IIC.  Mathematical Theory & Physical Reality. 

1. Physical Reality Is Completely Governed by
the Mathematics of Quantum Mechanics.

We see from the evaluation of quantum mechanics in section IIB that, everywhere it can be tested, the physical universe obeys the mathematics of quantum mechanics.  So our first conclusion is that  physical existence—including our brains and bodies—is completely governed by mathematics, specifically the mathematics of quantum mechanics. 

2. Physical Reality Consists of the Wave Function Alone. 

Second, one of the goals of physics (in my opinion) is to find the true nature of physical reality.  In a strict philosophical sense, I suppose, one can never know that with absolute certainty.  But the philosophical stance is paralyzing.  We are interested instead in a pragmatic answer, with as much certainty as possible.  Our view is that, because of the successes and absence of failures of the theory, rigorously tested against the actual properties of matter, we can, with high confidence, deduce the true nature of physical existence from quantum mechanics.

What is the picture we get of matter?  One could take the point of view that the mathematics of quantum mechanics is simply describing the behavior of an objectively existing reality.  But as we will see (sections IIIA and IIIB and IIC3), the mathematics of quantum mechanics essentially precludes the existence of any form of matter other than the wave function.  There can be no particles or other objective forms of matter.  Thus the mathematics of quantum mechanics implies that the “true nature” of physical existence is that it consists of the wave function and the wave function alone.  (See also the Copenhagen interpretation in section IIIB3.)           

3. No Determinism in Quantum Mechanics. 

In the classical Newtonian scheme of physics, once the universe was set in motion, the flow of existence was uniquely determined for all time.  There was no freedom in the course of events, no free will.  But in quantum mechanics, that is not true.  Rather than determining a unique flow of events, quantum mechanics allows for many possible futures (sections IIE and IIF).  Thus the mathematical laws of quantum mechanics completely govern the physical universe and at the same time give the possibility of freedom!  The mathematics does not lock us into a deterministic future.

4. The Equations Always Hold. 

Finally, a physicist (or at least this physicist) would hope that the mathematical equations of physics always hold.  It is metaphysically awkward to suppose, for example, that one’s mind can influence when the equations govern matter and when they do not (section IIIB5).