Can You Tunnel Through the Floor? The Compound Probability and the Barrier Maths

"Could my foot quantum-tunnel through the floor?" is a genuine physics question with a definite answer: mathematically non-zero, physically never — and the *reason* is more interesting than the conclusion. ## There is no rule that an object tunnels as a unit The usual framing imagines the foot passing through as an object. Nothing requires that. Each atom tunnels independently, and the "whole foot" event is simply the **joint probability of every atom doing it simultaneously**. A foot holds on the order of 10^26 atoms, so the compound probability is that many tiny numbers multiplied together — which is where figures like 1 in 10^(10^30) come from. This reframing immediately raises the better question: since atoms tunnel independently, are we constantly losing single atoms through the floor, rarely, one at a time? ## Why even one atom is effectively never Tunnelling probability falls off as T ≈ exp(−2κd), where κ = √(2mV)/ℏ so it is **exponential in the barrier width times the square root of the mass**. Both terms are catastrophic here: - **Mass.** A carbon atom is roughly 22,000 times heavier than an electron. Tunnelling is an electron-scale phenomenon precisely because electrons are light. - **Width.** Tunnelling matters over distances of nanometres. A floor is on the order of 10^8 atomic spacings thick. A Fermi estimate for one atomic step: a carbon atom crossing a modest 3 eV barrier over 0.2 nm gives 2κd ≈ 530, so T ≈ e^−530 ≈ 10^−230 per attempt. Even allowing an entire sole in contact (~10^17 atoms) rattling at a lattice frequency of 10^13 Hz, the expected wait is on the order of 10^200 seconds — something like 10^182 times the age of the universe. And that is for **one atomic step**, not through a floor. The estimate is exponentially sensitive to the barrier height, but no plausible value rescues it. ## The premise fixes that matter more than the arithmetic **Atoms don't "miss" each other.** You do not stand on the floor because tiny balls block other tiny balls. Matter is mostly empty space; what holds you up is electromagnetic repulsion between electron clouds plus the Pauli exclusion principle. See Why Solids Are Solid: Electron Repulsion and the Pauli Exclusion Principle. **An atom can't just "fall through".** To leave your body an atom must first break its chemical bond — an energy cost of several eV — and then enter and be trapped by the floor. **Bond-breaking is the real gatekeeper**, and it is a thermal process (desorption), not tunnelling. The barrier that matters isn't the gap; it's the bond. **Competing clocks end the argument.** Long before tunnelling claims an atom you have died, the material has degraded, and the Sun has gone. On the timescales required, even proton decay — if it happens at all, with a half-life bounded below 10^34 years by Super-Kamiokande — would disassemble your atoms an enormous number of times over first. The atom stops existing as itself long before it tunnels. ## What is actually true You *do* constantly lose atoms, by ordinary thermodynamics rather than tunnelling — see Your Atoms Turn Over Constantly, By Evaporation Rather Than Tunnelling. Atoms *do* tunnel inside you constantly, over sub-nanometre distances, as measured physics — see Atom Tunnelling in Real Systems: Hydrogen in Metals and the Ammonia Inversion. And matter genuinely does shed pieces by tunnelling, in Alpha Decay: Gamow's 1928 Tunnelling Explanation. Add sliding contact and the answer changes entirely, though mostly for non-quantum reasons: Adhesive Wear: How Sliding Surfaces Transfer Atoms.