PeroK said:
The important point is that an electron is not a cat. And "alive" and "dead" are not fundamental quantum properties like spin. In the sense that, within reason, simply observing a cat doesn't cause the cat to assume a state of alive and dead.
I reformulate. Many sources I read said that the superposition means that the cat is both alive "
and" dead. But AFAIK, the addition in the wave function doesn't mean "and". The way I learned it, it means a sort of "or", so the superposition should say that the cat is dead or alive, with the appropriate probabilities. Is this correct? I'd like to figure out if and where I'm going wrong.
I've also read that " Schroedinger was wrong because quantum mechanics does imply that such superpositions are totally allowed and must be allowed and this fact can be experimentally verified – not really with cats but with objects of a characteristic size that has been increasing". And that "macroscopic objects have already been put to similar "general superposition states" and from a scientifically valid viewpoint, the thought experiment shows that superpositions are indeed always allowed – it is a postulate of quantum mechanics – even if such states are counterintuitive." Is this point of view correct?
This is the source of my confusion. Many sources say that "the cat is in a state that is a superposition of our "life states" alive and dead" means "the cat is both alive
and dead" until we open the box.
Other sources say that Schrodinger's cat is not both dead and alive any more than an electron simultaneously exists at every point in space, also because a system cannot be in multiple states at once. So Schrodinger's cat would be always in a single state: there would be an equal probability of us "measuring" the cat to be either alive or dead once we open the box. Therefore, "the cat is in a state that is a superposition of our "life states" alive and dead" would
not mean that "the cat is both alive and dead" until we open the box, because is in a single state, and this state is described as a superposition of life states.
I'm not speculating on any theory, I am just very confused. I'm describing some of the interpretations I read because I would like to see more clearly about which one is the most appropriate and reliable.
All this I say despite the fact that I am still aware that the cat represents a classical system. Therefore it does not behave like an electron. My question was not addressing so much Schroedinger's purpose (criticizing the Copenhagen interpretation) and the absurdity to which he wants to lead us. It was directed at the interpretation of "both alive and dead" and "superposition."
PeroK said:
The reason that the same formalism does not applies to cats
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 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 "cat" operator ##\sigma_{\hbox{cat}}## with eigenstate
$$
\vert\hbox{cat}\rangle= \cos\left(\textstyle\frac{\theta}{2}\right)\vert \hbox{dead}\rangle + e^{i\phi}\sin\left(\textstyle\frac{\theta}{2}\right)
\vert \hbox{alive}\rangle\, . \tag{2}
$$
The sense of the superposition ##(2)## as a single quantum state eigenstate of a non-existent ##\sigma_{\hbox{cat}}## operator, and thus analog of ##\vert \hat n\rangle## is rather abstract, but
maybe the sense of the superposition of alive and dead cat could be clear as a generalization of the right hand side of ##(1)## (??).
Does this description fit?
