__What if we...__

Let a Rational number stand for a *real* particle -- like a quark or an electron -- defined minimumly as a *detectable excitation of some underlying field*, a quantum fluctuation that brings with it the property of permanence and continuity of identity.

The Irrationals can then stand for *virtual* particles. Virtual particles *also* considered as excitations of this *underlying field* from which the *real* particles emerge, but manifested as the forces operating *between* real particles; that is, acting as *intermediaries* -- the mesesenger particles.

Here is where I have a problem: *In the literature*, virtual particles play two different roles. One: force-particles and the field supporting their existence. And two: emerging as matter/antimatter pairs from the vacuum [e.g., quark-antiquark pairs], borrowing energy for a Planck time, then dissolving back into the morass of potential quantum energy. In any event, each virtual particle model shares the concept of *virtual particles emerging from the vacuum of pre-space*.

So, we have quantum fluctuations, both real and virtual, underlying the reality of and giving *substance* to quantum space.

The *real* particle fluctuations -- corresponding to the Rationals -- are discrete (quanta) and may be considered as *nodes of a network*. Topologically, each node is compact in Hilbert space [infinite dimensional] and surrounded by a neighborhood of energy.

Interaction of the Rationals through virtual *entanglement* brings into being, or precipitates, the Irrationals, which may be thought of as dynamic interconnections -- bosons, force particles -- between nodal neighborhoods. Their *intermingling*, in turn, generates and defines the Real Numbers -- *the Continuum*.

One could argue that the particles and their interactions *arise* simultaneously, thereby occluding the logic of cause and effect. Nonetheless, the point is that their joining as continuous process produces the space we're familiar with.

Gravity, residing as *potential only* in quantum space, is an **effect** of this interaction and as such is not **fundamentally** a quantum phenomenon and cannot therefore be a gradient of the underlying virtual quantum field. With *time* it forms a *hypersurface* or *multi-dimensional manifold* -- the creation of the continuum of *spacetime* -- comprised of families of curves -- pathways, trajectories, histories -- in space. It acts to cohere and maintain the integrity of the quantum world, to give it sense and definition, as does an envelope of a tangential family of curves on an *ordinary* surface.

But for the sake of argument, if *virtual gravitons* -- the force-particles of a gravitational field -- can be construed as points (quanta) of those curves, then the manifold/field thus generated would be of the second order, the order of acceleration.

*But is that necessary*?