The previous post referenced a rather crude attempt to use
our conscious experience as the foundation of (quantum) physics.
Usually, consciousness does not even make an appearance in physics
and some sort of "psychophysical parallelism" (different states of a
correlate with different conscious experience) is the only (hidden) assumption.
An interesting example is the notorious measurement problem in quantum physics.
(A slightly related classical example was provided earlier.)
Just to quickly recapitulate the main issue: Assume that a quantum system
|s> can be in two states |u> and/or |d>. An Observer,
initially in the state |I>, subsequently interacts with |s>
in such a way that |u>|I> evolves into |u>|U>, while |d>|I> evolves into
|d>|D>. With |U> we denote an observer who is sure to have observed
the system as |u>, while |D> is the observer in a state with conscious experience of |d>.
The measurement problem arises if we consider the interaction of
this observer with a state |s> in a superposition a|u> + b|d>, which then leads to an observer being in the superposition a|U> + b|D>; Schroedinger's Cat, Wigner's friend and all that.
The argument can be made much more precise, see here and here, and one does not have to assume
that |U> or |D> are necessarily pure states (and the observer state will in general incorporate entanglement with the environment etc.).
We find this superposition of observer states absurd because
we assign a specific conscious experience to a specific observer state following the assumption of
"psychophysical parallelism"; But
while we know what sort of conscious experience one would assign to |I> , |D> and
|U> , we do not know what conscious state should be assigned to a state
a|U> + b|D>. We would assume it has to be some experience of confusion, a superposition of
consciousness, which we normally do not experience.
At this point physicists introduced various
assumptions about a 'collapse' of the wave function to eliminate such
superpositions of observers, they threatened to pull a gun whenever Schroedinger's Cat
was mentioned and even worse began a long philosophical debate about various interpretations
of quantum physics.
But following an argument made by Sidney Coleman (in this video clip [at about 40min.]), this is really not necessary. Consider again the wave function |Y> of You the observer and
assume that there is an operator C which tells us if You the observer has
a normal classical conscious experience, so that C|Y> = |Y> if you are in a normal conscious state
and C|Y> = 0 if not [*].
Returning to our measurment problem, we have to assume that C|D> = |D> and also C|U> = |U>,
but then it follows from the linearity of quantum operators that even if
|Y> = a|U> + b|D> we have C|Y> = aC|U> + bC|D> = |Y>. In other words we have to conclude that You the observer has a normal classical conscious experience even in a superposition state after the quantum experiment.
This argument is at the basis of the 'many worlds interpretation' [x], which
assigns a normal classical conscious experience to the components
of the wave function |Y> and then shows that this does not lead to contradictions with
our everyday experience for superpositions of such components. A subtle shift in our
assumptions of "psychophysical parallelism" with drastic consequences.
A 'collapse' of wave functions seems no longer necessary (and the act of pulling a gun would only create yet another superposition of states 8-).
[*] Obviously we do not know what such an operator would look like, but if we believe in "psychophysical parallelism" we have to assume it can be constructed. Notice that if we would not believe in "psychophysical parallelism" then there would not be a 'measurement problem' either.
[x] It is obvious that 'many worlds interpretation' is a really bad name and should be replaced
e.g. with 'many experiences'.