneously measured with arbitrary precision.
Governing formula
Δx Δp ≥ ℏ / 2, ΔE Δt ≥ ℏ / 2
SI unit
J·s (Action Units)
In depth
The uncertainty principle is an intrinsic wave property of quantum systems rather than an experimental measurement flaw. Mathematically, it arises because the position and momentum operators do not commute ([x̂, p̂] = i ℏ), meaning a wave packet of localized position requires a broad Fourier spectrum of momentum wavelengths.
Examples in the real world
Explaining why electrons in atoms do not collapse into the nucleus, and governing the lifetime-width of short-lived unstable resonance particles.