Quantum Tunnelling: Does the Wavefunction Describe Reality, or Just Probability?

Imagine throwing a ball at a solid wall. Unless it has enough energy to break through or travel over it, the ball will bounce back.

That is what classical physics predicts.

But at the quantum level, nature behaves differently. An electron can encounter an energy barrier that it cannot classically overcome and still have a probability of appearing on the other side.

This phenomenon is called quantum tunnelling. It is one of the most fascinating predictions of quantum mechanics, and it raises a deeper question: what exactly is a wavefunction? Does it describe physical reality, or is it simply a mathematical tool?

1. How can a particle cross a barrier?

Quantum mechanics describes particles using a mathematical function called the wavefunction, represented by ψ (psi).

For a particle described in position space, the squared magnitude of its wavefunction, |ψ|², gives the probability density of finding it at a particular location.

When an electron approaches a potential-energy barrier, its wavefunction does not necessarily stop at the boundary. It can extend into the barrier and decrease in amplitude. If the barrier is sufficiently thin, the wavefunction can extend beyond it, producing a non-zero probability of detecting the electron on the other side.

That is quantum tunnelling.

The particle does not need to borrow energy or violate the conservation of energy. The probability of tunnelling depends on factors such as the particle's mass and energy, and the barrier's height and width.

A thicker or higher barrier generally makes tunnelling less likely.

2. Is the particle in two places at once?

Quantum tunnelling is sometimes explained by saying that a particle exists in multiple places simultaneously. This is an oversimplification.

The more accurate explanation comes from the Schrödinger equation, which describes how a quantum state evolves.

When a quantum state encounters a barrier, its mathematical solution can contain both reflected and transmitted components. The transmitted component gives a probability of detecting the particle beyond the barrier.

Superposition helps describe the possible outcomes, but tunnelling is specifically explained through the behavior of the wavefunction in a potential barrier.

3. How do we know tunnelling actually happens?

Quantum tunnelling is not just a mathematical prediction. Scientists use it in real technologies.

Consider the scanning tunnelling microscope (STM). It brings an extremely sharp conducting tip close to a surface. Electrons can tunnel across the tiny gap between the tip and the surface, producing a measurable electrical current.

Because this current changes dramatically with distance, researchers can use it to map surfaces at atomic resolution.

Tunnelling also helps explain alpha decay, in which particles escape atomic nuclei through an energy barrier.

These applications demonstrate that tunnelling has measurable consequences in the physical world.

4. Is the wavefunction real?

Here is where physics becomes especially interesting.

The wavefunction allows scientists to calculate the probabilities of different measurement outcomes. But what does it actually represent?

The Copenhagen family of interpretations generally treats the wavefunction as central to predicting measurement outcomes. However, interpretations differ on what the wavefunction means physically.

For example:

• Bohmian mechanics describes particles with definite positions, guided by a wavefunction.
• Many-worlds interpretations take the universal wavefunction seriously and do not introduce a special collapse during measurement.
• Other approaches treat the wavefunction as representing information or expectations about a quantum system.

These interpretations offer different explanations of quantum reality, even though they can sometimes make identical experimental predictions.

This is why observing a quantum phenomenon does not necessarily settle every philosophical question about it.

5. Does measurement create reality?

The relationship between measurement and quantum states is known as the measurement problem.

When a quantum system interacts with its surroundings, information about it spreads into the environment. This process, called decoherence, helps explain why quantum interference becomes difficult to observe in large, interacting systems.

However, decoherence alone does not settle why a particular measurement outcome occurs. Different interpretations address this question differently.

Importantly, quantum mechanics does not require human consciousness to make an experiment work. A detector can record an outcome without someone watching it.

6. What does quantum tunnelling tell us?

Quantum tunnelling shows that the natural world does not always follow the intuitive rules we develop from everyday experience.

We have strong experimental evidence that tunnelling occurs. Its predictions are used in technologies such as scanning tunnelling microscopes and help explain processes in nuclear physics.

But understanding what the wavefunction ultimately represents is a different question.

Perhaps it describes a physical feature of reality that we do not yet fully understand. Perhaps it is a mathematical description of the information available to us.

We should distinguish between what experiments establish and what interpretations suggest.

Quantum mechanics predicts nature with extraordinary accuracy. Understanding exactly what those predictions tell us about reality remains one of physics' most fascinating challenges.

References

1. NIST – Scanning Tunneling Microscope
2. Internet Encyclopedia of Philosophy – Interpretations of Quantum Mechanics
3. Aharonov, Y., Anandan, J. and Vaidman, L. (1993). Meaning of the Wave Function. Physical Review A.
4. Adlam, E. (2021). Foundations of Quantum Mechanics. Cambridge University Press.