Quantum tunnelling and the prospects of human teleportation

While carrying out an experiment, Friedrich Hund observed a very unique phenomenon. Little did he know that what he was observing before his very eyes was quantum tunnelling¹. It is a quantum mechanical phenomenon – which casually violates the fundamentals of classical mechanics – where a particle penetrates through a potential energy barrier that has energy greater than the particle’s kinetic energy.² For simplicity, picture it this way:³

A pink ball rolls along a smooth level surface with a kinetic energy of 200J (assume that it does not lose or gain any energy during this process). Then, the ball approaches a really tall hill. The (gravitational potential) energy that the ball would possess if it was at the peak of the hill would be 500J.

In the classical world, this will result in the ball (currently with 200J of kinetic energy (KE)) not being able to climb over the hill. It will simply roll partially up the hill, never reaching the peak, and roll back down. This is because the ball does not have enough energy to overcome the gravitational potential energy (GPE) at the peak of the really tall hill. The ball will only be able to climb the hill and appear on the other side if it had an initial KE equivalent to or more than the GPE at the peak of the hill, that is 500J. The ball is confined by the first law of thermodynamics, or in layman’s terms, the principle of conservation of energy.⁴

In the quantum world, however, things turn out quite differently. You would be surprised to see that the same pink ball with 200J of KE might just magically appear on the other side of the really tall hill. The thing is, the secret behind this ‘magic trick’ was actually just the pink ball “tunnelling” through the hill.

Quantum tunnelling is indeed a thought-provoking concept, maybe even bizarre to a handful of people. However, this phenomenon occurs more commonly in the real world than you might think! The first application of quantum tunnelling in the real world is in Scanning Tunnelling Microscopy (STM)⁵, which is a type of microscope. The STM works is that the tip of a sharp conducting needle, such as one made of tungsten⁶, is placed at a very tiny distance (when I say ‘tiny’ I mean angstrom-scale tiny, which is equivalent to one ten-billionth of a metre) from the sample surface. A small voltage is then applied between the probe tip and the sample surface and bingo! The electrons start tunnelling across this gap. This produces a very detailed topographical image of the sample surface.

Another very enthralling real-world application of quantum tunnelling lies in the heart of our solar system⁷ and it is quite possibly the reason why we humans (or – before you call me out for being anthropocentric – any other possible forms of life, extraterrestrial or not, assuming that they also need sunlight to survive) can exist. In high school, we’ve been taught that the reason the Sun shines is due to the nuclear fusion of protons into helium nuclei. Whatever they taught us in high school isn’t entirely wrong, but it’s an overgeneralization, so to speak. In reality, the temperature of the Sun isn’t hot enough for nuclear fusion to occur.⁸ This means that protons do not receive enough energy to overcome the repulsive forces between them. The protons overcome this by quantum tunnelling. This occurs because protons (which are essentially quantum particles) behave as waves instead of particles in the quantum realm. Each proton is described by a wavefunction⁹ that has a small chance of interacting with the wavefunction of another proton. Quantum tunnelling allows these protons to fuse, releasing a large amount of heat and light energy in the process (sounds familiar?).

So back to the original question and its rather disappointing answer, the reason why we will probably never be able to quantum tunnel is due to how massive we are. The likelihood of a particle being able to quantum tunnel is determined by its mass and the thickness of the barrier.¹⁰

The reason why quantum particles such as electrons have a considerable likelihood of quantum tunnelling is due to their extremely small mass (the mass of an electron at rest is approximately 9.10938356 × 10-31kg). The average mass of an adult human on the other hand is about 62kg.¹¹ This makes the chances of humans ever experiencing quantum tunnelling so measly that they are almost zero.