a blog about things that I've been thinking hard about

The Cat is Not in a Mixed State because the Box Leaks Information (Very, Very Quickly)

13 April, 2006
the cat already died, or not

Before you opened the box, information about the cat's state leaked out.

Even a tiny amount of "leakage" results in decoherence.

Decoherence results in correlation of wave functions.

The correlated cat is, relative to your own quantum state, either dead or alive.


A Short Explanation of Schroedinger's Cat

My intention with this article was to write the shortest possible explanation of what is really going on with Schroedinger's Cat.

In the end I wrote two explanations – one short, and one slightly longer.

The shorter explanation is in the title of this article, and the longer one is in the blurb.

So, what did you think of them?

Spelling it Out in Even More Detail

When you do Schroedinger's thought experiment, you are required to think of the box as hiding the cat's state until after you open the lid to see what happened. Unfortunately, this isn't thinking, it's just fantasy. In real life, information about the cat's fate escapes very, very rapidly (approaching the speed of light, I think) as soon as the cat dies, or not, as the case may be. And there is no box ever made that can completely prevent the information from leaking out.

For example, if the cat is still alive, you will hear the cat moving around inside the box. If it dies, you will hear the muffled thump as it hits the floor. When you hear one sound or the other, you already "know" what happened to the cat, before you open the lid, even if you don't realise that you know it.

And the perception does not even have to be as direct as consciously perceiving a sound that the cat makes. As long as the cat's state is correlated with any macroscopic variable which is correlated with something else, even very indirectly, and you consciously perceive that something else, then the wave function of your consciousness is going to be correlated with the wave function of the cat.

Another issue is exactly how quickly the correlation propagates. For example, vibrational effects only travel at the speed of sound. If correlation is only propagated at the speed of sound, then a mixed state does exist for a finite measurable period of time.

But maybe other types of information propagation are sufficient. No doubt there are significant electromagnetic effects – probably the cat has a slight electric charge on it's fur. (Changes in static electric field would travel at close to the speed of light.) Maybe the difference in gravitational field between a live and a dead cat is enough to correlate your wave function and the cat's wave function. (And we know that gravitational waves travel at the speed of light.)

Self-Disclosure: An Everett Fan

I confess that I am a fan of the non-collapsing-wave-function-of-the-universe interpretation of quantum mechanics, otherwise known as the "Many Worlds" (Everett) interpretation. So I have to talk about the cat's wavefunction correlating with that of the observer, rather than the cat's wavefunction collapsing.

Whether you prefer Everett or Bohr (i.e. the Copenhagen interpretation), I don't think your preference makes a whole lot of difference to the correctness and relevance of the "leaky box" explanation.

Some References

The technical name for correlation caused by information leakage is decoherence. So if you want to research the topic via Google (or any other search engine), you need to search for "Schroedinger's Cat" and "decoherence".

Some interesting links I found from this search are:

Follow-up Questions

Even as the concept of decoherence saves us from having to imagine the mixed alive/dead cat state, it does leave a few questions open. These are mostly along the lines of: if we can't really prepare a cat in a mixed state which survives for an indefinite period of time, how much can we do?

Four questions that I can think of are:

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