We all know Schrödinger's thought experiment: he proposed that one visualize placing a cat in a box with a flask of poison gas, doomed if a uranium atom happens to decay during the five minutes it is in the box, but free to live another (eight? nine?) lives otherwise. His suggestion was that the entire apparatus, cat included, enters a quantum superposition state. Opening the box and observing the cat causes the state to collapse: you'll either see a happy living cat, or a feline tragedy.
There is no need to actually perform the experiment: you can never actually observe a superposition state, and doing the experiment once to see whether the cat survives would just be cruel; it wouldn't answer any questions. The challenge is to explain how to apply quantum mechanics to the situation such a setup creates. Does quantum mechanisms operate only at small scale, or does it genuinely have large-scale implications? In the early 1900's, it was common to assume that the quantum world was somehow disconnected from the world of larger material objects. The experiment sets up a scenario in which, at least at first glance, a small-scale phenomenon shapes a large-scale outcome.
The physics community debated the meaning of this strange scenario endlessly, but were unable to resolve their views: one group held that indeed, the cat ends up in a superposition state resolved only by opening the box. A second community insisted that the outcome was "observed" when the uranium either did or did not decay. Yet another community questioned whether the problem was properly posed. Ultimately, exhaustion set in, at which point they agreed that it might be best to stop arguing.
One reason for not arguing this question to a conclusion is that irrespective of the interpretation of the experiment, Schrödinger's equation for predicting the evolution of state in a system of particles works quite well, so the debate centers not on the physics, per se, but rather on the best way to explain the physics. But while the cat story was intended to elevate the model to a more intuitive level, it only left everyone baffled. So the decision to not argue about it was really an agreement that whatever the experiment illustrates, it definitely doesn't help explain the physics.
In fact, the many-worlds model resolves this puzzle, for those willing to accept that there are an infinity of worlds, all equally real. But let's not go there, and instead focus on the statement of the puzzle itself.
As a computer scientist, it strikes me that a key part of the confusion is this: Can statements about quantum mechanics be made about cats? I'm putting statements in italics because I want to emphasize that I'm asking a syntax question, not a semantic one. Can the phrase "quantum superposition" be used as a modifier for "cat", as we might use "angry cat" or "happy cat"? Is it correct to talk about "quantum superposition of a cat"?
One of my favorite courses to teach is Cornell’s CS2110, our second programming class, where we introduce abstractions and object oriented computing. To me, there is nothing more foundational about computing than the shift in perspective that occurs when we define a new data type, instantiate it, and endow it with operations that have semantic meaning only with respect to the new abstraction.
With CS2110 in mind, let me pose a slightly different version of the cat question. Suppose that I define a new data type, a “foo”, and a true/false property “shimmer.” Given a foo object, you can always ask whether or not it shimmers. But now let's introduce a second unrelated data type, one we'll call "bar". If bar has no shimmer property, you simply can't ask if a bar object shimmers.
Back to animals. If one pets a cat, it may or may not purr. You can pet a dog, but it will never purr. What would it even mean for a dog to purr? Asking "did that dog purr?" is thus a nonsense question. Without defining what purring means, for dogs, the words simply don't fit together into a meaningful question.
So... armed with this very basic insight about abstract data types, let's revisit our physics puzzle. Subatomic particles can be placed into superposition states But is the term "superposition" even relevant to a cat?
The cat in the box scenario conflates a “perceptual” abstraction (the cat) with a model related to the wave/particle duality (superposition). Superposition as properly defined is a specific phenomenon seen in a totally different setting: one involving elementary particles, as we define and model them. You can't simply take such a term and apply it willy-nilly.
This now leads to a second and surprisingly subtle question: What in fact, is a cat?
You might be tempted to say something about atoms, molecules, cells. This would be like saying something about computer memories and bits and how Java compiles to basic operations, if we were talking about data types. But just as memory locations change over time, a cat's atoms and molecules and cells are constantly changing. Schrödinger's cat started life as a single fertilized cell. It acquired most of its current mass as it grew to become an adult. So, defining a cat in terms of its constituent parts seem wrong.
Is there a cat definition that transcends the “moving parts”?
As a computer scientist, an appealing answer is to suggest that catness centers on information. This view would define the living cat as a biological program that implements all the various processes by which a cat comes into existence, grows, and also sustains itself. In this perspective, the cat is a distributed program, admittedly one more complex than anything we know how to create today.
This programming perspective can be used to talk about many kinds of things in our perceived world. Even inanimate objects like stones are, in some sense, as much about information as they are about their constituent atoms and molecules and crystals.
In fact an information perspective can even be used to assign a kind of discrete existence to things that have no physical embodiment. We often talk about properties such as love, anger, happiness. A cat purrs to express contentment. Yet there is no physical object that corresponds to this emotional state that causes the cat to purr: contentment, hence purring, is a state resulting from a form of information-based biological computation, performed by the cat (I should almost say that the computation is executed on a biological machine that evolves over time under control of that same biological computation).
If a cat is actually best understood by thinking about information in this sense, and Schrödinger's box is a form of information, what does it really mean to say that we have placed a cat in the box? Obviously, at some high level of abstraction, you open the box, pick up Fluffy, and gently place her in the box. You close it, wait a few minutes, then reopen the box and remove Fluffy. But as you can see, if we really try to pin down the semantics of each of these steps it gets somewhat tricky. Each one of them involves non-trivial definitions. Some of these seem extremely difficult to really define in a full, logical way -- perhaps it isn't even possible in some cases.
Think now about the process as it was understood by late 19th century and early 20'th century particle physicists. They started out on a path towards the basic structure of the universe. This involved an effort to understand the composition of atoms, which they eventually understood to be atoms composed of protons, neutrons and electrons. Today, of course, we know that protons, neutrons and electrons are themselves structures composed of more elementary entities called quarks, and that quarks in turn may arise from mathematical structures that modern string-theorists like to call m-branes. But let's focus just on elementary particles like the ones making up atoms. At normal energies, this is a reasonable thing to do (you don't see protons and neutrons and electrons behaving like a soup of quarks unless you force them to collide, which requires extremely high energies).
So we have atoms, and we have elementary particles within them. We can model these abstractly, and to first approximation, they reside on something foundational and ultimately, are "atomic" in the original Greek sense of the term: indivisible, irreducible, fundamental.
And, returning to our point, as it turns out we can and should talk about superposition for these elementary particles. In this statement, the term "superposition" is applicable to our way of abstracting and modelling the behavior of individual particles. Indeed, we are really forced to define terms like superposition and entanglement to develop a sensible physical description of particles like neutrons and protons and electrons. Lacking these terms and their associated physical laws, we end up with an incomplete mathematical characterization.
The terminology, viewed this way, is meaningful in the context where it was first proposed, and is part of the mathematical physics that works so incredibly well at predicting the evolution of state for quantum systems. However, the terminology isn't absolute. We can't necessarily translate physics statements about this particular model of elementary particles to totally different settings.
In particular, when we take a term such as quantum superposition and apply it to Fluffy, we arrive at a conundrum: Is it, in fact, meaningful to make such a statement about a cat in a box? Yes, we can write the statement easily enough: "the cat in the box is in a superposition state." Yet one must question the well-formedness of the resulting statement itself.
This issue is especially striking when we consider an information-based perspective on catness, because such a definition of what it means to be a cat, or a box, really transcends the physical realities of the constituent components of the cat and the box, and exists in a different semantic context. Arguably, each level of abstraction in a physical system needs its own set of definitions, meanings, and physical laws. While these layers of meaning obviously do emerge from more basic ones, including the layer at which the original quantum superposition abstraction was first recognized, it isn't always the case that a property or physical law from one layer carries over to another higher one. Rather, each higher layer is "emergent" and as such, could be quite distinct from the layers below it. My foo data type, for example, might be very remote from the Java JVM instruction set or the data values used to represent a particular foo instance.
Of particular note is that Fluffy is really the same cat, even though she grew from a kitten into an adult cat over the past few years. Fluffy's atoms are mostly different from when she was small, yet she is still the same cat. So here we have an emergent notion of Fluffy that actually departs from the subatomic components of Fluffy in two senses: first, Fluffy endures even through her constituent atoms may be entirely different. And second, the behavior of Fluffy's atoms might not actually be evident at the higher level where Fluffy herself really exists. There is a disconnect between the layers of reality.
This brings me to a recently published book about quantum physics: What is Real? The Unfinished Quest for the Meaning of Quantum Physics, by Adam Becker (I recommend it highly). Becker describes a problem similar to the one I've outlined, and talks about the struggle Neils Bohr went through, trying to explain why measurement of quantum phenomena was (in his eyes) deeply problematic. For him, the cat in the box puzzle was simply an incorrectly posed problem. I think we would say today that his objection comes down to a “type checking” error.
When you try to talk about quantum superposition states in relation to cats, you are combining two abstractions from completely different type systems. And this simply isn’t well founded, a point that Bohr apparently fought to express to colleagues (who often were totally unable to appreciate his view). Bohr perhaps didn't even arrive at the observation that the cat is really an information-based abstraction that sustains itself, a biological machine. His focus was on the cat as a huge assemblage of particles. But if you take this next step and think of the cat as a form of information you arrive at a further insight: the concept of superposition applicable to elementary particles might (conceivably) apply to assemblages of them. But how it could it possibly apply to a purely informational abstraction?
Even in the case of a cat viewed as a massive collection of particles, there is endless debate about whether such a collection is so entangled that we can think of it as a massive cat-particle, or is in fact a collection of independent particles, which would potentially have independent superposition states. Becker discusses this at length... unfortunately he doesn't use the language of computer science, because for me our perspective on this is far clearer. Yet he does a good job, in a more intuitive way of explaining things. Certainly his writing is far better than mine... I could never write a book for his audience.
Getting back to Bohr, I find in his views an attempt to express precisely this issue of type inconsistency. Schrödinger's experiment simply doesn't type-check.
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