The Coin-Toss Analogy: On Quantum Superposition and Ontic Uncertainty
This coin toss has nothing to do with The Witcher, unfortunately.
In this post, I introduce the coin-toss analogy, which is used to help discuss quantum superposition in terms of ontic uncertainty as opposed to epistemic uncertainty. To set up the analogy, I first explain some basic concepts of quantum mechanics in simplified terms.
Something that’s always been interesting to me is the concept of quantum superposition. It comes from the world of physics, specifically from the theory of quantum mechanics (QM), which I find that a lot of people often talk about, but only at a very surface level. I don’t blame them — quantum mechanics is a decently complicated topic and most of us don’t need to use quantum mechanics in our daily lives. And yet, I find myself thinking about it more often than not.
Without going into too much detail, quantum mechanics helps us understand the world by describing a variety of phenomena that happens on a very, very small scale. While classical mechanics describes things at a “macroscopic” or large scale, such as the interaction of a billiard ball striking another billiard ball, quantum mechanics cares about things at the absolute smallest of scales, such as at the atomic level. We’re talking about dealing with interactions of things like individual electrons or photons, which are fundamental particles of light. It turns out that at this very small scale, some really weird things happen that defy how we would ordinarily think about the world.
One of these weird things is quantum superposition, which I mentioned at the start of the post. It’s one of the most fundamental principles of quantum mechanics, though mathematically, it’s not a tremendously difficult thing to describe (it really just boils down to addition and probability, but with some flavor). For those who’ve taken linear algebra, quantum superposition can be described as a linear combination of vectors, where each vector represents a possible value that the system can take on. But outside of math speak, what does this actually mean in the real world? To understand this, we have to take a step back and talk about states of a system.
Here’s a simplified, macroscopic example: let’s say we have a system that consists of a single light switch, which can either be ON or OFF at any given moment. That is, the light switch has two states — an ON state and an OFF state. Let’s try this way of thinking for other things in our macroscopic world. Since I like sleeping so much, an example that comes to my mind is the fact that I can describe someone as being in an ASLEEP state or AWAKE state (though sometimes I get mixed up which is which for myself 😅). Can you think of your own examples that follow this pattern?
It’s worth mentioning that not all systems have to be binary (meaning that they only have two values to choose from). Another valid system is the volume on my laptop, with its state being the volume number at any given time. The weather forecast could be a system as well, with a selection of states such as CLOUD, SUN, RAIN, SNOW, etc. The interesting thing about the weather example is that your system can be a combination of states. The weather could be CLOUD + RAIN, for example.
Sound is yet another type of system that’s given as a popular example. You can imagine the state of what you hear as a combination of different sounds all added together. This combination of classical states is an example of classical superposition (that is, superposition at the macroscopic, non-spooky level) of the sound waves that hit your eardrum.
Furthermore, in a classical system, there are some logical truths that must hold with regard to states. Say we’re in a room with two instruments: a piano and a violin, and their respective musicians. At any given time in the room, there can be one of four states: PIANO SOUND but no VIOLIN SOUND, VIOLIN SOUND but no PIANO SOUND, neither of the two, or a combination of both PIANO SOUND + VIOLIN SOUND. What’s important to remember is that in a classical system, only one of these four is necessarily true at any given time. Take some time to think through and verify this statement, since it’s essential to understanding why quantum superposition is so weird. This will be important to remember down the line.
Let’s now switch gears and finally talk about quantum superposition. In order to do this, I want to introduce a simplified version of a well-known thought experiment that you may have heard of before (but don’t worry if you haven’t), called Schrödinger’s Cat.
Skipping over the history of Schrödinger’s Cat (which I actually find very important in certain contexts), the thought experiment is paraphrased as follows:
Imagine a cat placed in a steel chamber. Along with the cat in the chamber is a tiny bit of a radioactive substance, which has a 50% probability of one of its atoms decaying and 50% probability of no atoms decaying. If a device that measures radioactivity notices that an atom has decayed, a hammer will shatter a flask of hydrocyanic acid inside the chamber, which will kill the cat. Therefore, at the end of the hour, the cat will either be dead or alive, with equal probabilities, but we do not know which one until we open the steel chamber and observe what has happened inside.
Now here’s the part of quantum mechanics that’s weird. Without opening the steel chamber, can we say for sure that the cat is in an ALIVE state or a DEAD state? We cannot. We are uncertain about its state. In quantum mechanics terms, we therefore say that the cat is in a quantum superposition of the ALIVE and DEAD states. It is only once we observe, or measure, the system that it collapses into one of the two states with certainty.
This isn’t just a fictitious concept. For things at a very small atomic/subatomic scale, superposition naturally occurs, and the states of these systems are uncertain to us until we measure them. One common example deals with the property of spin in electrons. Spin in electrons can take on two values — SPIN-UP or SPIN-DOWN — just like how a light switch can have an ON value or an OFF value. Often, an electron may end up in an arrangement where its spin is in a superposition state of SPIN-UP and SPIN-DOWN, and only when we measure the electron’s spin can we say for certain that the electron is SPIN-UP or SPIN-DOWN.
A common question that’s usually asked at this point is, “So what exactly is the quantum superposition state?” Many people answer that it is when both states are true — the cat is both ALIVE and DEAD, or the electron is both SPIN-UP and SPIN-DOWN — but this is incorrect. Remember that the combination of both states happening at the same time is one of the four possibilities for classical superposition. What makes quantum superposition so wild and weird and interesting is that it is none of the four classical possibilities: (1) ALIVE, (2) DEAD, (3) ALIVE and DEAD, or (4) neither ALIVE nor DEAD. Instead, we had to come up with this new terminology to describe this new state that we realized quantum systems could be in — it is in (5) a superposition of ALIVE and DEAD. Not that both are true at the same time.
Don’t worry if this is confusing at first; even for some of the greatest minds in physics, such as Schrödinger and even Einstein, this was tough to grasp and accept. (In fact, Einstein was proven wrong about an extension of the superposition phenomenon called entanglement that he was unable to ever accept as true, even to his deathbed.)
It would be convenient and far easier if we could explain quantum superposition as two states (e.g., both ALIVE and DEAD) being true at the same time. You could simply say that you put a cat in a box, and until you open it, you don’t know if the cat is alive or dead, and therefore it is both alive and dead. However… this is merely a handy, but false simplification. Quantum superposition is a unique state of its own, characterized by our uncertainty of whether the cat is alive, dead, both alive or dead, or neither.
But what does this physically mean?
For Schrödinger, this potentially meant that the cat was in a state of “blurred reality”, one where the value of its existence is totally uncertain. At first, physicists like Einstein rejected this conclusion and hypothesized that it was merely our own understanding of the world that was blurry. The argument was that although we do not know whether the cat is alive or dead, that is merely a gap in our own knowledge, and in reality the cat must necessarily be one or the other. However, actual experimentation in the form of Bell’s Theorem would show — shockingly — that this is not true. It’s not just that we have a blurry view of reality, but that reality itself is indeed blurry. For me, this is above all else the most interesting thing about quantum mechanics, and the thing I find myself thinking about the most.
To explain just how interesting or weird this is, I introduce a coin-toss analogy. Imagine that you flip a coin and right as it lands, you cover it up. At that moment in time, you do not know whether the coin landed HEADS or TAILS. In our macroscopic reality, we know that the coin is for certain either HEADS or TAILS at that moment — we just don’t know which one it is. I call this an epistemic uncertainty, with the word ‘epistemic’ meaning ‘relating to knowledge’. That is, it is our knowledge about the world that is blurry. However, what is so shaking about quantum superposition in the real world is that it is an ontic uncertainty, with the word ‘ontic’ meaning ‘relating to physical or factual reality’. If there really was ontic uncertainty about the coin, it would mean that while it is covered up, the coin isn’t HEADS or TAILS, and our act of uncovering the coin would cause it to become HEADS or TAILS. In fact, this can be said for Schrödinger’s Cat — until we open the steel chamber, the cat is in a superposition of ALIVE or DEAD, and it is our measurement of the system that causes the cat to be ALIVE or DEAD. I use the coin toss analogy as a way to distinguish the type of uncertainty that we have about macroscopic systems (epistemic) and the type of uncertainty that we have about superposition states (ontic). So until systems in superposition states are observed or measured, they exist in some kind of absolutely unknown, blurry reality. And this blurred reality is constantly happening in the world around us, at least at a subatomic scale. That’s wild to me.
Some final notes, just to wrap a few things up.
To start with, a lot of the explanations in this post are simplified, so I apologize if I miss any nuances and details. I realize I could take some time to really sit and think about better ways to break down the concept of quantum superposition, but really I just wanted to get to the coin-toss analogy and the weirdness of ontic uncertainty as quickly as I could. I imagine dedicating some future writings to having even more introductory explanations to simplify things further. By the way, for anyone curious, the typical starting point for discussing quantum mechanics and quantum superposition is Young’s double-slit experiment, which is famous for showing that entities such as light can be described as either a particle or wave, which contradicts classical physics. I usually feel like quantum superposition can be discussed without talking about the double-slit experiment, as I do in this post. On that note, a very good article about Bell’s Theorem and the blurriness of reality versus our sight of reality was published by Aatish Bhatia here in Wired, if you would like to follow some of the math used in Bell’s Theorem.
Next, I’d be remiss not to mention that Schrödinger didn’t take his Cat thought experiment completely seriously. Some have even considered it an attempt at trolling the physics community at their lack of clear boundary between where quantum mechanics and classical mechanics become valid. It was clear to Schrödinger that a whole cat would never be in a quantum superposition of ALIVE and DEAD, because a cat is most definitely macroscopic enough that classical mechanics would take over at that point. The more important question, for Schrödinger, was at which moment system would collapse into either the ALIVE or DEAD state, and whether it was the human measurement that caused it to happen. This, of course, would be a problem, because it would require the existence of a (human) observer to exist in order for collapse to ever occur. In quantum mechanics, this is called the measurement problem, which is its own interesting thing. Note that there are various different interpretations of quantum mechanics that give their own attempts at answering this problem. Again going back to Einstein, he rejected this problem by asserting that reality was never blurry to begin with, that the cat was already ALIVE or DEAD regardless of us checking on it. This is where his well-known quote, “God does not play dice with the universe,” comes from. Einstein clarified that he did not believe in a personal God, but that he could not accept that reality at any time could be left to a mere probability of being in one state or another. As Bell showed, Einstein was wrong.
By the way, as a complete aside, when I first heard of Einstein’s quote in this context, I couldn’t help but think of the philosophy of George Berkeley (for whom the city of Berkeley where UC Berkeley is located is named after). Berkeley was an Irish philosopher who argued for a theory called immaterialism, where matter is merely an idea within our minds. In somewhat quantum mechanics speak, this means that reality only exists from our observation of it. Sounds… somewhat familiar, doesn’t it? If you remove the observer, then reality isn’t defined. (Or in other words, if a tree falls in a forest, and no one’s around… well, the forest doesn’t exist because no one’s around.) Of course, someone asked Berkeley: if a person leaves a room and thus stops observing it, does it mean the room ceases to exist? For Berkeley, who was a Christian bishop, the answer was that it still exists because God is always observing reality. Einstein was definitely acquainted with Berkeley’s philosophy of immaterialism, so sometimes I wonder if his quote was in some ways referential to Berkeley’s God being the observer that prevents reality from being blurry.
Finally, as an ex-computer scientist, I want to conclude by mentioning an application of quantum superposition that’s actually very actively being researched today — quantum computing. It’s not just that quantum superposition is an interesting and weird phenomena in reality for us to study, but we can also make use of it for exponentially faster computations. While our computers today use classical bits (1’s and 0’s) to represent information, the heart of quantum computing can be found in qubits (quantum bit), a unit of quantum information that can be 1, 0, or a superposition of 1 and 0. By making use of quantum superposition, we can store more information in a qubit than a classical bit and perform much faster computations on qubits. When I first learned about qubits, they were mostly theoretical. However, in the years that followed, we’ve made tremendous strides in quantum computing, with IBM boasting a 53-qubit computer (May 2019) and Google boasting a 72-qubit chip (March 2018). The two companies have fought over who can achieve “quantum supremacy” first, or in other words, who can create a quantum computer that can perform tasks that classical computers cannot. (There’s also been backlash around the need to use the term “supremacy” to describe this achievement.) It’s a pretty amazing race to watch, because it could totally revolutionize what we can do with computers, at least in my opinion. It’s also really neat to see an example of how our pursuit of knowledge about how the universe operates doesn’t just stop at gaining some deeper understanding of a theoretical “Truth”, but that these discoveries can actually be used to advance various human technologies we might never have thought of before. On the flip side, it’s incredible to me to know that so many of the practical applications we have are only made possible by deeply interesting phenomena, like the “blurred reality” of quantum superposition. And maybe that’s why I think about it so much, with a sense of wonder.
References
Albert, D.Z. (1994). Quantum Mechanics and Experience. Harvard University Press.
Trimmer, John D. (1980). “The Present Situation in Quantum Mechanics: A Translation of Schrödinger's “Cat Paradox” Paper”. Proceedings of the American Philosophical Society. 124 (5): 323–338.
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Wells Lucas Santo is a queer, Southeast Asian educator on the social implications of technology, based in Oakland, CA. He is also an advocate for Asian American & QTPOC equity. A fan of boba, anime, and music, you can catch him and his hot takes throughout the day on Twitter.