IVA. Nontechnical Introduction.

The question we are concerned with here is whether quantum mechanics is the final theory of the physical universe.  The answer we find carries with it a radical revision of our ideas about the nature of physical reality.  The change in vision can be likened to the image Plato paints in book VII of the Republic.  In his analogy, we are like prisoners in a cave, chained so we cannot even move our heads.  We face a wall at the back of the cave on which are thrown shadows of the events in the real world—people walking, trees bending in the wind and so on.  These shadows are a representation—a re-presentation—of the real world, but they are not the real world. 

What we will infer here is that we are in the same state as the prisoners in the cave.  Quantum mechanics implies that in the “real” or most basic physical realm, there is neither space nor time nor matter.  Instead these most basic concepts are like the shadows on the wall of the cave, a re-presentation of an underlying reality. 

How could we possibly infer this from quantum mechanics, which seems to be such a complete and successful theory of our space-time-matter world?  It is done through a branch of mathematics called, appropriately enough, representation theory.  In its original form, a mathematical equation will have such and such a form.  But one can construct another equation which is a  representation of the original equation.  It has the same structure as the original equation in many respects, but not in all.  There will be certain clues in the structure of the representational equation that it is indeed a representation of the original equation and not the original itself. 

What we will show is that quantum mechanics has exactly the characteristics one would expect if it were a representation of a deeper theory.  Space, time and matter do not appear in the original statement of this deeper theory; instead they are characteristics of the solutions of the equation.  It is the solutions - the state vectors of quantum mechanics - that we perceive, and we then construct our mental world around the characteristics of those solutions.