I would like to offer what is hopefully not an overly naive perspective on
determinism in Quantum Theory.
Quantum theory is generally said to destroy the determinism evident in
classical physics. While I won't dispute this point directly, I think there is
another way to interpret QT which is strictly causal.
QT is not considered casual in the classical sense because it seems to
require the abandonment of objective properties of quantum systems. Bohr wrote "
Atomic Systems should not even be thought of as possessing definite
properties in the absence of a specific experimental set ups designed to measure
these properties. " Most Quantum interpretations would agree with this point in
one form or another. ( Bohm's ideas being the exception)
Mathematically we express this by saying that quantum systems have no
definite eigenvalues. The eigenvalue of any quantum system does not exist
objectively , independent of a measurement process. Herein lies the disturbing
fact about QT that so troubled Einstein, Schrodinger and De Broglie to their
dying day.
However, there is another way to look at this, which at least for me ,
suggest a different take on this question. In classical physics we describe
physical state evolution using functional relationships. This presumes an
objective measurable value is always available independent of the measurement
process. However, in QT we must replace functions by operators which actually
have a much richer structure. This has generated what I will call the no
property fallacy espoused by Bohr.
It's certainly true that Quantum Systems do not posses the classical
properties we use in classical physics, but why is the notion of "Quantum
properties " overlooked in our search for objectivity in Quantum Theory? Objective
Quantum Properties are none other than what the wave function describes. This
seemingly simple ideas is rejected because these are not properties we can
measure in our laboratories, at least not directly. However, I would submit
there is no reason why the concept of objective physical properties are made to
depend on direct observation. This dependence is a holdover from the habits
of classical thinking. Empirical and observational are distinct notions. No
one has seen a quark but we believe they exist.
To illustrate this with a simple example we will take 10 grams of
palladium 103 , which has a half life of 17 days. ( Don't try this at home) We divide
it into ten samples and wait 17 days.
We then measure all ten samples and we find that in fact they all contain
precisely the same amount of Pd 103. ( 1/2 of its original value) . We have
demonstrated that evolution of the wave function is space translation invariant.
We can also take ten equal samples prepared at different times and make our
measurements after 17 days in each case. Here again we would precisely
measure the same amounts of Pd 103 in each sample. This illustrates the
invariance of wave function under time translation. These are, of course , two
fundamental symmetries of nature.
So we can say , be we so inclined to say, that QT doesn't mandate a
breakdown is casualty but rather it mandates the rejection of the results of
classical measurements as the objective properties of nature at the fundamental
level. These properties are really in no way fundamental , but rather are
emergent properties of nature due to the mathematics of large numbers. We are
fooled into defining these properties as fundamental because our sensory
abilities evolved to deal with large scale phenomena.
We can say a property is physical if it has empirical ramifications and
its specifics can be determined in principle by objective measurements. So in
QT we do retain both objective and physical properties and the causality of
nature is not really in doubt. Nevertheless , the irony should not be lost
that in our macro world we have a Universe with completely deterministic
"probabilities".
I don't mean to suggest that the above is deeply profound. It is not. But
I do think it offers a different perspective that may help calm any
metaphysical angst concerning the lawlessness of the Universe at its most fundamental
level. Or perhaps not.