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So if I understood correctly, Schrödinger's Cat is a thought experiment that puts a cat inside a box, and there's a mechanism that kills the cat with 50% probability based on a quantum process. The argument is that the cat now must be in a superposition of dead and alive.

This makes sense at first, but the state of the cat inside the box will affect the outside world in an observable way, right? For example if the cat dies, it might meow loudly which would be audible. If it didn't meow, it would produce a thud on the ground when it dies. And even if the ground was very solid, the redistribution of mass inside the box will affects its gravity field which means the whole universe theoretically immediately observe's the cat's death.

So extending this argument to all superpositions, the different states would cause different effects on the rest of the universe, usually a slight change in the gravity field is the minimum. This gravity perturbation would propagate throughout the universe, and even all the experimenters go to sleep with thick, thick earplugs, somebody or something in the universe is going to inadvertently observe the event and the superposition immediately collapses. Thus superpositions cannot exist beyond an extremely short amount of time.

What's wrong with my reasoning?

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7 Answers 7

up vote 8 down vote accepted

What's wrong with my reasoning?

Nothing! In fact you have more or less described decoherence. The idea is that any system inevitably interacts with its environment, and the more degrees of freedom the system has, i.e. the more complex it is, the faster it will interact with the rest of the universe and the superposed states will decohere.

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I don't think this addresses the issue. A decoherent superposition is still a superposition. The decoherence of the cat would be relevant if you were trying to diffract the cat through a double slit. Decoherence can be eliminated in principle. The fundamental issue raised by Schrodinger's cat is the possibility of nonclassical correlations between things that are separated from each other by macroscopic distances. This possibility is a fundamental type of weirdness in quantum mechanics. –  Ben Crowell May 4 '13 at 16:13
    
@BenCrowell You forget that the Physicist making the experiment is himself Decoherent. –  Karl Damgaard Asmussen Jun 21 '13 at 2:31

You don't explicitly say so, but you're assuming the Copenhagen interpretation (CI) rather than the many-worlds interpretation (MWI).

Your analysis is a perfectly good example of why the CI doesn't fundamentally make much sense. The CI treats measurement as a process that's different from other processes, even though measurement is a physical interaction that proceeds according to the same laws of physics as any other process. The CI says that measurement has the magic power to collapse the wavefunction, but that doesn't make sense because measurement isn't different from other physical processes. There is no fundamental distinction between a process in which a human looks inside the box and a process in which the cat interacts with the outside world through some other mechanism (the meow or the disturbance in the gravitational field).

The distinction between measurement and other processes is a psychological one, not a fundamental physical one, and the CI succeeds because it does a good job of describing the psychological experience of making a measurement.

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+1 Best argument against CI I've seen yet. Unfortunately I really dislike MWI too! –  Brandon Enright May 4 '13 at 16:42
    
@BrandonEnright CI is a kludge, but it is a very useful and tested kludge that allows us to do complex, sensitive experiments and interpret the results we see. I don't understand how MW allows one to interpret the results of laboratory experiments in a practical way (end rant). –  Jason A May 4 '13 at 18:21
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The fact that CI isn't perfect doesn't mean MWI is the right one. –  Bzazz May 4 '13 at 20:44
    
@JasonA: I agree that CI is a useful and tested kludge. However, I don't think that it's necessary to give experiments an interpretation, if "interpretation" means a psychologically compelling story about the experiment we've just done. MWI just isn't psychologically compelling because we can't feel our own brains to be in a superposition of states. –  Ben Crowell May 4 '13 at 21:10
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@EricDong: I don't think that's a correct characterization of MWI. MWI doesn't describe the universe as undergoing bifurcations at discrete moments in time, although people may depict it that way cartoonishly. –  Ben Crowell May 5 '13 at 14:31

I have always disliked this thought experiment because, even though it was proposed as an amplifier of quantum mechanical effects, it is really nothing more than a game on probability, and one can get random probabilities by many classical means.

Toss a coin, heads cat alive tails cat dead. The concept of both alive and dead is ridiculous in the macroscopic context. Certainly the cat would not care if it were a quantum mechanical or classical poison machine.

It appeals to people who cannot wrap their head around the concept that the square of the QM wave-function predicts a probability distribution in (x,y,z,t) for finding the whole particle at that (x,y,z,t), not a fraction of it. It says nothing about the particle being spread out all over the place: we know nothing until a measurement tells us, and in the case of the cat it is just an inhumane detector. An on-off light as a QM detector would do instead, it either will be be on or off: the neither on or off concept is ridiculous and unscientific, even if one were not looking at the light..

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The cat might care, since the coin is large enough that we can predict its motion, given enough information, using completely deterministic Newtonian physics to a sufficiently accurate degree to predict head/tails. Or so I think ;) –  user54609 May 6 '13 at 1:13

In my view you've muddied the waters. The cat is assumed to be unobservable. But if you allow sight and sound, then you are in fact observing the cat and the corresponding superimposition of wave functions will collapse.

If you want to worry about something, imagine the cat in a cage embedded in a wall but visible from both sides of the wall. On one side the cage is covered and the usual observers are present. They describe the cat as having a superimposition of wave functions. Now on the other side (and the two sides are not in communication) the cat is perfectly visible. In that case the cat is described by a single "pure state" wavefunction at all times. If the cat dies during the period of observation, those watching the cat describe the change in wavefunction as a change in state, much as we'd describe the electron in a hydrogen atom moving from energy level to energy level.

So in this situation we have TWO different but equally valid quantum descriptions for the cat. Rationalize this!

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Superpositions can exist without problem until infinity. Basically everything including me only exists if your look (measure it). QM is very weired and that why most who are responsible for QM like Schrödinger and Einstein felt very uncomfortable with its philosophical side effects. Thats where the cat comes in. From the scientist point of view it does matter when its decided if the cat dies or not.

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What's wrong with my reasoning?

The box is of course supposed to be "closed" such that any observations that may be collected "at the outside" allow the conclusion that "the cat is inside, not outside", but under no circumstance any characterization of the cat in terms of "live or dead" or "having survived or having died".

A "meow from the box", however loud and shrill and indeed unavoidably audible "at the outside", is in this sense not supposed to be in any way indicative of whether or not the cat is about to expire;
a "thud on the ground" is meant to be attributable to a "cat having fallen dead" just as well as to a "cat having fallen asleep, but living on".

The suitably idealized measurement operators "fate of the cat" (with value range "having survided" or "having died") and "confinement of the cat" (with value range "inside the box" or "outside the box") are meant to be strictly incompatible operators. Observations which are sufficient for determining the "fate of the cat" should therefore in turn not in any way indicate whether the cat "has been entirely inside the box, or outside the box". Just as the state of "being in the box" can formally be expressed as superposition of "having survived" and "having died" (and correspondingly the state of "being outside the box", too), the state of "having survived" should be formally expressible as superposition of "being in the box" and "being outside" (and likewise the state of "having died".

Specificly, after lifting the lid of the box (and vigorously shaking it, just in case), and again closing the lid, the cat might in any case be found "outside the box"; and it might then count as "having survided" if, after again lifting and then closing the lid even repeatedly it would at least sometimes be found again "inside the box"; or correspondingly as "having died in the box" if, after lifting and closing the lid repeatedly, it would always be found "outside the box".

What counts as “observation” in Schrödinger's Cat

When considering any particular measurement operator one can distinguish the (sets of) observations which allow some particular value to be derived as "result of the measurement", by applying the operator under consideration on one hand, and on the other hand any other (set of) observations. Both cases may include observations which were collected in actual trials as well as hypothetical descriptions of observations.

As sketched above, the (actual, or hypothetically imaginable) sets of observations which count towards determining whether "the cat is inside" or "the cat is outside" are different from the (actual, or hypothetically imaginable) sets of observations which count towards determining whether "the cat had survided" or "the cat had died".

And of course there are many other (actual, or hypothetically imaginable) observations which have no relevance to either determination.

and why are superpositions possible?

The salient description of the state of the cat before the lid had been lifted is of course "the cat is inside, not outside", which is an eigenstate of the "confinement operator". Expressing this state instead as "half surviving and half dead, with a suitable phase between these parts" makes the relation to eigenstates of the "fate operator" explicit, and depends on the relations between the correspondingly relevant sets of observations.

So -- writing some particular state as superposition is certainly possible as an abstract expression. However, and here I believe to side with Schrödinger, it seems unpalatable to consider any formal superposition if it couldn't be primarily understood as eigenstate of a suitable operator.

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Based on past experience and researching Schroëdinger's cat and superpositions, I would say that this is incorrect. Hearing a sound wave would technically be observation, and so would a photon of light(the redistribution of mass inside the box), so your points would be valid, except that they completely corrupt the experiment.

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I'm not exactly sure what the main point of the answer is, but hearing a sound wave from the cat is an observation that confirms it is alive. –  David Z Jun 20 '13 at 17:22
    
When I say sound wave, I mean the supposed thud from the cat, or the loud meow before it dies. –  user1861805 Jun 22 '13 at 14:09

protected by Qmechanic Jun 20 '13 at 15:30

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