IVI. Speculations on Gravity. 

It has been notoriously difficult to find a unified theory that includes both gravity and quantum mechanics.  I will suggest here that the connection is simple and more obvious than it seems.  (In fact it seems so obvious that one suspects there must be a simple reason why it cannot be so.)

We first note that, through group representation theory, the property of mass is a consequence of the invariance of conventional quantum mechanics under special relativity.  So one has a suspicion that general relativity, which essentially deals with the way in which mass affects the macroscopic universe, should follow from a proper theory of quantum mechanics that is invariant under special relativity.  Second, we know that the presence of a particle polarizes the vacuum.  That is, the particle changes the (short-range) structure of the vacuum.  Third, in our underlying theory approach, space and time are not basic attributes of the physical universe.  Instead they are derivative concepts (derived from the action of the translation operators; see Sec. IVD2) ).  Thus it is reasonable to have a theory involving the structure of space and time.

These observations suggest the following:  Everything remains the same in quantum mechanics except that concentrations of matter slightly affect the long-range, macroscopic structure of the vacuum.  More specifically, when there is matter present, the vacuum state is not invariant under translations.  The variation in the properties of the vacuum would presumably affect the flight of free particles (free particle wave functions).

 How might the structure of the vacuum be affected?  If one has a Dirac-like vacuum, it might affect the local density of states over large distances.  Or if one uses a molecular model  for the vacuum, as in Sec. IVF2, it might alter the spacing between molecules over large distances.  The gravitational constant G would be a macroscopic measure of the response of the vacuum to the presence of matter.  Its smallness indicates that the response is slight.

So the conjecture is that the theory of gravity is a macroscopic theory of the vacuum.  What specific reasoning is to be used to translate these ideas equations?  At the present time, I do not know.  But presumably the energy-momentum tensor, defined in some macroscopic fashion, is the source term in a suitably invariant equation.