Home▸Quantum Physics▸Vacuum Fluctuation

Time-Energy Uncertainty Simulator

Watch virtual particle-antiparticle pairs borrow energy from the quantum vacuum and pay it back within a lifetime set by Heisenberg's time-energy uncertainty relation, ΔE·Δt ≥ ħ/2 — tune the borrowed energy and watch the lifetime shrink.

Quantum Physics2DEasy60 FPS📱 Mobile-adapted⇄ 3D version

Quantum mechanics allows the vacuum to briefly violate energy conservation, as long as it pays the debt back fast enough. This simulator visualizes that trade-off directly: virtual electron-positron pairs pop into existence out of pure vacuum fluctuation, each one borrowing an energy ΔE, and each one is forced to annihilate after a lifetime Δt set by ΔE·Δt ≥ ħ/2 — Heisenberg's time-energy uncertainty relation. Raise the borrowed energy and watch every pair's lifetime collapse; lower it and pairs linger. A live log-log plot confirms the inverse relationship pair by pair against the theoretical curve, the same physics behind the Casimir effect, the Lamb shift, and Hawking radiation.

⚙ Under the hood

Explore the real-time energy uncertainty principle where virtual particle pairs borrow energy for a limited duration governed by the Heisenberg Uncertainty Principle.

Quantum MechanicsVacuum FluctuationHeisenberg Uncertainty

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install