Special Sub-Topic: The Curious Tale of Schrodinger's Cat
|The curious situation of Erwin Schrödinger's cat sets physicists to growling, but it's actually quite simple to describe. The unfortunate feline is sealed into a box. The box has plenty of air, but it also has a vial of poisonous gas -- which will be released if a single unstable atom (also in the box) decays. Why did Schrödinger choose radioactive decay as the quantum process that would trigger the paradox?|
Because it is a truly random process. It turns out that it's hard to devise something that's truly random. Even seemingly random things, like the "random number generator" built into your computer (or FunTrivia's), often have an underlying pattern -- they're pseudo-random. For a paradox like that of Schrödinger's cat -- which relies on the outside observer not knowing or predicting what's happening inside the box until it's been opened -- we really do need something random to drive the action. The radioactive decay of an atom is one of the few truly random processes in nature: we can predict the decay of a large number of atoms pretty well (it's governed by their half-life, the length of time after which we expect half the atoms in a sample to have decayed), but we can't predict at what moment any single atom will decay.
|So Schrödinger's cat is in a box, along with a poisonous gas that will be released if one atom undergoes radioactive decay. Which of these items can be used to detect the decay of an atom, and thus to cause the release of the gas?|
A Geiger counter. Geiger counters, named for physicist Hans Geiger, detect ionizing radiation -- that is, radiation with enough energy to strip an electron from an atom or a molecule. The design is simple: a typical Geiger counter is a metal tube filled with an inert gas like helium. A thin wire runs along the center of the tube, and it carries a high voltage relative to the tube walls. When a particle of ionizing radiation passes through the tube, it ionizes an atom of the gas -- and the newly freed components of that atom ionize other atoms in a cascade. The gas is thus briefly able to conduct electricity, leading to a current on the wire. This current might rotate a needle on a dial or register as a distinctive click, depending on the device's design. A Geiger counter is a magnificently sensitive instrument, which is why Schrödinger pressed it into service for his imaginary experiment; in his set-up, a single count would release a hammer, which in turn would smash the vial of poisonous gas.
|Let's take a quantum-mechanical look at what's happening to Schrödinger's cat. Either the atom has decayed and the cat is in quantum heaven, or the atom and the cat are intact. Physicists describe this kind of situation with something called a wave function, which includes what important information?|
The probability of observing each possible outcome. A wave function is a mathematical way of describing a physical system, so named because, in quantum mechanics, it helps to think of physical objects as waves. Wave functions, which are really vectors, can be constructed by adding up the perpendicular unit vectors for each possible state of the system, with each state vector multiplied by a complex coefficient. Squaring that coefficient gives the probability of measuring the system in the corresponding state.
If you find this confusing, you're in very good company. The paradox of Schrödinger's cat is designed to illuminate the gaps in this idea: what does a wave function really signify physically, and just what is involved in a measurement? Continue on, and you'll see that physicists disagree on these matters even today.
|The box is sealed. Schrödinger's cat is inside with its owner's deadly apparatus. You might think that it's either alive or dead, but you'd be wrong: many quantum physicists would say that it's BOTH alive and dead. The cat somehow exists in both possible states until the universe is forced to make up its mind. What is this strange situation called?|
A superposition of states. The idea here is that -- until we somehow force the universe's hand -- a physical system simultaneously exists in all the states that are available to it. This is why, when discussing atomic structure, we no longer talk about an electron having some well-defined orbit like a planet does; instead, we talk about an electron "cloud," because the electron is everywhere that it's allowed to be. This is strange enough behavior for electrons; for a cat, it's much harder to swallow!
|The mathematical description of Schrödinger's cat is made even more complicated by the fact that it doesn't just describe the cat. If you know the state of the cat, you also know the state of the radioactive atom and (eventually) of the observer. What is the name for this deep connection between the quantum states of different physical objects?|
Entanglement. Entanglement may seem a simple concept, but it gives rise to some very strange behavior. In this case, for example, entanglement forces a classical entity (the cat) to behave in a distinctly quantum way. In other scenarios, it can lead to things like the measurement of one particle affecting the behavior of its entangled partner -- even when the two are light years apart, a phenomenon Albert Einstein famously mocked as "spooky action at a distance." Entanglement is the basis of the emerging field of quantum cryptography, where researchers honor Schrödinger's feline by calling certain flavors of entanglement "cat states."
|Well, this is awkward: we have a cat in a box, and it's somehow both alive and dead at the same time. What's a physicist to do? According to the popular Copenhagen interpretation, this confused state of affairs won't last forever. At what point does it say the cat will settle into a single, well-defined state of being?|
When it is observed. The cat's status is described by a wave function showing equal parts liveness and deadness. When the cat's state is measured, only one of these possibilities is observed, and the wave function collapses to just that one outcome: another measurement, taken immediately afterward, will yield the same result. The Copenhagen interpretation is powerful, but leaves some important issues unsettled -- particularly the question of just what "measurement" means. Can the cat (or even the Geiger counter or the decaying atom) observe itself and collapse its own wave function? Or is the only observer worth mentioning the one standing ready to open the box -- and if so, what makes him or her special?
|Another school of thought tries to avoid the Copenhagen interpretation's problems entirely, by proposing a branching universe. The idea is that the cat is still both alive and dead after the box is opened, but that the universe has branched: one universe has a live cat and the other has a dead cat, and the two proceed independently of each other. What is this method for interpreting quantum mechanics called?|
Many-worlds interpretation. First formulated in 1957 by Hugh Everett, the many-worlds interpretation holds that every possible outcome of a quantum process really does happen -- but each in its own universe, decoupled from each other and not affecting each other in any way. In this interpretation, the observer isn't special -- he or she is just one of a number of identical observers in newly separated universes -- so these embarrassing observation-related paradoxes just fall away. Plus, the idea of a (perhaps infinitely) branching multiverse makes for excellent science fiction.
|Still other physicists argue that the Schrödinger's cat problem is a problem only because it's too narrow in scope. Of course it doesn't make sense if you think about a single cat: you have to think about hundreds or thousands of cats, each in an identical box. What term, more familiar in statistical mechanics or in dance troupes, describes this situation?|
Ensemble. "Ensemble" is French for "together," and in physics it refers to a large collection of identical experiments -- temperature baths, engines, cats in boxes, whatever. The key here is that the laws of statistics have greater predictive power for larger numbers of measurements. For example, it's easy to predict the outcome of 1000 coin tosses -- 500 heads and 500 tails -- and be right to within less than a percent (a couple of flips). It's much harder to predict the outcome of ten flips to that level of precision. Proponents of the ensemble interpretation argue that it's meaningless to talk about this experiment as applied to a single cat, and that's why you see apparent contradictions. When you're talking about 100,000 cats, you avoid the messy situation of having a single cat be half-dead and half-alive.
|At this point, you might be wondering how normal cats manage to get through the day without triggering multiple physical and philosophical paradoxes. Luckily, cats usually behave according to the much more intuitive rules of classical physics. But a cat is made of quantum particles; why wouldn't it behave as a quantum object? Name the mechanism by which quantum systems give rise to classical behavior.|
Quantum decoherence. Classical physics -- the physics developed by the likes of Galileo, Newton, and Maxwell -- does a great job of explaining most of the physics we see on an everyday basis. But when you start looking more closely, classical physics begins to break down: we need general relativity to explain Mercury's orbit, for example, and quantum mechanics to explain everything from the workings of atoms to the light emitted by stars. Quantum decoherence explains how, on large scales, quantum behavior gives way to something that can be approximated by classical laws. Through interaction with its environment, the system essentially loses information, and the different components of its wave function no longer interfere with each other.
|Schrödinger's cat and its box never really existed, of course: they were figments of Erwin Schrödinger's fertile imagination. The quantum feline is part of a long, grand tradition in physics: that of reasoning through some hypothetical (and often technically impossible) situation in order to understand the implications of a theory. What is this type of exercise called?|
A thought experiment. A thought experiment (also called a gedanken experiment, from the German) is a more rigorous way of asking, "Hey, what if ...?" Like Schrödinger's cat, it can be used to explore the quirks or inconsistencies of a theory. Or a thought experiment might help you to formulate the theory in the first place. For example, Albert Einstein worked through many of the concepts in his theory of special relativity by conducting thought experiments: imagining an observer traveling alongside a beam of light, for example, or in an elevator orbiting the earth in free fall.
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