Monday, November 18, 2013

Schrödinger’s cat


Schrödinger’s cat is often used to illustrate the absurd nature of quantum mechanics. Schrödinger devised the thought experiment to highlight the paradox implicit in the fact of entanglement. We are told that the cat is neither alive or dead (or alternatively, that is both alive and dead) until we open the lid of the box, at which point the wave function describing the cat’s state is said to collapse into one or the other state. See this article for a good description of this thought experiment.

We are told that opening the box is an “observation”, and that it is the act of observation that causes the wave function to collapse. Opening the box kills the cat, or saves its life. Schrödinger devised this absurd thought experiment in order to clarify the paradoxes that appear to arise from entanglement.


I understand entanglement as follows: two particles interact. They leave each other’s vicinity. The mathematics of quantum mechanics imply that until one of the particles is “observed” or “measured”, we cannot know which particle is in which state. However, when one of the articles is observed to have State S, the other will be in the complementary state S’. The usual interpretation is that until the measurement is done, the particles are in both states, which are said to be superposed on each other. The measurement forces the collapse of the indefinite state of the measured particle into one of the two possible states.


Experiments have been done that show precisely this state of affairs. The question is whether the interpretation of the model is correct: Are the two particles actually in indefinite states until they are measured? Or is it merely the case that we cannot know which particle is in which state until we measure one of them? Note that measurement is an interaction. So the more accurate question is, Are particles that have interacted in some indefinite state until their next interaction? Or is it the case that we cannot know anything about the states of particles unless and until we arrange some interaction that results in effects large enough that we can both observe those effects and infer the states that caused them?



I think that QM is ultimately about the limits of knowledge, about what we can and cannot know about particles. Until we measure the particles, we can’t know what the result will be. More importantly, according to Heisenberg’s principle, the act of measuring the particles changes their states. Measurement or observation is not a privileged interaction. It’s just the one of many possible interactions, and it will be followed by another one, and then another one, and so on.


The Copenhagen interpretation argues that the two particles are in superposed states until they are measured, at which point one of two possible states becomes real in some sense, and thus constrains the next interaction. The many-worlds interpretation argues that whenever the function collapses, both possible outcomes become real, and ontologically separated from each other. I think both interpretations miss a fundamental point: QM, like any other theory, is a model. A model explains the observations (data) that have been observed or predicted. It can’t explain what isn’t part of it or isn't implied by it. Interpreting QM ontologically or metaphysically is absurd.


Schrodinger’s cat is alive or dead, as the case may, before we open the box. Our observation doesn’t cause cat to live or die: the radioactive atom that did or did not decay caused that.   
           

WEK 2013-11-18

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