Through a Quantum Tunnel

The phenomenon of quantum tunneling is best explained with a narrative:

You are at the bottom of a hill and need to roll a ball up the hill and down the other side.

Classically, the only option is to push the ball all the way up and roll it down. This would be a test of endurance and not to mention physically taxing.


But if you are in the quantum world you can dig a virtual hole and “probably” get to the other side of the mountain without expending as much energy as the classical ‘you’. 

This behavior is called ‘tunneling’.


The reason why you would be able to pull this off in a quantum system is that there is a small probability of finding the particle in a certain location that extends to the other side of the hill.

Or if one were to put it more formally:

The wavefunction of the particle is a continous function and it cannot abruptly just collapse near the mountain/wall/barrier.

Instead it decays exponentially inside the barrier and extends onto the far side of the barrier as well.

This implies that there is a finite probability for the particle to tunnel through the barrier and get to the other side.


How big can the mountain be?

Since the wavefunction decays exponentially inside the barrier, it is no surprise that thinner the mountain, the better the chances for the particle to tunnel through.


                                  Dependence on Barrier width

Can humans be tunneled through a barrier?

All this while, our discussion was primarily for simple quantum mechanical entities such as electrons, protons and so on.

And even for these systems merely increasing the barrier width would drastically bring down the probability.


Now if we were to scale this up to a system as complex as ours with billions and billions of atoms trying to tunnel through a wall couple of centimeters thick, nature just says ‘Sorry dude, Not gonna happen’.


Okay so maybe not the best way to break out of jail if you are a human I suppose.

But if you were a bouncing droplet, there might still be some hope. Check out the latest FYFD post on Hydrodynamic Quantum tunneling.

In case you had missed out, here are the previous posts on this collaborative series on Pilot wave Hydrodynamics with FYFD 1) Introduction; 2) Chladni patterns; 3) Faraday instability; 4) Walking droplets; 5) Droplet lattices; 6) Quantum double-slit experiments, 7) Hydrodynamic Single and Double slit experiments