> 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 [1],
more or less) who think [2][3][4] 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 [5], Fock [6],
Barut [7], 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.

[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.' 

[2] Carlo Rovelli
Relational Quantum Mechanics

[3] David Mermin
What is quantum mechanics trying to tell us?

[4] Aage Bohr

[5] Max Born:
'Quite generally, how could we rely on probability 
predictions if by this notion we do not refer to 
something real and objective?'

[6] 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).

[7] A.O.Barut

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