David Campbell wrote:
<< My other question regards the accuracy of simplified descriptions of
tunneling. In Not a Chance, R. C. Sproul objects to a simple description of
tunneling as an electron popping out of existence in one spot and appearing
in another. If I remember correctly, wave functions do not provide much of
an absolute limit on the location of a particle (although the probability is
quite low for distant places), so that in a way tunneling might be viewed as
a low-probability region becoming a high-probability region rather than an
actual example of non-continuity. I did not think much of his argument, but
am wondering how much the argument reflects an overly simple version of
quantum ideas rather than a real issue.
>>
George Murphy already basically gave the short answer to this.
However, it might be useful to point out that quantum mechanics
is far from a clearly understood subject. On the one hand, Josephson
junctions would not work if quantum tunneling didn't occur.
So generally speaking, everyone agrees on the phenomenological
aspects of QM. The problems mostly stem from the interpretation.
On the one extreme are those who think that such states as spin
are transmitted instantaneously over vast universe and hence,
the entire universe is in essense, "connected". There is some
evidence that this is so in regards to quantum entanglement of
photons. The last I heard, it remains unknown for particles such
as electrons which, aside from superconductors, typically show
coherent effects over distances on the scale of perhaps nanometers.
The Pauli exclusion principle also seems applicable to all numbers
of identical particles. So, much as it seem contrary to caveats
on scalability, QM seems to work as though the universe might be
connected.
At the other extreme is the view that there must be "hidden
variables" somewhere in the puzzle. Although Einstein is
often criticized as "wrong" for arguing with Bohr about this
matter, I don't think it is so simple. Part of our job
as physicists is to get at the core of what makes things work.
To be content with some half-baked hand-waving argument runs
counter to that objective. In light of the above,
David Bohm's pilot wave model is an honest attempt to wrestle
with the problem from this angle. On the other hand, expecting
that this "core" should be something "predictable" may also
reflect problems with our way of thinking as physicists.
In any case, at least recognize that it is far from an easy
topic even for the best thinkers on these matters. Problems
come with either direction you chose.
By Grace along do we proceed,
Wayne
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