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Shrodinger's Box

You've probably heard of Shrodinger's Cat thought experiment. You take a cat, put it in a box, along with a poison releasing device triggered by the decay of a radioactive atom. The trick is that quantum mechanics states that, until observed, the decaying atom is both decayed and not decayed simultaneously. Which means the poison is both released and not, and the cat is both alive and dead. At most until we open the box, look inside, and see a cat that is either alive or dead.

Now let's ignore the zombie cat for a moment and consider the box.

What if the box is transparent ? Then we see the cat live or die in real time as the events unfold. We are observing the box's content at all times, it is never noticeably in a superposition of states. We can conclude that it is not the opening of the box that breaks the spell, it is observing what's inside, which in the case of a transparent box, happens immediately, not leaving any chance for the cat to become a zombie.

Now what if the box is transparent, but you close your eyes ? Is the cat a zombie while you're not watching ? Maybe ? Now consider that while you close your eyes, I silently enter the room and watch the cat. For me the cat will be alive or dead. Is it possible for the cat to be a zombie for you but not for me ?
No, because as soon as the cat dies I can simply tell you that it's dead.

So the only way you can construct the experiment in a way that you can entertain the thought that the cat
is both alive and dead, is with a box that can contain the cat and not leak any information about the state of the cat to you or anybody (or anything!) else
outside the box. (alternatively you could also put yourself in such a box)

But how would you build such a box ? Consider the various ways information about the cat can leak out of the box. Vibrations of the cat's movement, infrared emissions from the cat's heat, gravity fluctuations from the change of the energy state, neutrinos from outer space interacting with the cat, etc.

It is not possible to build such a box. Which means the cat cannot be zombie either.

To be more precise, it is not possible to build a box for