Understanding The Conscious Observer: Young's Double Slit Experiment

[Nugatory]

It's worth noting that that 2 and 4 involve consciousness - insofar as an "agent" is conscious of a belief or conscious of assigning a probability.

Indeed it is (there might be some dispute about #2, but "insofar" leaves much room for general agreement with your point).

However, this is involving consciousness in a different and much less pop-woo sense than in the question that started this thread.

 

[DarMM]

It's worth noting that that 2 and 4 involve consciousness - insofar as an "agent" is conscious of a belief or conscious of assigning a probability.

2 involves consciousness as much as Statistical Mechanics does, so I guess it depends on how much one thinks Statistical Mechanics involves a conscious agent.

4 does involve a reasoning agent, but it could be a non-conscious computer. It just depicts a large part of QM, especially the Born Rule, as normative rules for how such an agent should "mesh" their probabilities for different observations.

Note that it is still open whether experiments or measurements in QM have single objective outcomes. They may have multiple, e.g. Many Worlds, or they may only exist relative to the observer, e.g. QBism (though here it would be relative to all observers who share the same environmental context). So it might not make sense to speak of the objective "out there in the world" results of a measurement.

 

[strangerep]

Can we say instead that a wave function is a representation of an underlying group?

[...] I meant because basis states are linearly independent functions, maybe they can always provide a basis for a representation of a given group.

Advanced quantization is essentially a procedure of finding a unitary representation space (Hilbert space) for the dynamical group applicable to the (class of) systems being modeled. The group elements are represented by unitary operators acting on the Hilbert space.

The wave function by itself is not a "representation", rather the particular Hilbert space is chosen (constructed) such that it "carries" a unitary representation of the relevant dynamical group.