My question is quite simple. In the thought experiment of Schroedinger's cat: When the scientist measures the state of the cat, its wavefunction collapses into either the alive or dead state. But wouldn't then the scientist in turn be in a superposition of measuring dead respectively alive until someone opens the door to the laboratory and asks the scientist about the outcome of the experiment (and therefore measures the state of the system)?
This is is known as the Wigner's friend thought experiment. According to the many World's interpretation, the superpositions are not a problem. The whole universe ends up in a superposition where all experimental outcomes are realized, but such a superposition is entangled with the environment, from a macroscopic point of view it takes the form of a superposition over a set of consistent histories.
In a bubble chamber experiment, film was the detecting medium, but film was taken automatically, by the thousands of frames. These bobbins of film went to the various laboratories involved in the experiment, and were scanned for interesting events which were measured and the cross sections for the interactions recorded.
This is a clear example of an experimental measurement of a quantum mechanical level interaction . It is easy to see where the quantum mechanical level ends and the classical regime begins. There has never been a doubt whether the events recorded on the films were there or disappeared at the next scanning, (i.e. had a quantum mechanical probability to have disappeared). The film record is demonstrably permanent and therefore classical. The cat thought experiment could be carried out in a laboratory easily (fortunately no sadist has done so) . In what follows I make the analogy film - cat, pointing up where the quantum mechanical regime to be studied is and where the recording classical regime.
Here is the first Omega minus seen, the cherry at the bottom of the decuplet pyramid, a prediction of the quark model.
The bubble chamber picture of the first omega-minus. An incoming K- meson interacts with a proton in the liquid hydrogen of the bubble chamber and produces an omega-minus, a K° and a K+ meson which all decay into other particles. Neutral particles which produce no tracks in the chamber are shown by dashed lines. The presence and properties of the neutral particles are established by analysis of the tracks of their charged decay products and application of the laws of conservation of mass and energy.
The omega minus was there from the exposure of the film. That is the detector. Any scanner will find it again and again, because the film is not a quantum mechanical state. It is a macroscopic classical detector. The quantum mechanical state was when the K- interacted with a proton in the bubble chamber, which had a probability of manifesting in the chamber. The recording of the event is detection.
In an analogous way, the cat in this (misguided in my opinion) thought experiment is the detector, the film, on which the experiment with the radioactive probabilities is recorded. It is the radioactive probabilities that are in a quantum mechanical state. The cat is the film. Until looked at, similar to the film being blank or recorded with an event, it is guessed to be dead or alive. Whatever it is, is decided by the quantum mechanical probability, and will be a stable solution of the problem.
Let us see more detail, from the wikipedia article:
One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter, there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer that shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The first atomic decay would have poisoned it.
The quantum mechanical probability in this version, is the probability that the radioactive substance will decay within the hour. This probability is controlled by the quantum mechanical wave function of the nucleus, (the analogue of the K- proton interaction) multiplied by the number of nuclei in the radioactive sample. The further steps in the experimental setup are macroscopic: the trigger of discharging the tube, the breaking of the poison and the cat are the detector setup (analogue of hydrogen bubble chamber, camera, film). The cat is the film because it is the permanent record of what happened within that hour (analogue of a film frame being a permanent record of whether there is an interaction or not).
Please note that the cat is a superfluous sacrifice to a vague analogy. The counter would have been enough if it was recorded on an audio tape. The cat takes the place of the tape. The quantum mechanical probability function controlling the event is the original decay probability function.
Cat and film are in the classical regime, because h_bar is such a small number that the Heisenberg Uncertainty is always satisfied by macroscopic ensembles, larger than nano dimensions. True quantum mechanical behaviors, i.e. controlled by a probability density, appear macroscopically only in very special situations (as superconductivity for an example).
In general macroscopic objects are in the classical regime, the framework of the density matrix helps acquiring an intuition how the transition happens, between quantum mechanical wave functions and classical dimensions.
It depends of what interpretation of quantum mechanics you are using. By interpretation it is meant that the mathematical predictions of the quantum mechanics formalism are the same, but the philosophical meaning of each is what differs. In the copenhagen interpretation that you seem to describe, the wave function collapses when a conscious observer makes a measurement. Before the measurement the system can be in a superposition of states. It is supposed that the cat is not conscious thus, in that interpretation the wave function does not collapse and the cat is in a superposition of states. If a human opens the box then the function collapses to either live or death. The human observer will not be in a superposition of states.
But this is an old interpretation and the are many others. In particular, in the Bohm interpretation there is no wave function collapse and the cat is in a specific state (either alive or death) regardless of he being observed or not.
This is an excellent question and stresses one of the weird features of quantum mechanics.
Indeed, the scientist would in turn be in a superposition. And we could even measure this if we'd be able to maintain coherence of such large systems.
Ultimately, your question is asking for the solution of the Measurement problem: Why don't we see any superpositions? There are no cats running around half dead and half alive. Neither do we see scientists being in a superposition of having measured this or the other.
However, the measurement problem has remained an unsolved problem. All we have are some interpretations.
In Schrodinger's cat experiment, the scientist is assumed to be an "classical observer" of the state of the cat, and thus all observations made by the scientist are assumed to be classical observations adhering to physics as we knew it before quantum mechanics came along. The thought experiment focuses on what sorts of statements about reality that scientist could make which are consistent with the predictions coming from quantum mechanics despite doing some operation (i.e. waveform collapse) to get a classical measurement out of a quantum mechanical system.
If you choose not to presume that the scientist is not a classical observer, but rather an entity bound by merely quantum mechanics, it is reasonable to instead assume that the scientist and the cat (and the radioactive isotope) become entangled by their interaction. This is a completely valid interpretation of QM, it just doesn't explore the philosophical question that Schrodinger's cat was intended to explore.
The philosophical side of the question is also why the topic of consciousness comes up regarding Schrodinger's cat. If you really start digging at the philosophy of science, it all eventually boils down to the question of what does it mean to observe the world, as a conscious living being. When we think about "observations" intuitively, disregarding QM for a moment, the observations we make fit well with the "classical" model of the world. They fit rather poorly with the QM world. Thus it is this classical intuitive observer that we need to line up with the data we observe, or we must admit that we have a contradiction in our observations.
On the practical side, it is extremely difficult to get macroscopic objects to exhibit non-trivial quantum behavior because the particles in such objects are typically very decoherent. Thus, they are well modeled by using the Central Limit Theorem, ensuring the variance around the expectation is so small that we can squint and hand wave it away for all intents and purposes.
Large classical objects such as cats or humans are next to impossible to place in a superposition of states. They basically decohere immediately.
As far as i know the largest object placed in a superposition is a micromechanical resonator and there is currently work being done on placing a bacterium in a QM superposition ( quantum superposition of a classical object,Schrodinger's bacterium).
My understanding is that it is not the cat that is in a superposition but rather only the radioactive decay. The state of the cat is merely unknown.
At any rate, it comes down to interpretation. Some people may argue S-cat is ridiculous and worthless but the fact is that it holds a special place in physics as well as our culture and thinking on S-cat as one learns and grows can be invaluable to many.
Schrodinger, I take it, was dramatising the epistemological and ontological paradoxes implicit in QM by considering a cat as opposed to a particle contained in a box; and hugely succesfull too, as we're still discussing it almost a century on, and its probably more widely known that his eponymous equation.
Cats, compared to particles, are vastly macroscopic objects; so being classical objects, QM doesn't apply.
If we 'undramatise' the picture, by replacing Schrodingers cat, Wigner and Wigners friend with particles and consider interactions as measurements, then we get an interpretation of QM defended by Rovelli as relational QM; he quotes Simon Kochen in '79 saying:
The basic change in the classical framework which we advocate lies in dropping the assumption of the absoluteness of physical properties of interacting systems… Thus quantum mechanical properties acquire an interactive or relational character.
He does suggest that it has a family resemblence with Everetts many-worlds ontology, but its different in kind as this is relative.
The cat has no quantum state, it is a classical object, which, along with everything else in the experiment, is just "overhead" to make it accessible to the general public.
There is the decaying lump of radioactives, and the Geiger counter (detector). This is the quantum level stuff; the rest is just classical embellishment. It makes no sense whatsoever to consider the cat or the whole system to be part of the quantum state, much less so the experimenter who opens the door to find out whether the cat is alive or dead. The cat is certainly not a "detector" in this experiment, it is just the extended "display" of the Geiger detector. That's what Schrödinger wanted to point out.
Schrödinger himself (according to his original, if translated, quote, on Wikipedia) posed his paradoxon quite tongue-in-cheek; take it for what it is, don't try to interpret too much.
For the cat (which is the subject of the experiment), it is irrelevant if you observe it or not. Its state will be the same at a given 't'. Also, that state is not dependent on the observation happening or not (although, opening the door when the cat is alive will influence the cat's behavior, but that is another matter).
Universally, it is the observer that is irrelevant, not that state of the cat that is dual.
Not knowing something does not mean it is both ways simultaneously, but it means it can be one or the other way.
"It's not Schrödinger ... it's the cat !" --> to quote myself.