Does the particle 'actually' pass through the barrier, or does it teleport?

Neither classical metaphor quite fits. The particle is described by a wavefunction that extends through the barrier — not a localized object that suddenly appears on the other side. If you measure where the particle is, you might find it inside the barrier or beyond, with probabilities given by the wavefunction. The quantum-mechanical answer is that 'where the particle is' isn't a definite question until you measure. The wavefunction is the real thing; the particle picture is an approximation that breaks down at the barrier.

How thick a barrier can be tunneled?

Very thin barriers — typically atoms thick. The tunneling probability decays exponentially with barrier width. A barrier 1 nm thick might give a tunneling probability of 10⁻³ for a typical electron; a barrier 10 nm thick gives roughly 10⁻³⁰; a barrier 1 μm thick is effectively impassable. This is why tunneling matters at atomic scales but doesn't help you walk through walls — the human-scale tunneling probability is vanishingly small.

Does tunneling violate energy conservation?

No. The particle's total energy is the same before and after tunneling — what's different is that classically you'd need extra energy to climb the barrier, but quantum-mechanically you don't. The 'tunneled' particle never had MORE energy than it started with; it just emerges with the same energy on the other side. Quantum mechanics doesn't violate conservation laws; it just describes how probability distributes around them in ways that classical intuition doesn't anticipate.

Quantum Tunneling Explained — Walls That Aren't Really Walls

The strange phenomenon

Imagine rolling a ball up a hill. If the ball doesn't have enough kinetic energy to reach the top, it rolls back. Always. No matter how many times you try, a ball without enough energy never appears on the other side.

Now imagine an electron approaching an energy barrier — say, a thin insulating layer in a circuit. The electron doesn't classically have enough energy to overcome the barrier. Classically, it should bounce back.

Quantum-mechanically, sometimes it appears on the other side.

This is quantum tunneling. It happens because particles in quantum mechanics aren't little balls — they're described by wavefunctions that behave more like waves than objects. And waves do strange things at barriers.

What's actually happening

The mathematical description: a quantum particle of energy E approaches a barrier of height V > E (so classically the particle can't get over). The particle's wavefunction inside the barrier doesn't go to zero — it decays exponentially.

If the barrier is finite in width, the wavefunction's exponential decay can leave a small but nonzero amplitude on the other side. The probability of finding the particle past the barrier is the square of that amplitude, which is small but not zero.

The probability of tunneling depends on:

Barrier height (more shortfall in classical energy = exponentially smaller tunneling probability).
Barrier width (thicker barrier = exponentially smaller probability).
Particle mass (heavier particle = exponentially smaller probability — which is why tunneling matters most for electrons and protons, less for heavier nuclei, and is negligible for macroscopic objects).

A rough formula for the tunneling probability through a square barrier of height V and width L for a particle of mass m and energy E:

T ≈ exp(-2L·√(2m(V-E))/ℏ)

The exponential is what makes tunneling extreme: a small change in barrier width can change the tunneling rate by many orders of magnitude. For a 1 nm barrier with typical parameters, T might be 10⁻³. For a 10 nm barrier, T ≈ 10⁻³⁰. For a 1 μm barrier, T is essentially zero.

This exponential sensitivity is also what makes tunneling so useful for atomic-scale measurement (scanning tunneling microscopes) — the current depends so steeply on distance that sub-angstrom resolution is achievable.

Wave picture: not really "through"

The "tunneling" metaphor suggests the particle physically passes through the barrier like a creature digging a tunnel. The quantum reality is stranger.

The particle is described by a wavefunction — a complex-valued function that gives the probability amplitude of finding the particle at each point. Outside the barrier (on either side), the wavefunction oscillates like a sine wave. Inside the barrier, the wavefunction decays exponentially.

The wavefunction is the real, smoothly-continuous mathematical object. It's not that a "particle" decides to dig through; it's that the wave nature of the particle gives some probability of finding it on the other side after the barrier is encountered. The particle never "had to be inside the barrier" in any classical sense — it's a wave that extends through.

When you measure the particle's position, you find it somewhere — sometimes on the original side (most of the time), sometimes inside the barrier (rarely), sometimes on the far side (occasionally). The measurement outcome is probabilistic, drawn from the wavefunction.

Calling it "tunneling" is partly a residue of trying to use classical intuitions. The phenomenon is real and consequential; the metaphor is imperfect.

The Sun runs on tunneling

The Sun produces energy by fusing hydrogen into helium in its core. The temperature there is about 15 million K — extremely hot, but actually NOT hot enough for fusion to happen classically.

Two protons need to come close enough together for the strong nuclear force to bind them. But protons repel each other electrically (both positive), and that repulsion grows steeply as they get closer. The classical energy needed for two protons to overcome the Coulomb barrier at solar core temperatures is many millions of times what they actually have at 15 million K.

Yet fusion happens. Why?

Because protons tunnel through the Coulomb barrier. They don't classically have enough energy, but quantum mechanics gives a small probability of crossing. The probability is tiny per encounter — but the Sun has 10⁵⁷ protons in its core, and they're constantly bouncing around. Even a tiny tunneling probability times an enormous number of attempts equals an enormous fusion rate.

The Sun fuses about 600 million tonnes of hydrogen per second into helium. About 4 million tonnes of that gets converted to energy (E = mc²) and radiated away as sunlight, neutrinos, and other forms. Earth receives a tiny fraction of this — enough to drive almost all of biology, weather, and climate.

Without quantum tunneling, the Sun wouldn't shine. And we wouldn't be here.

The same physics applies to other fusion reactions in larger stars (which can fuse helium into heavier elements). Most of the elements heavier than helium were made in stars, and tunneling enabled the fusion processes that produced them.

Radioactive alpha decay

Some heavy nuclei (uranium, polonium, americium, others) spontaneously emit alpha particles — clusters of two protons and two neutrons (i.e., helium-4 nuclei). The alpha particle inside the nucleus is bound by the strong nuclear force; the energy barrier preventing it from escaping is the combined nuclear-and-Coulomb potential.

Classically, the alpha shouldn't escape — its energy is below the barrier height. Quantum-mechanically, it tunnels out, with a probability that depends exponentially on the barrier.

This explains an otherwise mysterious feature of radioactivity: the wild variation in half-lives. Uranium-238 has a half-life of 4.5 billion years. Polonium-212 has a half-life of 0.3 microseconds. Same kind of decay (alpha), 10²² difference in rate. Why?

Because the tunneling probability is exponentially sensitive to barrier height and width. A small difference in nuclear energy levels translates to a vast difference in decay rate. George Gamow worked this out in 1928, providing one of the first major successes of quantum mechanics applied to nuclear physics.

The Gamow theory of alpha decay correctly predicts the relationship between alpha-particle energy and half-life across all known alpha-emitting nuclei — the Geiger-Nuttall law. Quantum tunneling provides a satisfying, quantitatively accurate explanation.

Scanning tunneling microscope

In 1981, Gerd Binnig and Heinrich Rohrer at IBM Zürich invented the scanning tunneling microscope (STM). They won the Nobel Prize for it in 1986.

How it works: a sharp metal tip (ideally sharp to a single atom) is brought very close to a conducting surface — typically within 1 nanometer. A small voltage is applied between tip and surface. The classical expectation: no current flows (the tip isn't touching the surface). The quantum reality: electrons tunnel between tip and surface, producing a measurable current that depends exponentially on the gap.

By scanning the tip across the surface and recording the tunneling current at each point, you can build a map of the surface topology with sub-atomic resolution. Individual atoms appear as bumps in the image.

The STM revolutionized surface science. It can:

Image individual atoms on metal and semiconductor surfaces.
Move atoms around one at a time (IBM famously spelled "IBM" with 35 xenon atoms in 1989).
Probe electronic states with spatial resolution.
Study chemical reactions at the atomic scale.

Related techniques: atomic force microscopy (AFM), scanning probe microscopy more broadly. These tools are foundational to modern nanotechnology.

Flash memory

Almost every flash memory chip, solid-state drive, and memory card stores bits using quantum tunneling.

A flash memory cell is a transistor with an extra "floating gate" — a piece of conductor (or, in modern 3D NAND, a charge-trap dielectric layer) completely surrounded by insulating oxide. The structure is electrically isolated; if you put electrons in it, they stay there for years (until you tell them to leave).

To write a bit: apply a high voltage. Electrons tunnel through the thin oxide barrier into the floating gate. The presence (or absence) of stored electrons changes the transistor's threshold voltage — which can be read as a 0 or 1.

To erase: apply the opposite high voltage. Electrons tunnel back out.

The tunneling here is engineered to be slow enough that electrons don't leak out during normal use (so data persists for years without power), but fast enough to write/erase in microseconds.

This is everywhere now: smartphones, laptops, SSDs, USB sticks, cameras, embedded electronics. Hundreds of exabytes of flash memory ship per year. Every byte is engineered quantum tunneling.

Tunnel diodes and Josephson junctions

Two more specific applications worth mentioning:

Tunnel diodes (invented in the late 1950s; Leo Esaki received the 1973 Nobel Prize in Physics for the discovery of electron tunneling in semiconductors, shared with Ivar Giaever and Brian Josephson): semiconductor diodes designed to operate in a regime where tunneling produces a "negative differential resistance" — meaning increased voltage produces DECREASED current in a particular range. This odd behavior is useful for high-frequency oscillators and amplifiers; tunnel diodes can operate in the gigahertz to terahertz range.

Josephson junctions (Brian Josephson, 1973 Nobel Prize): two superconductors separated by a thin insulating barrier. Cooper pairs (the pairs of electrons that carry supercurrent in a superconductor) can tunnel through the barrier coherently. The tunneling current depends on the phase difference of the two superconductors' wavefunctions — producing precisely quantized effects useful for:

SQUIDs: ultra-sensitive magnetic field sensors.
Quantum voltage standards: extremely precise voltage references.
Superconducting qubits: the basis for most current quantum computers.

The Josephson effect is one of the most striking macroscopic quantum phenomena — quantum behavior visible at circuit scales, used routinely in laboratory and industrial precision measurement.

Tunneling in chemistry

Quantum tunneling matters in many chemical reactions, especially those involving hydrogen atoms. Hydrogen has the smallest mass of any nucleus, so its tunneling probability through molecular barriers can be significant.

Examples:

Hydrogen abstraction reactions: a hydrogen atom transferring from one molecule to another can occur via tunneling even at temperatures where classical activation energy isn't met.
Enzyme catalysis: some enzymes accelerate reactions partly by reducing the barrier width for hydrogen tunneling.
Astrochemistry: at extremely low temperatures in interstellar clouds, reactions that classically wouldn't occur can still happen via tunneling.

The tunneling contribution to reaction rates is a real and growing area of chemistry research, partly because experimental techniques (specifically deuterium substitution, since heavier deuterium tunnels much less than hydrogen) let chemists separate tunneling from classical contributions.

Cosmological tunneling speculation

In the very early universe, some theories of vacuum stability involve cosmological tunneling — the possibility that our vacuum state isn't truly stable but is meta-stable, and could quantum-tunnel into a lower-energy state at some point. If that happened, a "true vacuum bubble" would expand at the speed of light, destroying everything in its path.

The probability of this happening per unit volume per unit time is extremely low (or zero, if our vacuum is actually stable). Theoretical estimates depend on details of particle physics we don't fully understand. Even pessimistic estimates suggest a timescale far beyond the current age of the universe.

This is genuinely speculative physics, but it's not crank — it's based on extrapolating the Higgs boson's measured mass through the Standard Model equations. It's also, you might note, very much not something to worry about on human timescales.

If you'd like a guided 5-minute course on quantum tunneling and its applications, NerdSip can generate one.

The takeaway

Quantum tunneling is a wave-mechanical phenomenon: a particle whose classical energy isn't enough to cross an energy barrier has some probability of appearing on the other side anyway. The probability decays exponentially with barrier width, height, and particle mass. Real consequences: the Sun runs on tunneling fusion (protons tunneling through their Coulomb barrier); radioactive alpha decay is tunneling out of nuclei; scanning tunneling microscopes image atoms via tunneling current; flash memory stores trillions of bits per chip by tunneling electrons through oxide barriers; tunnel diodes and Josephson junctions are engineered tunneling devices. The phenomenon is everywhere once you know what to look for, and many modern technologies depend on it directly.