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Imagine: you're late for work, there's a locked door in front of you, and suddenly – bam! – you walk right through it like Kitty Pryde from «X-Men». Sounds cool? Quantum mechanics says it's theoretically possible. Practically – well, I have news for you, and it's not great. But let's sort out exactly why physicists started talking about walking through walls in the first place and what this has to do with a wave function that acts like a drunk freshman.
Quantum Mechanics: Where Everything Goes Wrong (Compared to Real Life)
First, you need to understand one simple thing: quantum mechanics is a parallel universe with its own rules. In our macroworld (that is, the world of big objects – from apples to planets), everything works according to Newton's laws of classical physics. You throw a ball – it flies in a parabola. You run into a wall – you get a bruise and, possibly, a concussion.
In the microworld of elementary particles, it's different. There, electrons, protons, and other subatomic squad members live by laws that seem absurd at first glance. A particle can be in two places at once. It can pass through barriers that, by all laws of physics, should stop it. It can exist in a state of superposition – that is, be both «yes» and «no» simultaneously until you look at it.
Sound like nonsense? Erwin Schrödinger thought so too when he came up with his famous thought experiment with the cat – the very one that is both alive and dead at the same time until you open the box. Schrödinger wanted to highlight the absurdity of quantum mechanics, but ended up creating one of the most influential memes in the history of science. Irony of fate, folks.
What Is Quantum Tunneling (And What Do Tunnels Have to Do With It)
Now for the main event: quantum tunneling – a phenomenon where a particle passes through an energy barrier it shouldn't theoretically be able to overcome. Imagine rolling a ball up a hill, but you don't have enough strength to get it to the top. In classical physics, the ball rolls back. In quantum mechanics, the ball might suddenly appear on the other side, as if it dug a tunnel. Hence the name.
But there are no physical tunnels, of course. This is a purely quantum effect arising because particles in the microworld behave not like billiard balls, but like waves. And this is where the magic of math kicks in.
In quantum mechanics, every particle is described by a wave function – a mathematical entity that shows the probability of finding the particle in a specific place. The wave function can enter areas where a classical particle cannot go. If an electron faces a barrier (like a thin layer of insulator), its wave function doesn't cut off abruptly at the border – it decays gradually, penetrating inside. And if the barrier is thin enough, the wave function can «leak» to the other side.
This means there is a non-zero probability of detecting the electron on the other side of the barrier, even though it didn't have enough energy to overcome it. It just… tunneled. As if it teleported, but without special effects and dramatic music.
The Math That Makes the Impossible Possible
Now for a bit of formulas, but I promise – without going overboard. The probability of tunneling depends on three things: the barrier's height, its width, and the particle's mass. The higher and wider the barrier, the lower the probability. The lighter the particle, the better the odds.
There is a simplified formula: tunneling probability decreases exponentially with barrier growth. Specifically, it's proportional to exp(-2kd), where k is linked to barrier height and particle mass, and d is the barrier width. An exponent means things change very, very fast. Increase the barrier slightly – the probability crashes by thousands of times.
For an electron with its tiny mass, passing through a nanometer barrier is business as usual. For an atom, it's already tougher. For a 70-kilogram human – well, more on that later. Spoiler: don't get your hopes up.
Where Tunneling Works in Real Life 🔬
Quantum tunneling isn't just a fun theoretical toy. It's a real phenomenon without which modern civilization would be straight-up… not modern.
Scanning Tunneling Microscope. One of the most impressive tools in nanotechnology. Its operation is based on bringing an ultra-sharp needle to atomic distances from a sample surface, causing electrons to tunnel between the needle and the sample. By measuring the tunneling current, you can build a surface map with atomic resolution – literally seeing individual atoms. They gave a Nobel Prize for this invention in 1986, and absolutely deservedly so.
Radioactive decay. Alpha decay – when a nucleus ejects an alpha particle (two protons and two neutrons) – is also an example of tunneling. The alpha particle is trapped in a potential well and cannot leave the nucleus according to classical laws. But thanks to tunneling, it can. That's exactly why uranium-238 decays, even though the alpha particle lacks the energy to overcome the nuclear barrier.
Thermonuclear fusion in the Sun. Yes, our luminary runs on tunneling too. Protons in the center of the Sun must get close enough for nuclear forces to kick in and fusion to occur. But protons are positively charged and repel each other. A temperature of 15 million degrees doesn't give them enough energy to overcome the Coulomb barrier. Tunneling allows them to occasionally get closer than classical physics permits. And then – bam! – fusion. Without tunneling, the Sun wouldn't shine, and we'd be slightly frozen. Thanks, quantum mechanics. 🌞
Tunnel diodes and transistors. In modern electronics, tunneling is used everywhere. Tunnel diodes switch very quickly, and in some transistors, electrons pass through thinnest layers of dielectric. Your smartphone partially runs on quantum effects – surprise!
And Now About Humans and Walls
Okay, electrons can tunnel, the Sun shines, microscopes draw atoms – all wonderful. But can you walk through a wall?
Technically – yes. Quantum mechanics doesn't forbid it. All your atoms obey the same laws as an electron.
Practically – forget it.
Let's do the math. Take a wall 20 centimeters thick. Your body has about 10^28 atoms (that's a one with 28 zeros). For you to pass through the wall, all these atoms must tunnel simultaneously.
The probability of a single atom tunneling through a macroscopic barrier is negligible – around 10^(-billion). Now raise that number to the power of 10^28. You get a probability so small that mathematicians start having an existential crisis.
To understand the scale: the expected time for such an event exceeds the age of the Universe by… well, so much that there aren't enough atoms in the observable Universe to write this number down. You'd sooner wait for all the atoms in your body to accidentally end up in the next room due to Brownian motion (which is also practically impossible).
Why Mass Is the Main Enemy of Tunneling
Remember the exponent in the formula? The particle mass was in there. An electron weighs about 9 × 10^(-31) kilograms. A proton is 1836 times heavier. A hydrogen atom is even heavier. You are about 70 kilograms.
The greater the mass, the weaker the quantum effects. This is linked to the de Broglie wavelength – every particle corresponds to a wave, and its length is inversely proportional to mass. For an electron, it's comparable to the size of an atom, so quantum effects are noticeable. For you, the wavelength is around 10^(-36) meters. That's trillions of trillions of times smaller than an atom.
With such a wavelength, you are a fully classical object. No quantum tricks. You cannot tunnel, be in superposition, or interfere with yourself (although many manage the latter without quantum mechanics).
Decoherence: Why the Quantum World Doesn't Leak Into Ours
There is one more problem – decoherence. This is the process where a quantum system interacts with its environment and loses its quantum properties. Quantum superposition is extremely fragile: the slightest interaction with the outside world – and that's it, the superposition collapses.
For an isolated electron in a vacuum, quantum effects can be observed for a long time. For a molecule, it's already harder. For an object the size of a virus, it's almost impossible at room temperature. For a human, it's not even up for discussion.
Your body continuously interacts with the surrounding world: air, light, thermal radiation. Every such interaction is a measurement that destroys quantum states. The decoherence time for macro-objects is roughly 10^(-40) seconds. That's faster than you can say «quantum».
And that's why we don't see quantum effects in everyday life. Schrödinger's cat is either alive or dead because the «cat» system is too big and too «noisy» to maintain superposition.
What If We Try Really, Really Hard?
Let's say you don't give up and want to increase your odds of tunneling. What can be done?
Reduce the barrier. The thinner the wall, the higher the probability. But even if you reduce the thickness to paper (0.1 mm), the probability for a macro-object will still be zero – within any reasonable precision.
Reduce mass. Sadly, not much room to maneuver here. You can lose weight, but the difference between 70 and 50 kilograms is negligible compared to the difference between a human and an electron.
Cool to absolute zero. At very low temperatures, quantum effects manifest more strongly. But absolute zero is unattainable, and even at temperatures close to it, macro-objects don't tunnel. Plus, you wouldn't survive such cooling.
Wait a very long time. Theoretically, anything is possible – but the times we are talking about exceed the age of the Universe to the power of the age of the Universe. That is literally not a hyperbole.
Why Then Don't Atoms Fall Through Each Other?
A funny paradox: if tunneling exists, why don't we fall through the floor? After all, atoms are 99.9999% empty space.
Answer: the Pauli exclusion principle and electrostatic repulsion. Electrons occupy specific quantum levels, and two electrons cannot be in the exact same state. When atoms get close, their electron clouds start «shoving» – not due to physical collision, but due to quantum rules.
Add electrostatics: electrons are negatively charged and repel each other. When you sit on a chair, the electrons in your body repel the electrons in the chair. This creates the sensation of solidity.
So you don't fall through the chair not because tunneling «doesn't work», but because its probability is negligible, and stronger forces completely dominate.
Quantum Mechanics in Pop Culture: When Physics Cries
We can't ignore how quantum mechanics is used in movies and literature. Usually – incorrectly.
«Ant-Man» shrinks to «quantum sizes» and enters the «Quantum Realm». Sounds spectacular, but physically, it's pure fantasy. Quantum effects don't depend on the size of the object per se – they are defined by mass and energy.
In «Rick and Morty» there is a device for walking through walls. That is, of course, fantasy, but the authors at least don't pretend it's realistic physics.
In «Interstellar» a five-dimensional space appears – and although it's a big movie, Kip Thorne did try to keep the physics within bounds. Quantum mechanics, truth be told, barely figures in there.
The main problem is that the word «quantum» has become a marketing buzzword for everything weird. Quantum magic, quantum healing, quantum psychology – all this is pseudoscience. If someone sells you a «quantum health bracelet» – run. It's a scam.
So Is There Any Chance at All?
Honestly? No.
The probability of a human tunneling through a wall is so small it can be considered zero. Quantum mechanics works great – but only at its own scales: for electrons, atoms, molecules. Not for people, cats, cars, and planets.
The macroworld lives by classical laws – and, frankly, that's wonderful. Imagine the chaos if things sometimes tunneled: you put your phone on the table – and it ends up inside the table. You pour coffee – and it goes through the bottom of the mug. A nightmare.
Let quantum effects stay in the microworld, where they ensure the operation of transistors, lasers, solar panels, and all modern electronics. There, they are beautiful. But don't expect them to help you walk through a wall.
Epilogue: The Beauty of the Impossible
Quantum mechanics is, perhaps, the weirdest and most counterintuitive theory in physics. It describes a world we cannot observe directly – a world with rules contradicting common sense. And that's exactly what makes it so mesmerizing.
Tunneling is one of the most poetic quantum phenomena. The idea that a particle can pass where the path is closed, that barriers are not absolute, that probability is capable of defeating impossibility – this idea goes far beyond physics.
Unfortunately (or fortunately), it doesn't work for humans. We cannot tunnel through walls, bypass obstacles by the power of probability, or rely on quantum uncertainty. We have to look for doors, build ladders, and walk around mountains.
But knowing that somewhere at the quantum level such miracles are possible – even with a probability tending to zero – makes the world a little more magical. And reminds us that physics is full of wonders, even if they are hidden at scales we will never see.
So next time you stand before a locked door, you can comfort yourself with the thought: theoretically, you could walk right through it. You'd just have to wait longer than the Universe has existed. For now – look for your keys. 🔑
