Can I infer that Schrödinger's cat is dead without opening the box, if I wait a thousand years?

Question

Say I have Schrödinger's cat in a sealed box. It is neither alive nor dead.

Given that cats have a lifespan of ~20 years, if I wait a thousand years, I should be able to infer with 100% certainty that the cat is dead. But if I can say with 100% certainty that the cat is dead, then I have "collapsed the wavefunction" without performing a measurement. How does that make sense?

The only way this seems to make sense is if cats are actually $\hat{cats}$, and the "cats operator" turns $\frac{1}{\sqrt{2}}\left(|dead\rangle+|alive\rangle\right)$ into $|dead\rangle$ over a period of approximately 20 years - but that conclusion seems rather bizarre on an intuitive level.

Answer 1

You have not collapsed the wave function. It will now be

$$\frac{1}{\sqrt{2}} \Big(| \mathrm{cat\ dead\ of\ old\ age}\rangle + | \mathrm{cat\ dead\ of\ cyanide\ poisoning}\rangle\Big).$$

(Of course, this assumes you left twenty years of food for the cat in the box.)

Answer 2

You are missing the point of the experiment. When we do the real experiment with simpler substitutes for the cat, both dead and alive refer to states that are stable eigenfunctions of the Hamiltonian, and so should stay as they are no matter how much time you wait.

It is phrased as a cat just so that you get a gut feeling that it is weird.

Answer 3

if I can say with 100% certainty that the cat is dead, then I have "collapsed the wavefunction"

I don't think so. "Collapsing the wave function" implies knowing the exact quantum state of every particle of matter inside the box. When we say that the cat either is "alive" or "dead" we're reducing all of that incomprehensible complexity to two macro states—two mutually exclusive subsets of the set of all possible states. Knowing whether the cat is alive or dead really is just a proxy for knowing the complete state of the contents of the box. It only gives you a single bit of information about the state, but what is represented by that single bit is enough to seed the philosophical discussion about what "collapse the wave function" really means.

After the cat's remains have been mouldering for 1000 years—when "alive" is the null set, and "dead" encompasses every possible state—then knowing that the cat must be dead tells you nothing at all about which of all of the possible states the box contents have reached.

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See also, @J.G.'s comment on your question. Maybe what I've said here is just an expansion of J.G.'s more concise observation.

Answer 4

The states "dead" and "alive" are obviously a simplification of the actual state of the cat. The full state of the cat is much more complicated - and includes the state of every single cell in its body, and so on. This full state evolves over time (according to the Schrodinger equation, according to the Hamiltonian operator H).

So the state you called "alive" continues to evolve according to H, and after 1000 years, it will evolve into something that looks like a decayed cat body. Both "dead" and "alive" states will evolve over 1000 years to something that looks the same. You can call the resulting state "decayed" - you can't call it "dead" because it's not the same "dead" that you get immediately after the mechanism kills a cat (which looks nothing like a decayed cat skelaton).

Answer 5

No. Schrödinger's experiment was a thought one, and was meant to show the paradox emerging from certain applications of quantum mechanics. It is not intended to get an experimental result, but rather illustrate a paradox of quantum superposition applied to real world objects. You are trying way too hard to be "smart", overthinking said thought experiment without understanding its purpose and conclusions, and getting something which makes no sense in the real world.

Answer 6

Being alive actually implies a whole lot of irreversible thermodynamic processes taking place. Same can be said about aging or dying. In this sense, the whole Schrödinger equation does not make sense (more precisely, it should not be taken literally), since the irreversible dynamics of cat dying excludes its possibility of being in a superposition of states.

Schrödinger likely was aware of that, since he was among the first to think seriously about the physics of life - see his book What is life?

Remark: But what did the cat die from?
Assuming that we can put a leaving creature into a superposition, and the cat is definitely dead after a thousand of years, the Schrödinger's question only changes from alive/dead to determining the cause of death: natural/poisoning.

Answer 7

There can't be a continuous time evolution operator that takes $\frac{1}{\sqrt{2}}\left(|dead\rangle+|alive\rangle\right)$ to $|dead\rangle$ and also takes $|dead\rangle$ to $|dead\rangle$, because it wouldn't be unitary. (It wouldn't be invertible; also, by linearity it would have to take $|alive\rangle$ to $(\sqrt2{-}1)|dead\rangle$, which isn't properly normalized.)

Time evolution could take $|alive\rangle$ to $|dead'\rangle$ and $|dead\rangle$ to $|dead''\rangle$, where $|dead'\rangle$ and $|dead''\rangle$ are orthogonal states in the subspace of ways to skin a cat, which has dimension greater than 1. One of them could be identical to $|dead\rangle$, but "realistically" neither would be. There would still be a collapse when you broke the seal and exposed the remains to the environment, because the environment interacts with more than just the deadness property of the remains.

Answer 8

In the Schrodinger's Cat thought experiment, the state of the cat is not really the interesting thing. Part of apparatus is a radioactive substance and Geiger counter. When the Geiger counter detects a decay of the substance, it triggers release of a poisonous gas that kills the cat.

While we know that the cat will eventually die due to natural aging, what we're really interested in is whether the substance has decayed, as this is a random quantum-mechanical process. The cat's aliveness is simply a proxy for that, intended to be more illustrative of the strange implications of QM. We could easily remove the cat from this process and talk about whether the box has any of the gas in it; if the gas is colored red, we could say that until we open the box, it contains a superposition of clear air and red gas.

For the purposes of this experiment, other causes of the cat dying or the gas being released are irrelevant.

Answer 9

All the smart and correct explanations have already been made, however, consider this:

The experiment has not changed at all, just the definitions did (slightly).

Now the question that cannot be answered until you open the box is no longer "did the cat die, or did the cat live", it is "did the cat die from the random poison trigger thing, or did the cat die from old age/starvation/whatever".

This can then be rewritten as two following questions instead, only answered by opening the box:

"did the random trigger thing happen (and the cat died from it)" OR "did the random trigger thing not happen (and the cat stayed alive)"

and

"did the random trigger thing happen (and the cat died from it)" OR "did the random trigger thing not happen (and the cat died by other means)".

The statements in parentheses are observations made by opening the box, while the statements outside are the information gained by making these observations.

If the observation part is removed, the questions become both the same (i.e., "did the random trigger thing happen?"), while the observed state of the cat is different by how the experiment is conducted, the thing that is uncertain until those observations are made is exactly the same, and therefore, the exact same "something that can be one or the other, but is unknown until it is observed" situation applies.

The cat is just an indicator of the state - if we change the way the indicator works, we are not changing the state in any way.

Therefore, the whole Schrödinger's cat experiment is essentially the same, although none of the possible outcomes are favourable for the cat.

Answer 10

There are no physical laws stating that cats have a life time of (for example) 20, 50, .... years.

It follows that the observer can only know the state of the cat (alive or dead) is by opening the box.

Answer 11

Yes, you can infer the cat is dead after 1,000 years, but you can't infer that the cat died of cyanide poisoning or old age, actually you can probably infer it didn't die of old age since it would starve to death within a week or two, but you can't infer if it was poisoned or starved to death. Strange that you say "how does that make sense?" since the entire point of Schrodeingers thought experiments was to demonstrate the absurdity of the Copenhagen interpretation, i.e. it doesn't make sense if the way its originally intended.

Whenever I hear or read "collapsed the wavefunction" my brain translates the phrase into "Abracadabra".

Answer 12

No, because this misses the point. It's not important that the metaphor uses a cat. Getting into irrelevant hypotheticals, like how it would eat, or its natural lifespan, isn't a meaningful way to engage with the topic.

Now, if that's your idea of a fun party conversation, go for it! :D

Answer 13

If the reasoning of alive or dead is the point, then equally there is no scientific method/proof that the cat still exists until the box is opened.