Roll a marble toward a hill. If it is not moving fast enough to reach the top, it rolls back, every single time. Quantum particles mostly behave the same way, but not always. Sometimes a particle that lacks the energy to climb over a barrier turns up on the other side anyway. This is tunneling, and without it the sun would not shine.

Waves leak through barriers

In classical physics, a barrier that a particle lacks the energy to cross is absolutely forbidden. In quantum mechanics the particle is described by a wave, and waves do not stop dead at a barrier. Inside the barrier the wavefunction no longer ripples; it shrinks rapidly with distance. But if the barrier is thin enough, the wave shrinks inside the barrier without vanishing, and a little of it is left on the far side. Because the square of the wave gives probability, a particle has a small but real chance of appearing beyond a barrier it could never climb over.

The particle does not borrow energy, dig a hole or sneak over the top. It is found on the far side with the same energy it started with.

Thin and low barriers

The chance of tunneling depends very strongly on the barrier. A thinner or lower barrier makes tunneling more likely, while a wider or higher barrier, or a heavier particle, sharply reduces the chance. Doubling the width of a barrier does not halve the chance; it can cut it by a factor of thousands or millions. This is why electrons, which are very light, tunnel readily across gaps a few atoms wide, while you will never walk through a wall. For a person the chance is not zero, but it is unimaginably small: you could throw yourself at a wall every second for many times the age of the universe and still not expect to pass through.

The first triumph: radioactive decay

Alpha decay had puzzled physicists. Some heavy nuclei, such as uranium, eject alpha particles, clumps of two protons and two neutrons. Inside the nucleus, the strong nuclear force holds them in; just outside, electrical repulsion takes over, and together the two form a barrier the alpha particle does not have enough energy to climb. In 1928 George Gamow, and independently Ronald Gurney and Edward Condon, showed that alpha particles escape the nucleus by tunneling through this barrier.

The theory explained a puzzling pattern: small differences in energy lead to enormous differences in half life, because the tunneling chance is so sensitive. Uranium 238 has a half life of about 4.5 billion years. Polonium 212, whose alpha particles carry only about twice the energy, has a half life of less than a millionth of a second.

Seeing and storing with tunneling

In 1981 Gerd Binnig and Heinrich Rohrer at IBM in Zurich built the scanning tunneling microscope. A sharp needle is held just above a surface, and the microscope measures the electrons tunneling across the tiny gap. Because the current changes enormously with the width of the gap, scanning the needle back and forth maps the surface atom by atom. They shared the 1986 Nobel Prize with Ernst Ruska, the electron microscope pioneer from level 2.

Tunneling also runs through electronics. In 1957 the Japanese physicist Leo Esaki made the tunnel diode, and later shared the 1973 Nobel Prize. Today the most widespread use is flash memory, in phones and USB drives, which in many designs stores data by tunneling electrons through a thin insulating layer into a trapped region, where they stay until erased. Tunneling is also a headache for chip designers: as transistors shrink, electrons leak through insulating layers only a few atoms thick, wasting power.

Worked example: how the sun shines

The sun is powered by fusing hydrogen nuclei, which are single protons, into helium. To fuse, two protons must get close enough for the strong nuclear force to grab them. But protons are positively charged and repel one another, and that repulsion forms a barrier. The sun's core is about 15 million degrees Celsius, scorchingly hot by human standards, yet a classical calculation shows this is far too cool: a typical proton there has only about a thousandth of the energy needed to climb the barrier. By classical physics alone, the sun should not be shining.

Tunneling resolves the puzzle. A proton does not need to climb the whole barrier; it has a small chance of tunneling through it. The chance in any one encounter is tiny, but the core holds an enormous number of protons colliding constantly, and enough of them succeed to produce the sun's steady output. The slowness is a blessing. Partly because tunneling is so unlikely, a typical proton in the core waits billions of years before it fuses, which is why the sun has shone steadily for about 4.6 billion years and has billions of years left. If fusion were easy, the sun would have burned out long before life could appear. Every bit of sunlight that reaches a leaf exists because particles crossed a wall they could not climb.