In this thought-experiment a cat is placed in a box set with a bottle poison that will release and kill it depending on whether or not a certain radioactive particle decays. The box is kept closed and it is asked "is the cat alive or dead?" Since the decay of the particle is a quantum mechanical process- it is represented by a state function. This function remains in a "superposition state" until it is observed whether the particle has decayed or not. The cat is presumably and unfortunately entangled with this function- it's own life/death is in a superposition state until it is indeed observed to have dodged the bullet or not. Schrodinger used this thought experiment in an attempt to show the ridiculousness of certain aspects of quantum theory. His motives were clear in devising it and are well documented in his correspondences with Einstein.
My question is not about the cat, the particle, or Schrodinger. I want to know about the box. The box that contains this scenario must effectively isolate the outside observer from any information about what is (or could be is perhaps more correct) going inside of it. So what sort of box would qualify? It seems that such a box could not have any interaction at all with the outside universe- no gravitational or thermal effects- anything. Otherwise would not some kind of information about what was going on inside escape without it being opened?
And this being said- were such a box constructed would it not be entirely cut off from reality and how could we be sure it even contained a cat still or was even there at all?
Is this experiment possible or are the problems I outline above a deterrent to it's physical possibility?