Thanks alot Ronald for bringing to my attention the "Big Questions On Line" site, I liked it very much, and read with great interest the essay of Stephen Barr. I would like to make the following remarks :
Indeed QM has thrown a monkey in our materialistic thinking. Consciousness is unmeasurable, just as i wroye that you can describe consciousness as a singulairity, a dimesnionless point (in fact undescribable).
I also fully agree with Barr that "jumps" in wave function are not described in the Schrodinger equation, and that these "jumps" or "wave collapses" are only "caused" by intelligent observers (consciousness) and not by a "inanimate physical device".
Barr couples the obeservers KNOWLEDGE to the wavefunction so that knowledge is the cause of a discontnuous jump, in my perception it is consciousness that is the "cause" of an event (collapse) via entanglement of the causal part of our consciousness and the non causal part in Total Simultaneity, we are not far from each other but there is a difference.
In fact in my perception it is our "non causal consciousness (the part in TS)" which is what I call an alpha-probability in Total Simultaneity , that is eternal, (compare it to a point on an endless line with infinities on both sides, so the point itself has no specific (non causal) place on the line). Every moment we are making "in the future" a choice for what Barr cals an "discontinuous jump" or collapse of the wave function. The "knowledge" of Barr is eternal in my opinion. For the MWI I advise you to read my essay where I treated it.
So for your prime question about the theological interpretation I fully agree with Stephen Barr, all this does not provide an argument for the existance of GOD, but it does indirectly. The eternal alpha-points of our non causal consciousness are part of the "ALL", this is a non causal for us causal creatures ununderstandable dimension, and it is also the origin of our causal life-lines. It is a non-materialistic approach of the explanation of our "reality".
My perception also solves the so called "solipsistic approach, because after the so called "subjective simultaneity sphere", I introduce the idea of the "objective simultaneity sphere" which is the result of the fom formed by the SSS's, all the cutting circles are the common experiences, causing the "decoherence" (a communal wave function collapse leading to the reality as perceived together).
I hope to answered your questions.
regards
Wilhelmus