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VAuroch comments on Decoherence - Less Wrong
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If instead we'd started out with a big light-gray square - meaning that both particles had amplitude-factors widely spread - then the second law of thermodynamics would prohibit the combined system from developing into a tight dark-gray diagonal line.
What would the result look like, then? Amplitude would still flow towards configurations where the thingies are at the same horizontal position.
Not really. If both particles are widely-spread, then they will remain widely spread. Say the heavy particle is evenly distributed across the interval [0,2] and the light particle spread evenly across [0,3]. Then the resulting system will have both particles spread evenly across [0,2.0] (approximately; the large particle will move out somewhat), and the light particle will be approx. 50% more dense at each of those points.