The answer is no -- Schrodinger's Cat is not possible, even in principle.
In the following analysis, all of the superpositions will be location superpositions. There are lots of different types of superpositions, such as spin, momentum, etc., but every actual measurement in the real world is arguably a position measurement (e.g., spin measurements are done by measuring where a particle lands after its spin interacts with a magnetic field). So here’s how I’ll set up the SC thought experiment. At time t0, the cat, measurement apparatus, box, etc., are thermally isolated so that (somehow) no photons, correlated to the rest of the universe, can correlate to the events inside the box and thus prematurely decohere a quantum superposition. I’ll even go a step further and place the box in deep intergalactic space where the spacetime has essentially zero curvature to prevent the possibility that gravitons could correlate to the events inside the box and thus gravitationally decohere a superposition. I’ll also set it up so that, when the experiment begins at t0, a tiny object is in a location superposition |A> + |B>, where eigenstates |A> and |B> correspond to locations A and B separated by distance D. (I’ve left out coefficients, but assume they are equal.) The experiment is designed so that the object remains in superposition until time t1, when the location of the object is measured by amplifying the quantum object with a measuring device so that measurement of the object at location A would result in some macroscopic mass (such as an indicator pointer of the measuring device) being located at position MA in state |MA>, while a measurement at location B would result in the macroscopic mass being located at position MB in state |MB>. Finally, the experiment is designed so that location of the macroscopic mass at position MA would result, at later time t2, in a live cat in state |live>, while location at position MB would result in a dead cat in state |dead>. Here’s the question: at time t2, is the resulting system described by the superposition |A>|MA>|live> + |B>|MB>|dead>, or by the mixed state of 50% |A>|MA>|live> and 50% |B>|MB>|dead>?
First of all, I’m not sure why decoherence doesn’t immediately solve this problem. At time t0, the measuring device, the cat, and the box are already well correlated with each other; the only thing that is not well correlated is the tiny object. In fact, that’s not even true... the tiny object is well correlated to everything in the box in the sense that it will NOT be detected in locations X, Y, Z, etc.; instead, the only lack of correlation (and lack of fact) is whether it is located at A or B. But as soon as anything in the box correlates to the tiny object’s location at A or B, then a superposition no longer exists and a mixed (i.e., non-quantum) state emerges. So it seems to me that the superposition has already decohered at time t1 when the measuring device, which is already correlated to the cat and box, entangles with the tiny object. In other words, it seems logically necessary that at t1, the combination of object with measuring device has already reduced to the mixed state 50% |A>|MA> and 50% |B>|MB>, so clearly by later time t2 the cat is, indeed, either dead or alive and not in a quantum superposition. Having said that, a proponent of SC would reply something like: “OK, yes, decoherence has happened relative to the box, but the box is thermally isolated from the universe, so the superposition has not decohered relative to the universe and outside observers.” But this is incorrect.
When I set up the experiment at time t0, the box (including the cat and measuring device inside) was already extremely well correlated to me and the rest of the universe. Those correlations don’t magically disappear by “isolating.” In fact, Heisenberg’s Uncertainty Principle (HUP) tells us that correlations are quite robust and long-lasting, and the development of quantum “fuzziness” becomes more and more difficult as the mass of an object increases: Δx(mΔv) ≥ ℏ/2.
Let’s start by considering a tiny dust particle, which is much, much, much larger than any object that has currently demonstrated quantum interference. We’ll assume it is a 50μm diameter sphere with a density of 1000 kg/m3 and an impact with a green photon (λ ≈ 500nm) has just localized it. How long will it take for its location fuzziness to exceed distance D of, say, 1μm? Letting Δv = ℏ/2mΔx ≈ 1 x 10^-17 m/s, it would take 10^11 seconds (around 3200 years) for the location uncertainty to reach a spread of 1μm. In other words, if we sent a dust particle into deep space, its location relative to other objects in the universe is so well defined due to its correlations to those objects that it would take several millennia for the universe to “forget” where the dust particle is within the resolution of 1μm. Information would still exist to localize the dust particle to a resolution of around 1μm, but not less. But this rough calculation depends on a huge assumption: that new correlation information isn’t created in that time! In reality, the universe is full of particles and photons that constantly bathe (and thus localize) objects. I haven’t done the calculation to determine just how many localizing impacts a dust particle in deep space could expect over 3200 years, but it’s more than a handful. So there’s really no chance for a dust particle to become delocalized relative to the universe.
So what about the box containing Schrodinger’s Cat? I have absolutely no idea how large the box would need to be to “thermally isolate” it so that information from inside does not leak out – probably enormous so that correlated photons bouncing around inside the box have sufficient wall thickness to thermalize before being exposed to the rest of the universe – but for the sake of argument let’s say the whole experiment (cat included) has a mass of a few kg. It will now take 10^11 times longer, or around 300 trillion years – or 20,000 times longer than the current age of the universe – for the box to become delocalized from the rest of the universe by 1μm, assuming it can somehow avoid interacting with even a single stray photon passing by. Impossible.
What does this tell us? It tells us that the SC box will necessarily be localized relative to the universe (including any external observer) to a precision much, much smaller than the distance D that distinguishes eigenstates |A> and |B> of the tiny object in superposition. Thus, when the measuring device inside the box decoheres the superposition relative to the box, it also does so relative to the rest of the universe. If there is a fact about the tiny object’s position (say, in location A) relative to the box, then there is also necessarily a fact about its position relative to the universe – i.e., decoherence within the box necessitates decoherence in general. An outside observer may not know its position until he opens the box and looks, but the fact exists before that moment. When a new fact emerges about the tiny object’s location due to interaction and correlation with the measuring device inside the box, then that new fact eliminates the quantum superposition relative to the rest of the universe, too.
And, by the way, the conclusion doesn’t change by arbitrarily reducing the distance D. A philosopher might reply that if we make D really small, then eventually localization of the tiny object relative to the box might not localize it relative to the universe. Fine. But ultimately, to make the SC experiment work, we have to amplify whatever distance distinguishes eigenstates |A> and |B> to some large macroscopic distance. For instance, the macroscopic mass of the measuring device has eigenstates |MA> and |MB> which are necessarily distinguishable over a large (i.e., macroscopic) distance – say 1cm, which is 10^4 larger than D=1μm. (Even at the extreme end, to sustain a superposition of the cat, if there is an atom in a blood cell that would have been in its head in state |live> at a particular time that is in its tail in state |dead>, then quantum fuzziness would be required on the order of 1m.)
What this tells us is that quantum amplification doesn’t create a problem where none existed. If there is no physical possibility, even in principle, of creating a macroscopic quantum superposition by sending a kilogram-scale object into deep space and waiting for quantum fuzziness to appear – whether or not you try to “thermally isolate” it – then you can’t stuff a kilogram-scale cat in a box and depend on quantum amplification to outsmart nature. There simply is no way, even in principle, to adequately isolate a macroscopic object (cat included) to allow the existence of a macroscopic quantum superposition.
