I know of no significant advance in science that did not require major inputs from both cerebral hemispheres. This is not true for art, where apparently there are no experiments by which capable, dedicated and unbiased observers can determine to their mutual satisfaction which works are great.
There are many hypotheses in physics of almost comparable brilliance and elegance that have beenrejected because they did not survive such a confrontation with experiment. In my view, the human condition would be greatly improved if such confrontations and willingness to reject hypotheses were a regular part of our social, political, economic, religious and cultural lives.