Godfrey: > There is no energy flux directly associated with > wave-functions (like with electomagnetic or > mechanical waves) but is a probability density > and a probability flux associated with the square > of linear functionals of the wave-function.
The question, at this point, should be: probability of what? Because, leaving aside those who think (Weinberg, Dyson, etc.) that only fields exist and are real, there are at least a couple of solutions. There are physicists (followers of Bohr , more or less) who think  that quantum physics is about 'correlations without correlata', or about 'fotuitousness and clicks'. There are physicists (followers of Einstein, and his idea of Gespensterfeld, etc.) like Born , Fock , Barut , etc., who think that a 'probability' wave, even in 3n-dimensional space, is a real thing, much more than a mathematical tool, and who also think that physics is not just about apparata, or clicks. s. [1[ Niels Bohr: 'However, since the discovery of the quantum of action, we know that the classical ideal cannot be attained in the description of atomic phenomena. In particular, any attempt at an ordering in space-time leads to a break in the causal chain, since such an attempt is bound up with an essential exchange of momentum and energy between the individuals and the measuring rods and clocks used for observation; and just this exchange cannot be taken into account if the measuring instruments are to fulfil their purpose. Conversely, any conclusion, based in an unambiguous manner upon the strict conservation of energy and momentum, with regard to the dynamical behaviour of the individual units obviously necessitates a complete renunciation of following their course in space and time.'  Carlo Rovelli Relational Quantum Mechanics http://www.arxiv.org/abs/quant-ph/9609002  David Mermin What is quantum mechanics trying to tell us? http://www.arxiv.org/abs/quant-ph/9801057  Aage Bohr http://www.physicstoday.org/vol-57/iss-10/p15.html  Max Born: 'Quite generally, how could we rely on probability predictions if by this notion we do not refer to something real and objective?'  V.A.Fock 'Disskussija S Nilsom Borom', in 'Voprosy Filosofii', 1964 (a memorandum, about the interpretation of QM and the meaning of wavefunction, he gave to Bohr, in Copenhagen, 1957, who read it and changed his mind about several points, but not all).  A.O.Barut http://streaming.ictp.trieste.it/preprints/P/87/157.pdf