Dear Cristinel
I enjoyed going through your engaging essay - every topic you chose was interesting, pertinent, beautifully explained and illustrated and thought-provoking. As a mathematician you should know how fertile and precocious the field is - so many different ways to express the same situation. Combine that with the cleverness and imagination of a Feynman or a Wheeler and you get truly mind-boggling choices in how to represent the Universe. Unfortunately It=It and one feels that the simpler a model is the more probably it is right - a single universe vs. many - one history instead of multiple ones etc, local causality vs. probability.
The delayed-choice beam-splitter experiment is brilliant. Sadly it has been now made meaningless after Eric Reiter's experiments, backed by solid theoretical and historical analysis of the issues involved, with beam-splitters showing that light-quanta do not 'choose' one path or another, but as waves (not point photons) are detected by both detectors simultaneously. Reiter reported about this in his 2012 fqxi essay and on his website unquantum.net . How such an important experimental challenge demolishing the inherent probability in Nature (the Born Rule) can be so neglected by the physics community is beyond me.
With best wishes, Vladimir