Determinism of the wave function

[nomadreid]

There are four commonplaces that I am not sure how to mesh together, or if this is not possible, which one(s) is/are an () oversimplification(s)/wrong, and why.

(1) the wavefunction is deterministic.
(2) a collapse or decoherence or splitting into worlds (take your choice) makes the wave function lose information,
(3) which value the wave function takes on when measured cannot be derived
(4) all quantum processes are reversible
(5) information is never lost (except maybe via a black hole).

(2) and (5) directly contradict each other,
(2) and (4) indirectly contradict each other,
(1) and (3) directly contradict each other

So, what is wrong?

 

[javierR]

I can't really do the question justice in the time and space I have.
A very useful framework is that of consistent histories. A history is a collection of projector operators at successive times. The history corresponding to the unitary evolution according to Schrödinger's equation (which is therefore deterministic) is called a unitary history.

If you consider other histories (in consistent fashion according to the criteria of the framework, which you can find in the literature--see below) they generally have pieces that are unitary evolutions as well as non-unitary evolutions. Wavefunction "collapse" does not appear to be a physical process, but rather corresponds to a non-unitary history, that does not result from Schrödinger's eqn, and therefore is not a deterministic history...these are stochastic histories as there are probabilities associated with these histories. The wavefunction is a useful tool for assigning these probabilities to various histories, but does not *necessarily* represent the actual physical state of a system. Therefore, you also have to be careful when interpreting what is happening to information in the system using this framework. In particular, you can't conclude that information is lost by looking at the wavefunction collapse as a physical process.

Macroscopic processes are not generally reversible due to changes in entropy, and it is these types of subsystems that should be regarded in measurement theory (unless you're dealing with reasonably non-destructive measurements).

For more about consistent histories interpretation of quantum mechanics, see R. Griffiths' "Consistent Quantum Theory" or R. Omnes' "Understanding Quantum Mechanics"

 

[nomadreid]

javierR: Thank you for the references for literature on consistent histories. Unfortunately I do not presently have access to a good academic library, but I understand the concept from other sources which use the concept implicitly.
Of course, I slipped up in mentioning decoherence and loss of information in the same context. One cannot consider information lost with decoherence. Just hard to access.
Therefore I suppose my main question becomes: does measurement affect the evolution of the wave function? That is, given initial conditions, and a period of time thereafter, would the values of the wave function be the same whether or not there were a measurement in between?

(Random: The set of measurement points form a sparse set of the set of values of the wave function over time, and hence is insignificant, i.e, measure zero. Reality consists of measurements. Ergo, reality is insignificant. :-) )