If it’s impossible to predict the exact time of tunneling, that means amplitude is going to multiple branches, which, when they entangle with a larger system, decohere.
That is not quite the conventional meaning of decoherence, though. Of course, if I recall from your QM sequence, it is, indeed, yours. Let me explain what I think the difference is between the two phenomena: a spin measurement and the tuneling process.
During an interaction such as spin measurement, a factorized state of a quantum system becomes entangled with the (quantum) state of the classical system as some of the terms in the product state decay away (according to Zurek, anyhow). The remaining “pointer” states correspond to what is usually termed “different worlds” in the MWI model. I believe that this is your interpretation of the model, as well.
Now, consider radioactive decay, or, to simplify it, a similar process: relaxation process of an excited atom to its ground state, resulting in an emission of a photon. This particular problem (spontaneous emission) requires QFT, since the number of particles is conserved in QM (though Albert Einstein was the first to analyze it). Specifically, the product state of an excited atom and the ground (vacuum) state of the electromagnetic field evolves into a ground state of the atom and an excited state of the field (well, one of almost infinitely many excited states of the field, the “almost” part being due to the Planck-scale cutoff). There is virtually no chance of the original state to reappear, as it occupies almost zero volume in the phase space (this phase space includes space, momentum, position, spin, etc.). I believe even time is a part of it.
To call radioactive decay “decoherence”, one would have to identify the ground state of the field (electromagnetic vacuum) with the classical system that “measures” the excited atom. Calling a vacuum state a classical system seems like a bit of a stretch.
An alternative approach is that the measurement happens when an emitted photon is actually detected by some (classical) external environment, or when the atom’s state is measured directly by some other means.
I am not sure if there is a way to distinguish between the two experimentally. For example, Anton Zeilinger showed that hot fullerene molecules self-interfere less than cold ones, due to the emission of “soft photons” (i.e. radiating heat). His explanation is that the emitted radiation causes decoherence of the fullerene molecule’s factorized state, due to the interaction with the (unspecified) environment, and hotter molecules emit shorter-wave radiation, thus constraining the molecule’s position (sorry, I cannot find the relevant citation).
If you identify each of the branches in the MWI model with each possible excited state of the electromagnetic field, you would have to assume that the worlds keep splitting away forever, as all possible (measured) emission times must happen somewhere. This is even more of a stretch than calling the vacuum state a classical system.
Feel free to correct me if I misunderstood your point of view.
That is not quite the conventional meaning of decoherence, though. Of course, if I recall from your QM sequence, it is, indeed, yours. Let me explain what I think the difference is between the two phenomena: a spin measurement and the tuneling process.
During an interaction such as spin measurement, a factorized state of a quantum system becomes entangled with the (quantum) state of the classical system as some of the terms in the product state decay away (according to Zurek, anyhow). The remaining “pointer” states correspond to what is usually termed “different worlds” in the MWI model. I believe that this is your interpretation of the model, as well.
Now, consider radioactive decay, or, to simplify it, a similar process: relaxation process of an excited atom to its ground state, resulting in an emission of a photon. This particular problem (spontaneous emission) requires QFT, since the number of particles is conserved in QM (though Albert Einstein was the first to analyze it). Specifically, the product state of an excited atom and the ground (vacuum) state of the electromagnetic field evolves into a ground state of the atom and an excited state of the field (well, one of almost infinitely many excited states of the field, the “almost” part being due to the Planck-scale cutoff). There is virtually no chance of the original state to reappear, as it occupies almost zero volume in the phase space (this phase space includes space, momentum, position, spin, etc.). I believe even time is a part of it.
To call radioactive decay “decoherence”, one would have to identify the ground state of the field (electromagnetic vacuum) with the classical system that “measures” the excited atom. Calling a vacuum state a classical system seems like a bit of a stretch.
An alternative approach is that the measurement happens when an emitted photon is actually detected by some (classical) external environment, or when the atom’s state is measured directly by some other means.
I am not sure if there is a way to distinguish between the two experimentally. For example, Anton Zeilinger showed that hot fullerene molecules self-interfere less than cold ones, due to the emission of “soft photons” (i.e. radiating heat). His explanation is that the emitted radiation causes decoherence of the fullerene molecule’s factorized state, due to the interaction with the (unspecified) environment, and hotter molecules emit shorter-wave radiation, thus constraining the molecule’s position (sorry, I cannot find the relevant citation).
If you identify each of the branches in the MWI model with each possible excited state of the electromagnetic field, you would have to assume that the worlds keep splitting away forever, as all possible (measured) emission times must happen somewhere. This is even more of a stretch than calling the vacuum state a classical system.
Feel free to correct me if I misunderstood your point of view.