I recommend that you read the first part of this series first.
The idea that the wave function W is only an incomplete description of the
reality R is as old as quantum theory itself.
Already at the Solvay conference of 1927 Louis deBroglie suggested to add
'hidden variables' with W being only a 'pilot wave'.
During the 1930s Albert Einstein published several thought experiments
(the most famous being the EPR paper) to demonstrate that W was obviously incomplete.
Consider the following 1-dimensional thought experiment.
A particle enters a detector of (great) length L at time tI and we determine its momentum p = mv
with high precision, knowing that this will lead to large uncertainty dx in its position x.
At a later time tF we turn the detector on, which will now determine the position x of the particle
with high precision and leave dp large. But although we assume that Heisenberg's uncertainty relation
holds for each measurement, we can now reconstruct the path of the particle between tI and tF,
knowing v(tI) and x(tF) with high precision and assuming conservation of momentum (just as we can
reconstruct the path which the photon must have taken in the Mach-Zehnder interferometer, once we know which
But this reconstructed path R(t) for tF > t > tI is not described at all by the wave function W(t); This suggests
that W provides for an incomplete description of reality only.
A consistent theory of hidden variables for non-relativistic quantum theory was later formulated by David Bohm
and attempts have been made to generalize it to relativistic field theories (1, 2).
By the way, notice that the 'hidden variables' are actually the particle and pointer positions
we observe in a measurement (while we never experience the
wave function directly).
An even more elegant way to introduce hidden variables is to refer to (human) consciousness as selection
principle. This works especially well, because on one hand one cannot deny the reality
of our conscious experience, on the other hand it never directly shows up in physics.
John v. Neumann was the first to mention it, Wigner and his
friend made the idea popular and Henry Stapp worked out some concrete proposals.
Actual experiments, using EEGs to test the influence of consciousness on quantum experiments, have been proposed, as described in this paper.
Of course, in a section about quantum theory and consciousness I have to mention Roger Penrose. He does not only think that W is incomplete, but assumes that current quantum theory is actually wrong, because
it ignores the effects of (quantum) gravitation. He also proposed an actual experiment to test his idea.
There are many other proposals to modify quantum theory and I only mention the Ghirardi-Rimini-Weber theory,
which assumes real sporadic collapse of the wave function.
continue to part 3.