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5 comentarios en “Jeroglifico. Biografia matematica.”

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  2. Hmmm. I’m not sure I agree with the premise. Perhaps you sldohun’t try to generalize the percent sign in the first place.Why? Because, in a nutshell, it promotes a deceptive intuition, which is that superpositions really are, in some sense, mixtures of a particular basis.Of course, we all know and abhor the preferred ensemble fallacy. We still teach it that way, though: Here’s the |+> state; it’s a superposition of |0> and |1>. We do that because this stuff makes no sense at all to students at first, and a gentle seduction is needed. It’s wrong, though |+> isn’t a superposition of |0> and |1> in any fundamental sense, any more than it’s a superposition of a bajillion other orthogonal pairs. It’s a state all of its own, and it’s got rights, dammit! Every state is precious!Tuning down the facetious rhetoric, my point is that per cent is an ancient term that implies probabilistic, convex combination. Mud is 50% dirt and 50% water; take 100 parts of mud, and it can be separated into 50 of dirt and 50 of water. We have a concept like that in quantum mechanics, convex combination, and it works just like the classical case. Students often absorb the misconception that somehow classical mixture gets replaced with quantum superposition which, of course, isn’t true at all. Superposition is new, different, and freakin’ weird!I’d rather see somebody try to teach quantum mechanics _without_ using superposition notation (at least for a while), than see a snazzy notation for it. For one thing, more students might say, Wait, how the heck do we pick a basis? which is a darn good question. Superposition notation can imply a preferred basis, which in turn induces an unjustified comfortability with something that’s really a fairly major conceptual issue.*quietly breaks down soapbox, exits stage left*

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