Why do photons and speeding electrons have both wave features and particle features when common sense tells us that they should be either particle or wave and not an amalgam of both? And why is the velocity of light constant for all observers? These central questions of physics are reexamined in a new approach using an adaptation of an old method. In quantum physics Einstein's chief method of inquiry between 1905 and 1925 involved a comparison of the thermodynamic properties of matter quanta and radiation quanta (photons). In these pages the author seeks to extend that method beyond thermodynamics to see what new insights it can offer us.