On a flat surface, a straight line is the shortest distance between two points. The general term is geodesic, as on a curved surface like the earth, the shortest distance between the poles is a curved longitude. The shortest path between two points in all cases is a geodesic. Objects were said to move in straight lines by a property of their inherent mass called inertia. Newton showed that matter curved this path by the “force of gravity” then Einstein deduced that this “force” actually works by “curving” space to change the geodesic. Newton saw the earth as exerting a force to attract an apple but Einstein saw it bending space-time so the apple naturally “falls” to earth. He attributed object movement to matter’s ability to alter space and time.

If entities move by network transfers, light moves in straight lines by how the network transfers it, not by itself. Now suppose:

“A point in spacetime is … represented by the set of light rays that passes through it.” (S. Hawking & Penrose, 1996) p110

In network terms, a point in space is represented by the transfers available to a node, so the question of direction becomes “How does a node pass on a photon?” If a point in space is a quantum network node, all the ways it can receive a photon package from a neighbor and pass it on represent what it “does”. The photon doesn’t “decide” by itself where to go in empty space but is just passed on in a certain way by the network.

Every photon has a polarization plane at right angles to its transverse oscillation, so its transfer direction must be in the same plane. Let us call the set of neighbor transfers for any given plane a planar circle. Planar circles simplify the situation to an in-node/out-node transfer as shown in Figure 2.8, just as planar anyons simplify the quantum Hall effect (Collins, 2006).

The shortest “distance” between two network nodes that we call a straight line is then the path with the fewest transfers. The path of fewest transfers is then the fastest path of a constantly expanding wave, Chapter 3 argues that quantum entities move in “straight lines” because that is the fastest network route. Network transfers also explain why the sun’s gravity bends light around it, as in Chapter 5 the sun’s mass redefines the fastest path by changing the network load differentially around it. In both cases, the direction taken is defined by the fastest transfer path not the choices of the entity.

Figure 2.9 shows that for one node, a planar circle defines its transfer direction and a transverse circle defines its processing cycle. It is now proposed that just as planar circles define the directions of space, so processing transverse circles defines the passage of time.