No doubt quantum mechanics is very counter intuitive. Is it even possible to bring together quantum mechanics and relativity as a single (unified) entity ?
 
In past couple of years I have found that it makes much more sense to study quantum mechanics and relativity (cosmology) simultaneously. More ever, it has been very useful to listen to theoretical physicists as well as experimental physicists simultaneously. It rather awesome to listen to theoretical physicists bring in many rather crazy new ideas about the nature of physical reality and get quickly shot down by experimental physicists. And, it also awesome to watch observations (and claims) of experimental physicists get shot down by other experimental physicists on many instances as it more recently happened rather catastrophically with BICEP2 Experiment in early 2014.

Sometimes It could be useful to listen to pure mathematicians as they do have unique abilities to come up with creative solutions however more often than not many of their mathematical solutions do not seem to be congruent with the reality (or at least the realty we have understood so far). Any wonder String Theory has not gotten anywhere in the last 4 decades.

I have found Princeton theoretical physicist Nima Arkani-Hamed's (among many) explanations to be compelling even if it seems that bringing quantum mechanics and relativity is rather an impossible task in the real world or at least for now.

I know quantum mechanics and cosmology are two big ideas too big to be fully understood in this lifetime however these two big ideas are too intriguing to not make an attempt.