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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?

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Decoherence is discussed extensively in this article:

Interference phenomena are a well-known and crucial aspect of quantum mechanics, famously exemplified by the two-slit experiment. There are many situations, however, in which interference effects are artificially or spontaneously suppressed. The theory of decoherence is precisely the study of such situations.

Here is a simple tunneling example:

tunneling

According to classical physics, a particle of energy E less than the height U0 of a barrier could not penetrate - the region inside the barrier is classically forbidden. But the wavefunction associated with a free particle must be continuous at the barrier and will show an exponential decay inside the barrier. The wavefunction must also be continuous on the far side of the barrier, so there is a finite probability that the particle will tunnel through the barrier.

Note that the energy of the system does not change. It is not an interaction.

Interference effects are observed where the quantum mechanical solution of the specific system has a wavefunction that displays in the probability distribution interference effects, as in the double slit experiment.

The energy of the system changes for individual "electron slits" interactions that show the interference in the accumulation. Interference needs a large number of events to be seen.

In tunneling there is only one event, that has a probability to cross the barrier. As the link given by Connor shows that it is very unlikely to have a macroscopic tunneling, but this is independent from any interference effects becaus tunneling is not an interaction.

anna v
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I don't think decoherence has a connection to tunneling. Tunneling is due to evanescent wave transmission, not wave interference. Only the amplitude of the wave on the far side of the barrier matters.

John Doty
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