Quantum Tunneling: How Particles Pass Through Barriers That Should Stop Them

Picture a ball rolling toward a hill. If it doesn't have enough energy to reach the top, it rolls back down. Every time, no exceptions. That's just how hills work — in the world of baseballs, cars, and bowling balls.

Now shrink the ball down to the size of an electron, and shrink the hill down to the size of a few atoms, and something astonishing happens: sometimes the ball just appears on the other side. Not because it found a way around. Not because it got a boost of extra energy from somewhere. It passed through the hill, while still not having enough energy to go over it.

This is quantum tunneling, and it is not a fringe curiosity. It's why the Sun burns at the temperature it does, why your computer's flash memory can store data for years without power, why a 1981 IBM invention let scientists see individual atoms for the first time, and — more speculatively — why your DNA occasionally mutates. Nature, it turns out, doesn't just bend the rules of "can't get there from here." It routinely ignores them.

The Concept

Classical physics treats a particle as a little ball with a definite position and a definite amount of energy. If a barrier requires more energy than the ball has, the ball cannot pass — full stop. This is as intuitive as physics gets.

Quantum mechanics describes particles differently: not as point objects, but as spread-out waves of probability, described by something called a wave function. The square of that wave function at any point tells you the probability of finding the particle there. Crucially, when a quantum particle encounters an energy barrier it classically shouldn't be able to cross, its wave function doesn't simply vanish at the barrier's edge the way a classical ball would stop dead. Instead, it decays — shrinking exponentially the deeper it goes into the barrier — but it doesn't hit zero. There's a thin, rapidly fading thread of probability reaching into and sometimes all the way through the forbidden region.

If the barrier is thin enough, or low enough, that thread of probability can still have a non-negligible value when it reaches the far side. And a non-zero probability means: sometimes, the particle is just there. Not squeezed through a crack, not borrowing energy, not cheating the books — the probability itself was never zero, so measurement occasionally finds the particle on the other side.

The core mathematical insight — first worked out by German physicist Friedrich Hund in 1927 while studying molecules that oscillate between two configurations separated by an energy barrier — is that this "leak-through" probability drops off exponentially with three things: the barrier's width, the barrier's height relative to the particle's energy, and the square root of the particle's mass. That exponential sensitivity is the whole story. Make the barrier a little wider, or the particle a little heavier, and the tunneling probability doesn't just decrease — it collapses, often by many orders of magnitude. That's the reason tunneling is a headline phenomenon for electrons, protons, and alpha particles crossing barriers a few atomic diameters wide, and utterly irrelevant for you trying to walk through a wall.

Why It Matters

Radioactive decay. The first and most dramatic confirmation of tunneling came in 1928, when George Gamow — then at Göttingen — and, independently and within days of him, Ronald Gurney and Edward Condon at Princeton, used it to crack a decades-old puzzle about alpha decay. Heavy radioactive nuclei like uranium emit alpha particles (helium nuclei) that classically do not have enough energy to escape the strong nuclear force holding them in. Tunneling explained why they escape anyway, and — more impressively — explained why nuclei with almost identical alpha particle energies can have wildly different half-lives. Uranium-238 has a half-life of about 4.5 billion years. Polonium-214 has a half-life of roughly 160 microseconds. The alpha particles involved differ in energy by less than a factor of two. Because tunneling probability depends exponentially on that energy difference, a small change in energy produces a difference in half-life spanning roughly 21 orders of magnitude. Nothing in classical physics could have predicted that; tunneling nailed it almost immediately.

Seeing individual atoms. In 1981, Gerd Binnig and Heinrich Rohrer at IBM's Zurich research lab built the scanning tunneling microscope (STM). It works by bringing an atomically sharp needle tip extremely close to a conductive surface — close enough that electrons can tunnel across the gap between tip and surface even though they're not touching. Because the tunneling current depends so exponentially on the width of that gap, even sub-atomic changes in distance produce measurable changes in current, letting the instrument trace the literal bumps and valleys of individual atoms on a surface. Binnig and Rohrer won the Nobel Prize in Physics in 1986 for it (shared with Ernst Ruska, inventor of the electron microscope). It remains one of the cleanest pieces of engineering built entirely on top of a quantum "loophole."

The electronics in your pocket. Tunneling isn't just something physicists observe — it's something engineers now deliberately exploit. Leo Esaki's tunnel diode (1958) and Brian Josephson's theoretical prediction of tunneling between superconductors (soon after experimentally confirmed by Ivar Giaever) earned all three scientists a shared 1973 Nobel Prize. More practically for everyday life: flash memory — the chips inside USB drives, SSDs, and the storage in your phone — write and erase data by deliberately pushing electrons through a thin insulating barrier onto (or off of) a tiny floating gate, using a tunneling mechanism called Fowler-Nordheim tunneling, first described by Ralph Fowler and Lothar Nordheim in 1928. Every time you save a photo to a thumb drive, you're relying on a quantum effect that, by classical physics, shouldn't be able to happen.

Why stars shine at all. Inside the Sun's core, at a temperature around 15 million kelvin, protons are moving fast — but not nearly fast enough. The electric repulsion between two positively charged protons (the Coulomb barrier) requires far more energy to overcome classically than the Sun's core temperature provides; typical protons there carry something on the order of a thousandth of the energy that would be needed to smash through that barrier head-on. If stars relied purely on classical physics, the Sun's core would be too cool to fuse hydrogen, and it — along with essentially every star like it — simply wouldn't shine the way it does. Tunneling gives protons a small but real chance of fusing anyway, and with roughly 10^57 protons in the Sun colliding constantly, "small but real" becomes an enormous number of fusion events every second. Stars are, in a very literal sense, burning because of a quantum loophole.

The Details

It's worth sitting with just how exponentially sensitive tunneling is, because that sensitivity is the entire reason it matters in some situations and is irrelevant in others.

Imagine, purely as a thought experiment, scaling the same math up to a 50-kilogram person walking into a wall. The particle's mass enters the tunneling formula under a square root, but it still sits inside an exponent — and a kilogram-scale mass is about 10^28 times heavier than a proton. Run the numbers and the probability of a person tunneling through an ordinary wall comes out so small (something like 1 in 10 followed by thirty-some zeros) that it's not just unlikely, it's meaningless on any timescale the universe has existed for. This isn't a rigorously published figure — it's a standard back-of-envelope illustration physicists use — but it captures the right intuition: tunneling is a story about the very light and the very small, not a secret escape hatch for ordinary objects.

Biology offers a more contested frontier. There's solid, mainstream research showing that electrons and protons genuinely tunnel during certain enzyme-catalyzed reactions — enzymes like alcohol dehydrogenase, lactate dehydrogenase, and soybean lipoxygenase have all shown reaction rates that classical "over the barrier" chemistry can't fully explain, but that tunneling models can. This is an active, legitimate research area, though scientists are still debating exactly how large a role tunneling plays across biochemistry generally, versus being a secondary contributor in a handful of special cases.

Further out on the speculative end: physicist Per-Olov Löwdin proposed in 1963 that protons within DNA's base pairs (the hydrogen bonds linking, say, adenine and thymine) could occasionally tunnel into a slightly shifted position, potentially producing a copying error during DNA replication — a quantum mechanism for spontaneous mutation. Calculations put the tunneling probability for a given base pair at roughly one in a billion. Whether this actually contributes meaningfully to real mutation rates, or is simply swamped by other, more mundane sources of replication error, remains genuinely unresolved and is worth treating as an open question rather than settled fact.

What ties all of this together — from a uranium nucleus to a microscope tip to a dying star to, maybe, your own genome — is the same simple picture: a wave function that refuses to go all the way to zero inside a region it "shouldn't" be able to enter. Thin barrier, light particle, exponential sensitivity. That's the whole mechanism, showing up again and again at wildly different scales.

Takeaways

Quantum tunneling happens because particles are described by probability waves that decay, but never fully vanish, inside an energy barrier — leaving a real (if tiny) chance of finding the particle on the far side.
The effect is exponentially sensitive to barrier width, barrier height, and particle mass — which is why it dominates the physics of electrons and alpha particles, and is irrelevant for anything you can hold in your hand.
It was first worked out mathematically by Friedrich Hund in 1927, then used within the same year or two to solve two very different mysteries: alpha decay half-lives (Gamow, and independently Gurney and Condon, 1928) and electron emission in strong fields (Oppenheimer, and Fowler-Nordheim, 1927–28).
It's not just a theoretical curiosity — it underlies the scanning tunneling microscope, the Josephson junction, flash memory, and the nuclear fusion that powers every star like the Sun.
Some proposed biological applications — enzyme catalysis, DNA mutation — are real research frontiers, but range from well-supported to genuinely unsettled; it's worth distinguishing "measured in the lab" from "proposed and still debated."

Resources: For a deeper historical dive, Physics Today's retrospective on the early history of quantum tunneling covers the near-simultaneous 1927–28 breakthroughs in detail. The Nobel Prize's official site has first-hand accounts from Binnig, Rohrer, Esaki, Josephson, and Giaever on how their tunneling-based inventions came together.