Quantum tunneling is a very complex phenomenon that doesn’t listen to the classical laws of physics. So much so that it’s in its own category called quantum mechanics. I will explain the basics of one of its principles called Quantum Tunneling as well as go through a fun thought experiment of whether or not it’s possible for a human to quantum tunnel.
For starters, it’s important to understand that Quantum Tunneling doesn’t fall under classical physics, in that classical physics is exact and quantum tunneling is probabilistic. For example, in normal physics, you can pinpoint the exact location of a soccer ball rolling across the ground, but when studying particles in quantum mechanics, it is impossible to pinpoint with perfect accuracy where a particle is due to the Heisenberg Uncertainty Principle. Which states that there is a limit to how much we can know about the state of a particle at any given time.
So what does quantum tunneling do? Well, it’s easiest to explain with another example. The classic explanation uses the diagram below. In the first part of the diagram on the left, you will see that a ball is rolling down a hill and has enough momentum to carry itself over the second hill. But if it didn’t have enough momentum it would roll maybe halfway up the second hill and then roll back down until it eventually rests in between the two hills.
So far this is all classical physics like we are used to. But now looking at the second part of the image we can see how it could work under quantum mechanics. Even if the particle (an orange ball in this case) didn’t have enough energy to surmount the barrier (the second hill) we have a chance to observe the particle on the other side as if it went up and over the barrier. In reality, it didn’t go up and over but went straight through the barrier. This is a dumbed-down version of quantum tunneling, in reality, it’s more accurate to describe the particle as a wave function, which plots the probability of a particle being at that point. This can be seen in this excellent visual courtesy of Up And Atom on Youtube.
There is still much that is unknown about this process, and the field of quantum mechanics is still relatively new, so discoveries are constantly being made that will further our understanding of this interesting phenomenon. A heavily contested theory is that quantum tunneling allows particles to travel faster than light
It is even predicted that quantum tunneling may limit how small we can make computers, as if we make transistors too small, electrons could just tunnel past them, thus making them inoperable. We are running into a similar problem with how much faster we can make computers due to the speed of light being a limiting factor in how fast we can move electrons from one part of the computer to the next.
Fun Thought Experiment: Can we quantum tunnel?
But if a particle can essentially teleport through a wall, can you? If I said it was possible I wouldn’t be lying, but I also wouldn’t be telling the whole truth. It’s not impossible, but it’s extremely unlikely. But I’ll admit I was curious so I did a bit of research and found a student named Sophia Gad-Nasr who did some math about how likely it would be for a human to pass through a wall via quantum tunneling.
Making some assumptions about the weight of the person being about 150 pounds and the wall to tunnel through being 10cm thick. Running at the wall at 9 mph, using the Transmission Coefficient she found that the odds of a person quantum tunneling through that wall would be
1 in 1035.
1 in 100 000 000 000 000 000 000 000 000 000 000 000
To help you understand how incredibly low that chance is I did some math of my own to help give you some perspective. Let’s say all 8 billion people on the planet today stopped what they were doing and ran at a wall once every minute of every day of the year until someone quantum tunneled through.
We can multiply how many people are trying this experiment, in this case, 8 billion, by how many attempts we get per day. There is 1440 minutes/day, thus there are 1440 attempts per person per day. Then multiply that by 365 to see how many attempts we get per year. That comes out to:
4.2 * 1015 attempts/year
So dividing that number by the odds of it happening we can find out how many years it would take if we dedicated every human being on the planet to only doing this one task nonstop.
The answer is it would take 1019 years before we saw it happen just ONCE. That is so long that it is 724 million times longer than the universe has even existed for as of today.
There is a cool video on YouTube called Timelapse of the Future: A Journey to the End of Time which explores what the future of our universe looks like far into the future. If you want to see what the Universe would look like at the end of our experiment you would have to wait until the 5:45 minute mark in the video.
If you were to attempt this experiment just by yourself, it would take 8 billion times longer and you would have to wait until the 8:36 minute marker, where you would find little left in the universe to share your accomplishment with.
That’s just a fun thought experiment that I had when researching this topic and thought it would be a fun way to remember Quantum Tunneling. If you are interested in diving deeper into this topic I will leave a list of references that I found interesting that you may want to check out!