In this book, important conceptual developments of the two major revolutions of modern physics -- the quantum and relativity theories -- are presented in a nonmathematical, dialectical form of dialogue. The implications of conflicting philosophical attitudes of these revolutions in physics and applications to topics such as cosmology/astrophysics and high energy physics are emphasized. It is argued that for any substantial progress in our understanding of 21st century physics, it will be necessary to resolve these 20th century conflicts. These richly rewarding dialogues provide a starting point for discussions that could lead to such progress. An epilogue is presented on the philosophical advantage of the dialogue form for increased understanding.