A macroscopic object has the order of Avogadro’s number of particles. That’s over $10^{23}$. So the probability of all of them tunneling, at the same time, is on the order of that original small probability, to the $10^{23}$ power. And then on top of that, you have to factor in the chances of it happening in a place you can see it - as opposed to the enormous number of places in the universe you can’t. We can’t even imagine how small that is - we can’t even come close to imagining it. I’m perfectly comfortable dropping the nit-picking and calling something with that probability “impossible.”
If you think the point I’m trying to make is that this isn’t even worth talking about, you’re right. It’s not. It’s entertaining as a thought experiment, but these possibilities are utterly irrelevant to any aspect of real life.
Anyway, why does not environmental decoherence completely prevent from happening the quantum tunneling at macroscopic level?
