Author: William Black, Edited by Zena Lapp, Zuleirys Santana-Rodríguez, and Whit Froehlich

Quantum_Tunnel_Blueprint.png

Some say that studying a flower’s structure makes it less beautiful—that it’s best to appreciate the façade at face value, without details of underlying mechanisms. I wholly disagree. Knowledge of how a leaf photosynthesizes gives botanists greater awe for its elegance. Knowledge of how black holes tear at the fabric of spacetime gives physicists greater wonder for the universe. Knowledge of the quantum realm gave me a greater appreciation for Ant-Man and the Wasp. It can even give insights into where the Marvel Cinematic Universe (MCU) may be headed with Avengers: Endgame. To better understand how the quantum realm works, I’ll expound on the powers of Ghost, the main antagonist of Ant-Man and the Wasp, and how they relate to probability clouds, Schrödinger’s cat, quantum tunneling, and the current state of the MCU.

Ghost Acts Like a Quantum Particle

“““
Hank: Whoever stole the lab knew exactly what they were doing.
Hope: They also looked like they were phasing.
Scott: Phasing?
Hank: Quantum phasing. When an object moves through different states of matter.
Scott: Oh, yeah. That’s what I was thinking.
””” 

This quote from Ant-Man and the Wasp is confusing at best and flat-out incorrect at worst. It was my only real disappointment in the movie—I wish they had put more thought into explaining Ghost’s peculiar powers. A more thorough dive into the antagonist’s abilities would not only clarify her behavior, but would also give pedestrian insight into the paradox (1, notes at the end) of Schrödinger’s cat, quantum tunneling, and the fundamental nature of the quantum realm.

The character Ghost [played by Hannah John-Kamen] is a great example of quantum mechanics. I’ll focus on an epitomic example of her quantum nature in her first fight scene, at the restaurant. In this two-second clip, Wasp [played by Evangeline Lilly] sees Ghost approaching her and kicks a food cart in Ghost’s direction. Without breaking a sweat, Ghost dodges the food cart, in much the same way one quantum particle might dodge another.  

Screen Shot 2019-04-18 at 10.19.25 PM.pngBefore the cart would have hit her, we see Ghost appear in at least three positions at once, each dodging the cart in a different way. After the cart passes through, the image of her walking straight forward (without having dodged) becomes dominant, while the multiple dodge positions fade away.

This is just how a particle behaves on a microscopic scale: we see Ghost existing in many places at once, yet she doesn’t always interact with objects that pass through one of her possible positions. An electron, for example, exists in many places at once—it doesn’t stand in an exact spot around the nucleus.

While quantum mechanics has yet to be fully understood, that doesn’t preclude our partial understanding from being applicable. One can read the time on a clock without knowing how the gears mesh together; one can throw a baseball without understanding general relativity or even knowing of gravity. Though our understanding of quantum mechanics is imperfect, it still can accurately predict the behavior of many quantum systems; or, for our purposes, explain the powers of Ghost.

Buckle down for some science!

Falling Dice in Copenhagen

The leading theory in how the quantum realm works is known as the Copenhagen Interpretation of quantum mechanics (2). It holds that particles live as probabilities, existing in all possible states at once (a ‘probability cloud’) until they are ‘observed’ (3). It’s quite a bit like falling dice—having a set of possible outcomes, but no certain state until they hit the table.

As a die falls, it hasn’t chosen a side yet, so demanding an outcome of the roll already doesn’t make sense; one could equally argue that it’s on every side or that it’s on none of the sides. After the die hits the table, it’s forced to assume one of its possible sides, but until then, it’s up in the air. The best we can do is give probabilities of the possible outcomes. (Note that this doesn’t mean any outcome—a six sided die can only land on integer values one through six.)

Asking where a particle is at a given time is much like asking which side a die is on as it is still falling. Just like a falling die, a particle doesn’t have an exact position—it exists in many places at once. We can give a range of where we expect to find the particle and point out which places are most likely, but until it’s “observed”, the particle has no definite position. The quality of being in many states (4) at once is known as “quantum superposition.”

This is the true nature of particles: rather than having a definite position value, they exist as probabilities “smeared out” over space. This doesn’t quite mean they can be anywhere though, otherwise atoms couldn’t form. Just as we can assign probabilities to different dice rolls, we can know the probability of finding a particle in a specific place, or conversely, know the most likely place to observe the particle, such as an electron in an atom.

Here are a few cartoons of atoms, that you may have seen the likes of before:

Screen Shot 2019-04-18 at 10.19.10 PM

While the cartoons illustrate some of the structure and organization of the atom, they mislead millions into false beliefs, such as the idea that electrons actually orbit the nucleus, or that they have distinct concentric levels in which they reside.

Instead of orbiting around the nucleus, electrons exist in probability clouds. Electrons stay around the nucleus without an absolute position (until they’re interacted with). Their position probability is smeared out in distinct patterns called orbitals, which take on different shapes depending on the energy of the individual electron. A few orbital patterns are shown below:

800px-Atomic_orbitals_spdf_m-eigenstates

Here you see what are called “probability isocontours”, meaning surfaces which have e.g. a 50% likelihood of the particle being observed within that location, used to give a rough sense of the overall probability cloud. There are lower (but non-zero) probabilities of the electron being outside these shapes, in similar patterns.

This trait of being in multiple places at once—of existing as a smeared-out probability, like Ghost dodging the cart—is fundamental to understanding both the thought experiment of Schrödinger’s cat and the concept of quantum tunneling.

Schrödinger’s Cat

If the Copenhagen Interpretation seems confusing, you’re not alone. Erwin Schrödinger (now known as one of the fathers of quantum mechanics), disliked the idea of smeared existences so much that he devised a thought experiment to prove how ridiculous this was. His main argument was that in reality, we only ever measure single states—we never measure a particle to be in two positions at once! Whenever we measure a particle, it must appear in either one state or another.

Schrödinger put forward the following situation:

Schrodingers_cat.svg

Put a cat in a box with a deadly chemical. Add a radiation source with a 50% chance of emitting a particle within the time the cat is in the box. Aim a Geiger counter (a device that measures radiating particles) at the radiation source, and connect it to a hammer which would release the chemical and kill the cat. Then seal the box and wait.

Since we haven’t observed the cat yet, the Copenhagen Interpretation would imply it must be both alive and dead simultaneously. Herein lies the paradox: we know, logically, that cats cannot be half-alive or half-dead—there are no zombie cats!

There are several flaws with this thought experiment (that could be an essay in and of itself), but I’ll focus on the common misconception of “observation”. It’s tempting to interpret that the act of observing a particle forces it into one state or another and get grandiose ideas about human extramission—that our eyes have the power to change the world around us. While that holds true in metaphor, there’s nothing physically powerful about our sight: it’s merely our eyes ingesting photons and processing data.

It’s by sad historical coincidence that we’ve chosen the word “observation,” when a more accurate word would be “interaction.” Our opening a box doesn’t force reality to take a stand—it’s the interactions of particles that force it to take a stand. In the case of the cat, the radiation either occurs and is observed, or does not occur and isn’t observed. It’s not our opening of the box that forces the cat to be alive or dead—it’s the interaction between the radiation source and the Geiger counter. That’s what determines whether the cat actually dies or survives.

While the paradox breaks on such a large scale as a cat, such paradoxical states can and do exist for single particles, or even large collections of particles. These are known as “cat states” after Schrödinger’s thought experiment, in which particles are in opposite states at the same time. These states are what give quantum computing its power—the ability to possess both up-spin and down-spin simultaneously. While most computers only take on bit values of off (0) and on (1), quantum computers take any superposition between the two states, allowing for the full range of real numbers between zero and one. Another example of simultaneous states is that of a particle hitting a wall: while there’s some chance of it bouncing off like a tennis ball, there’s a calculable probability (no matter how small) that it passes through the wall. This is called quantum tunneling.

Splitting the Wavefunction with Quantum Tunneling

Simply put, quantum tunneling is when some particle goes through a solid surface. Since particles behave like probabilities, they have non-zero chances of being most anywhere. This is actually observed in ordinary computing, where it sets the floor for transistor size. As engineers strive to develop smaller and smaller transistors, quantum tunneling allows electrons to jump (‘tunnel’) between near (but not touching) wires. While this may seem like teleportation, it’s worth remembering that 1) electrons are waves too, just like light, and 2) they’re extremely unlikely to tunnel through more than a hair’s breadth of material (5).

Screen Shot 2019-04-18 at 10.19.50 PM.png

This picture depicts quantum tunneling. The green dots represent the wavefunction Ψ (pronounced “Psi”). The magnitude of the wavefunction (the distance of the green dots from the yellow axis) is related to the chance of finding the particle in that position (P=|ψ|2). Thus (at this snapshot),

  1. before the barrier is where we’re most likely to detect the particle (represented by the left red sphere),
  2. the barrier drastically decreases the wavefunction (which means the particle is less likely to be found across the barrier),
  3. but there’s still a chance of detecting the particle after the barrier (represented by the right red sphere).

Remember that the particle exists on both sides of the barrier at once, just like Schrödinger’s cat being both alive and dead. It stays on both sides until something interacts with the particle. Mathematically speaking, there’s a finite probability before the barrier, an exponential falloff inside the material, and a finite probability outside the barrier.

Suppose we shine a flashlight on the right side of the barrier—we will either see the particle or we will not. If a photon from our flashlight interacts with the particle, the photon will bounce off the particle (perhaps into our eyes or a detector we have set up). When the photon hits, the wavefunction of the particle bunches up in one spot. After interaction, the wavefunction relaxes, but now is more likely to be found on the right side than the left. On the other hand, if no photons interact with the particle, its position is just as ambiguous as it was before we turned on the flashlight.

The “quantum tunnel” in Ant-Man and the Wasp (used to shrink down to quantum sizes to visit the “Quantum Realm”) had nothing to do with quantum tunneling. Still, it was my favorite pun from the entire movie. Similarly, the “Quantum Realm” of the movie doesn’t have too much to do with the actual quantum realm—in reality, no human (much less a civilization) could exist at such a small size scale. But at that scale (6), the physics above becomes apparent: particles act like waves, multiple states exist at once, and tunneling looks like teleportation. Despite knowing how the quantum realm behaves on a larger scale, it’s still very much a black box—we have yet to understand the underlying mechanism for the behavior of particles. But as mentioned before, you can predict how a clock’s hands will move without knowing how the gears behind its face all mesh together.

Despite science often being inaccurate in films, its presence gives publicity to scientific ideas, which helps to fund the projects that drive us to new technologies. The communicators of Star Trek inspired the first cell phones (and cell phones now have many more functions than voice alone). Tony Stark used touchless interaction with screens just before the Leap Motion and Xbox Kinect were released. Hundreds of other technologies have appeared on the screen and inspired their own creation. With the quantum realm increasing in notoriety, we’ll hopefully see in years to come greater funding for and interest in technologies such as quantum computing.

Now that we’ve discussed some of the vocabulary and contingent science behind the quantum realm, we can discuss Ghost’s dodge in a more formal way. The dodge represents a smeared-out probability, where Ghost’s possible states (continue forwards, dodge left, dodge right, &c.) existed simultaneously. She then controls her phasing to select the non-interacting state, so she remains in a superposition of dodging in all possible ways until the cart passes through her position, effectively tunneling through the cart. Once the cart is gone, Ghost can continue forwards as if nothing happened, since, for her, nothing did happen—the possibility of interacting with the cart wasn’t selected.

Ghost-Ant-Man-and-the-wasp

After the carnage of Avengers: Infinity War, the Marvel Cinematic Universe is in a state of half alive, half dead. If the quantum realm plays as big a part in Avengers: Endgame as it’s hinted to, the universe itself may be in a supergalactic cat state. Though it’s just my guess, I believe they’ll use the Quantum Realm to attempt a superposition of both states, allowing for the victims of Thanos to live again.

No matter which state the Marvel Cinematic Universe selects, I hope you’ve gained some appreciation for the beauty of quantum mechanics, and in turn, some appreciation for Ghost and the quantum realm. While the quantum realm follows wildly different rules than we’re used to, there is a self-consistent logic which produces rules; it is predictable—as predictable as any dice roll.


good_pic_of_meWilliam received his bachelor’s in physics at Brigham Young University, studying the evolution of primordial black holes. He is currently a PhD student in the physics department at University of Michigan, working with galaxy clusters. He likes to write fantasy novels, participate in philosophical debates, and play D&D.

 

Footnotes
1. Technically speaking, it’s a thought experiment, but many refer to it as a paradox due to its apparently contradictory nature—more on this later.

2. Though it’s the leading interpretation, it only holds a plurality—never a majority! It’s a simple theory that works in calculations, despite its philosophical flaws. See The Many Interpretations of Quantum Mechanics (Graham P. Collins, Scientific American) for a simple summary.

3. A warning to the reader: The phrase “observing” the particle creates great confusion: it’s not that our cognizance changes the universe—it’s interactions with other particles, such as the inert gas in a Geiger counter, that acts as an observation or measurement. Otherwise, if particle states depended on sentient creatures knowing about them, the universe wouldn’t have a definite form at night—it would constantly be in flux until sunrise. It’s worth noting though that this is poorly understood—the exact definition and effects of measurement are still hotly debated issues (for a summary, see Wikipedia: Measurement Problem).

4. Technically, a position eigenstate (a function of position, e.g. “ψ(x)=sin(x)”) isn’t the same thing as a position outcome (a definite value, e.g. the expectation value of the function “⟨ψ(x)⟩=x0”, a certain location around the nucleus), but it’s a technicality I’m willing to break throughout this essay to ease transitions between topics (see David J. Griffiths’ Introduction to Quantum Mechanics for a more rigorous handling).

5. Tunnelling becomes problematic once transistors are thinner than about 7nm. Human hairs are about 20–200 μm in diameter, which is about ten thousand times larger than 7 nm. So electrons won’t be tunneling through human hairs any time soon!

6. The scale on order of the de Broglie wavelength.

Images
1. Banner
2. Ghost dodging cart
3. Classic atomic orbitals – WK Black
4. Complicated atomic orbitals
5. Schrodinger’s Cat
6. Tunneling
7. Ghost

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