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The birth of quantum theory
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And those fuzzy probabilities apply to more than just the position of a particle. A lot of fuzziness also attaches to a particle's speed, angular momentum, spin and so on. If it's something we're interested in measuring, chances are we don't know what we're going to get in advance. These fuzzy probabilities are known as quantum states. They're neat mathematical equations that summarize all the probabilities of the particle property we want to probe.
That's all well and good — if horrendously mind-bending — but the real fun begins when we get two particles to share a quantum state.
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In certain circumstances, we can connect two particles in a quantum way, so that a single mathematical equation describes both sets of probabilities simultaneously. At first, that sounds innocent enough and probably like something only academics would care about, but something funny pops up with this so-called "entangled" state of two particles.
Let's look at an extremely simple, but surprisingly realistic, example. In the first outcome, one particle has a spin pointing up if you don't know what " spin " means here, don't worry, that's the subject of another article and doesn't really matter for this example. The other particle has spin pointing down. In the second possible outcome, the spins are flipped.
So far, so good. We prepare our entangled quantum state, send our particles off on their merry ways and begin to make our measurement.
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Taking a peek at the first particle, we find a spin pointing up. It could've been down just as easily, but this is like flipping a coin, and we just happened to catch an up-spin particle. What does this tell us about the second particle? Because we carefully arranged our entangled quantum state, we now know with percent certainty that the second particle must be pointing down. Its quantum state was entangled with that of the first particle, and as soon as one revelation is made, both revelations are made.