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Berry’s phase is the stub about one of the most common applications of parallel transport in quantum physics, with its own applications in molecular and atomic physics, quantum computing and so on.
Aharonov and Rohrlich spend a lot of time discussing some of the finer points of Berry’s phase in their book Quantum Paradoxes. It might be worth adding it as a reference (though I disagree with one or two of their intepretational points).
go on…
Oops, sorry. I’ve been very busy this week. I will expand on this soon.
OK, so the big difference in how I view things compared to how they view things, is that they take the ability to make a continuous measurement as a given. Personally, I believe that what may appear to be continuous macroscopically is not continuous microscopically. I suppose this means I take the Bob Griffiths view (to some extent) that the world is ultimately quantum mechanical and it’s the classical world that is only an approximation.
My idea is a very subtle one and I’m sure I’m going to botch my explanation, but hopefully someone will get what I’m trying to say:
So, in particular, they say (p.168):
We can continuously observe any quantum state. If we continuously observe a decaying atom, it never decays; if we continuously check whether a particle has crossed a barrier, it never crosses. We can make a free particle scatter off a force-free region just by constantly checking whether the particle has entered the region. Indeed, we can induce any evolution we want in a quantum system.
I realize that what they’re trying to get at (I think) is that the act of observation in QM requires an interaction between observer and observed. I don’t deny that. But when you think about the mechanism by which an observer does this interacting on the most fundamental level - an exchange of some boson depending on the type of interaction - either the uncertainty principle limits the observer to a certain level of discreteness or the interaction must involve virtual bosons. As I am unaware of any device that has an unbroken chain of virtual exchanges from the observed quantum process to the observer’s mind, truly continuous observation must not be possible, at least given existing technology. Whether it is fundamentally prevented by QM is an open question. Perhaps things like entanglement are really just strings of virtual processes (which would make it possible for some people to interpret them as violating SR).
I have added many references before at Berry phase, and now also the reference to an article by Vladimir Arnold.
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