[I'm skipping over the meat of the discussion, so I apologize if I ignore anything.]
Rigorous scientific proof about the Law of Attraction seems very, very, unlikely. Science is only able to satisfactorily prove the most basic mechanical ideas about the universe.
There's a sort of sliding scale of proof as far as knowledge is concerned:
Tautologies, like mathematics, are always, always, always capable of being proven conclusively true, because they operate separately from reality. Mathematics is based on the idea of equality -- something equals itself and only itself. Everything in mathematics stems from this, and as long as this rule of equality is obeyed to the fullest, all mathematical ideas are fully sound and fully provable.
Hard sciences, like physics and chemistry, are heavily, heavily, heavily assumed to be true, although proof in physical science can only go as far as being 99.99...% true. We operate as though hard scientific laws are true, and as far as we know it is almost completely certain they are. But since they involve physical reality, consciousness, and perception, the idea of 100% certainty is a distant dream.
Medium-hard sciences, like biology and medicine, and soft sciences, like sociology and anthropology, are mostly true, but by this point there is large room for researcher bias, sample bias, and a whole score of other biases. Knowledge in these fields should be taken with a shaker of salt.
Philosophy, theology, metaphysics, and the like are so subjective that they are basically unprovable under any imaginable circumstances, ever.
In its current incarnation, the Law of Attraction seems mostly like a philosophical idea. It seems far beyond the scope of rigorous proof.
:Cheers,:
-PlanetaryNapkin
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