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That durned Schrödinger’s cat

Put me in that box at your own risk!

As today’s Google Doodle reminded me, today is the 126th anniversary of the birth of Austrian physicist Erwin Schrödinger. He happens to be one of very few of the founders of quantum mechanics whose name is widely known outside of physics, but for kind of an odd reason. If there is one area of quantum mechanics that has generated more writing — both sense and nonsense — than any other, it’s the thought experiment known as “Schrödinger’s cat”. I imagine I’m not alone among science writers in wishing sometimes that Schrödinger had never thought of that damn cat, or that he had picked a different metaphor. However, despite misinterpretations, popular misunderstanding, and overuse of the cat-as-metaphor, there’s still some life in the old feline.

Among working physicists, you’re far more likely to hear references to Schrödinger’s equation rather than his cat. That equation governs the behavior of quantum systems — electrons, atoms, molecules — and their interactions at low energy and low velocities. The complex emission and absorption spectra of atoms and molecules are (mostly) described by Schrödinger’s equation. However, like Einstein, Schrödinger never was comfortable with the standard interpretation of quantum mechanics, and his “cat” thought experiment was designed to illustrate exactly why.

In brief, the standard interpretation of quantum physics — known as the Copenhagen interpretation because it was developed by Danish physicist Niels Bohr — says that because microscopic objects such as electrons, atoms, etc. are inaccessible to us except through experiments, it makes no sense to talk about those objects having an independent reality. We only see electrons through measurement, and their characteristics depend strongly on what kind of experiment we do — in some experiments, electrons are very wave-like, experiencing diffraction and interference, while in other experiments and in every detector, electrons are particle-like, colliding and scattering and following straight-line trajectories.

The Copenhagen interpretation says this is as far as we can go: it doesn’t make sense to talk about electrons having a definite position before they are measured, or atoms existing in a particular state before the experiment. Instead, the best quantum mechanics can do is provide probabilities that the microscopic system has particular characteristics — the uncertainty isn’t a lack of knowledge on our part, but a fundamental property of nature. We cannot know the electron’s position or momentum or energy because it doesn’t have one, independent of measurement.

So how can we understand the process of determining an electron’s position? Our equipment is in some sense macroscopic: we manipulate it on our own scale, but it is made up of microscopic pieces. The challenge is how to understand that interaction between the equipment and the microscopic system being studied, and how the microscopic and macroscopic merge. Well, that’s not exactly true: some macroscopic systems (Bose-Einstein condensates, for example) are quantum in nature, bringing the weirdness into the human scale.

But what about a mixed system, in which there is an undoubtedly quantum system interacting with something that doesn’t really need quantum mechanics to describe it. And so we return to Schrödinger’s cat: imagine a closed box containing a radioactive substance and a live cat. (Warning to animal lovers: this isn’t a very nice experiment, but admittedly it’s only a thought experiment — it’s intended to be an illustrative example rather than a practical design.) There is also a vial of cyanide gas connected to a radiation detector, so that when the detector triggers, the vial opens, releasing the gas and killing the cat.

It’s simple enough: the rules governing the radioactive substance are quantum in nature, described using probabilities. The cat’s state of being doesn’t need quantum mechanics to understand: either it’s alive or it’s dead. (Other aspects of the cat aren’t important for this problem.) However, to describe the entire system using quantum mechanics leads to a paradox: the cat’s state of being is undetermined in the same way that an electron’s position is. Until you take a measurement (by opening the box in this case), the cat is in what is known as a superposition of states. It is neither dead nor alive, not because of lack of knowledge, but inherent uncertainty.

Schrödinger argued that this was a serious problem in interpreting quantum mechanics. We know the cat has to be alive or dead — there’s no meaningful sense in which it is both dead and alive at the same time. I won’t get into the question of whether the cat itself constitutes an observer, able to perform the “measurement” itself. If you want to remove consciousness (and cruelty) from the question, you could imagine a material that changes color when the Geiger counter triggers; the material exists in a superposition of red and blue until the box is opened. Similarly, you could argue that the Geiger counter that triggers the release of the cyanide gas constitutes a measurement, but you could imagine a simpler experiment in which the radiation directly changes the material’s color, removing the middle piece. The paradox remains. The main thing is that there should be a non-quantum system forced into a superposition by virtue of its interaction with a quantum system.

[Click for the full-sized comic. Credit: Zach Weinersmith]

[Click for the full-sized comic. Credit: Zach Weinersmith]

Lest you think this is purely academic, the physics version of asking how many angels can dance the Watusi on the head of a pin, we have a lot of devices that require quantum mechanics to work. Inside an ordinary digital camera, a small semiconductor device triggers when a photon — a particle of light — collides with it. Electrons are steered magnetically to trace patterns on the front of television screens to produce the images you see. (I had an argument with a Creationist colleague at Lambuth University, where I used to teach, about whether electrons could be said to exist or if they were speculative objects, since they cannot be seen directly. My response in part was to ask whether he had ever watched television.) The invisible and tiny manifest themselves macroscopically, whether or not a conscious observer is inserted into the system. Although these ordinary things don’t produce the kind of paradoxes inherent in the Schrödinger cat thought experiment, we still haven’t fully resolved the problem of interaction between quantum systems and things that (in a practical sense) don’t require quantum physics to describe.

I’ve mentioned in previous posts that I studied quantum measurement theory in my undergraduate days. That’s a fairly esoteric area of physics that actually grapples with these questions, and no real consensus exists on how to resolve the paradox. I won’t lie: I don’t have a nice simple pat answer to wrap things up. However, the real story of Schrödinger’s cat, as with so many myths in science, is more interesting — and far more illuminating — than the fake version.

[This post is based largely on a post I wrote two years ago. Don’t Lehrer me, bro.]

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