# What is the deal with the Schrodinger's cat? Why is it considered a paradox?

What is the deal with the Schrodinger's cat? Why is it considered a paradox?

Cat is a macro object. He can be only in 2 states - he's either dead or alive, the fact that you don't have the information about his state doesn't mean he is in both states at ones.

The sun in the Alpha-Centauri system has defined properties whether or not you have the information about its state. Plus, the current information about its state is going to reach you only several light years later, depending on how far away you are, why should it care about your "collapsing probability"?

Why don't physicists look at the "probability collapse" just as the transfer of the state information? It only collapses for you, not for the object itself. "Probability collapse" basically means "I now know the state of the object", but the object is always in one state or the other whether or not you have the information about its current state, isn't it?

The correct answer has been given by ZeroTheHero but I would like to add my two pennies worth.

Cat is a macro object. He can be only in 2 states

this is incorrect: any linear combination thereof is a possible state the particle (the cat) can be in; namely assuming that our observables of the whole theory have a set of (mutual) eigenstates $|a\rangle, |d\rangle$ where $a$ (respectively $d$) stands for "alive" (respectively "dead") then any linear combination $|\psi\rangle = c_1|a\rangle + c_2 |d\rangle$ is a good state for the theory.

the fact that you don't have the information about his state doesn't mean he is in both states at ones

nobody said the cat is ever in both states: it is in a linear combination thereof, whatever this means.

The sun in the Alpha-Centauri system has defined properties whether or not you have the information about its state

this is slightly incorrect as well. In classical mechanics an observable has a precise value: whether or not the observer is actually able to perform a measurement (with or without error) those values exist and are unique. In quantum mechanics, instead, the underlying assumption is that observables do not have precisely determined values - rather, their values are distributed with some probabilities and if we were able to perform an infinite amount of measurements then each and every single value would occur at least once (say, with non-zero probability); this is a postulate: whether or not it is true it is another matter (that we do not discuss in here) but the take home message is that there is no such thing as the precise values of an observable.

It only collapses for you, not for the object itself

well, we may say for sure that it collapses for us but we cannot infer that it does not collapse for the object as, by definition, our realm of understanding only extends to ourselves (therefore no statement about what truly happens to the object makes sense).

but the object is always in one state or the other whether or not you have the information about its current state, isn't it?

this is something that we cannot really tell, as it is outside the scope of the measurement, again. We can only tell what we have observed, but whether or not the object still maintains its initial state is unknown.

As a side note, notice that a cat (or the sun, or any other object that is macroscopic) undergoes some sort of quantum decoherence and hence it somehow behaves more or less classically (more or less).

Well first off, it's not a paradox. It's an illustration. Specifically, it's an illustration of:

Cat is a macro object. He can be only in 2 states

Macroscopic objects like cats have distinct states like "live" or "dead". Microscopic objects, like quantum observables, do not have two states, they can exist in a mixture. People did not like this, famously Einstein, and many simply threw up their hands and said 'well it's only microscopic so who cares!"

Schrodinger's cat is an attempt to show that that last statement is wrong.

The box contains a decaying atom which we knew beyond hope at that point really could be both decayed and not decayed at the same time. We call this "superposition". I should point out that most "observables" have much more than two states, like "position" which is basically continuous, but he deliberately chose one with two distinct states to make it simpler to understand.

Ok, so due to the setup, if the atom is decayed then the cat is dead, and if its not, he's alive. But the atom isn't either of those things, its both. So then what state is the cat in?

the fact that you don't have the information about his state doesn't mean he is in both states at ones.

That's exactly what it means.

I prefer to think of it in slightly different terms, I say there is a 50% real dead cat and a 50% real live cat. It's only when you collapse the state of that particle that one of those two becomes 100% real and the other 0% real. It is the purpose of the thought experiment to show that the weirdness "leaks out" of the microscopic world.

Now the pedants among the physics world generally dismiss this thought experiment with the wave of a hand. They tend to invoke a bit of magic called decoherence and suggest that you don't need to open the box because it's interactions with the real world essentially do that for you. You might not be looking inside, but certainly the photons from the sun are.

The problem is that it is possible to construct real-world experiments where the collapse can be isolated enough to end up with this same result. And this is the thing that really freaks people out, we still have no idea what "collapse" is, but it's core to the entire concept. There's various suggestions, and theories with no collapse, but none seem terribly convincing.

Now if you want to get really freaked out, what if there is someone watching you carry out the experiment? Does the original particle only collapse when they look at you? So does that mean you're only 50% real? That quickly leads to madness...

The sun in the Alpha-Centauri system has defined properties whether or not you have the information about its state

Nope, not at all. And this has been demonstrated in the lab, repeatedly. This is what Aspect's experiment showed, for instance, by changing the measurements in mid-flight of the particles.

• There are some incorrect points in this answer: a linear combination of basis elements (as element of a Hilbert space) is not a mixture: mixture states in QM are something different (described by the density matrix). Also "could be both decayed and not decayed at the same time. We call this superposition" no, not really: superposition doesn't mean it is both at the same time, it means it is another state which is constructed as combination of both. – gented Sep 13 '17 at 21:03
• Moreover "I prefer to think of it in slightly different terms, I say there is a 50% real dead cat and a 50% real live cat" again, this seems to miss the point: a superposition is not a little of this and a little of that, it is another state and that's it. – gented Sep 13 '17 at 21:07
• Both are true, but at the same time, are somewhat outside the context of this issue. Given the context of the thought experiment, the precise math of the state vector is not really interesting. Nor is the fact that those states are very similar for live and dead cats, even though that would seem to be a vital point at first glance. – Maury Markowitz Sep 14 '17 at 10:24
• No, again, this is a mistake. They are not true at the same time; the thought experiment makes sense only in the context of QM, where one can construct a state as linear combination of basis elements. If you disregard it then there is no point in discussing the QM anymore: it seems to me that you are trying to ontologically "interpret" the experiment when there is really nothing to interpret at all (if you write everything down correctly). – gented Sep 14 '17 at 11:24
• The statement "both are true" is referring to your statements. I am agreeing that your statements are correct. Are you saying they are not correct? Were you lying? /s – Maury Markowitz Sep 14 '17 at 13:06

The interesting feature of superpositions is that the total quantum state is not in either one or the other basis state of the superposition, only to be revealed upon measurement.

For instance, if you are asked to select from a blue and a green sox, place one in a box and give this box to a friend, the sox is NOT in a superposition of green and blue until your friend opens the box.

There is ample evidence to show that one must consider a quantum state as a true superposition, and that the measurement process causes the collapse. (See for instance the gedanken experiments with various Stern-Gerlach experiments in Feynman's lectures, in Sakurai's book or in the QM book by John Townsend.) In this sense, the cat is alive and dead until one opens the box.

The cat is clearly a macroscopic object that functions as a stand-in for a two-state system (such as a spin-1/2 particle if you want to tie this perhaps loosely with Stern-Gerlach apparatus - obviously here is there is no such thing as alive or dead along different axes), but superposition experiments on macroscopic objects have been proposed and appear to be within the realm of the possible. One application suggested in the linked article could be "a new technique for monitoring defects in biological molecules".

Edit

There is an obvious and essential difference between superpositions of states for some spin-1/2 particle and for a cat. If we have a pure spin-1/2 state $\vert \hat n\rangle$, then we can always find some linear combination of spin operators $\sigma_{\hat n}$ with $\vert \hat n\rangle$ as an eigenvector. Thus, it makes perfect sense to think of $\vert \hat n\rangle$ as a single state, which can be expanded in - say - a basis of eigenstates of $\sigma_z$ so that $$\vert \hat n\rangle = \cos\left(\textstyle\frac{\theta}{2}\right)\vert +\rangle_z + e^{i\phi}\sin\left(\textstyle\frac{\theta}{2}\right) \vert -\rangle_z\, , \tag{1}$$ for some $\theta$ and $\phi$. Whether one chooses to describe (1) as a state that is spin-up and spin-down (with suitable probabilities) until one makes a measurement with $\sigma_z$, or as a single quantum state expanded on two basis states is a matter of semantics: both description will lead to the same results. If we measure $\sigma_z$: some of the time the outcome will be spin-up, some of the time the outcome will be spin-down. Moreover, if we measure in the direction $\hat n$, there will be a single outcome.

Of course, things are different for a cat. There is no "zombie" operator $\sigma_{\hbox{zombie}}$ with eigenstate $$\vert\hbox{zombie}\rangle= \cos\left(\textstyle\frac{\theta}{2}\right)\vert \hbox{dead}\rangle + e^{i\phi}\sin\left(\textstyle\frac{\theta}{2}\right) \vert \hbox{alive}\rangle\, . \tag{2}$$ The sense of the superposition (2) as a single quantum state eigenstate of a non-existent $\sigma_{\hbox{zombie}}$ operator, and thus analog of $\vert \hat n\rangle$ is rather abstract, but the sense of the superposition of alive and dead cat is quite clear as a generalization of the right hand side of (1).

• Thanks for the clarification. Too bad we didn't evolve to understand quantum mechanics on the lowest level. It's fascinating how we can build quantum computers but don't really understand everything about the quantum processes themselves – Un1 Sep 13 '17 at 19:48
• @ZeroTheHero why do you say "In this sense, the cat is alive and dead until one opens the box." I thought it (the quantum state) was in a superposition, which is different from being in 2 states at once in that the wave function hasn't collapsed into any state. – thermomagnetic condensed boson Sep 13 '17 at 20:34
• @no_choice99 You are not incorrect: the semantics of what is a superposition is subtle: a superposition (of two basis states) is one quantum state but with two possible outcomes. – ZeroTheHero Sep 13 '17 at 21:26
• I don't understand why it matters at all to find an operator having $|\hat{n}\rangle$ (or in your terminology $|\textrm{zombie}\rangle$) as eigenstate: a linear combination is always a "good" quantum state whether or not it is eigenstate of some operators. – gented Sep 14 '17 at 9:01
• @GennaroTedesco We like to think that the choice of basis states is a matter of convenience, that expanding a vector is this basis is convenient etc. But here we don't really have a choice of basis, hence the "inconvenience" in the language. – ZeroTheHero Sep 14 '17 at 12:44

Schrödinger's thought experiment was intended to discredit certain non- intuitive implications of quantum mechanics. There's not really a paradox

## protected by Qmechanic♦Sep 13 '17 at 20:57

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