Objects tend to move in straight lines, defined as the shortest distance between two points. The general term is geodesic, because on a curved surface like the earth, the shortest distance between the poles is a curved longitude. A geodesic is a straight line on a curved surface, but why do objects move in straight lines at all?
Billiard balls on a table are said to move in straight lines by a property of matter called inertia, the tendency to continue in the same direction. Inertia makes an arrow shot into the air fly up but then it falls to the ground, so Newton proposed that a force from the earth pulls it down, called gravity. The arrow’s movement was then explained by its inertia plus the force of gravity, with space just a passive context. In this view, objects naturally move in straight lines unless some force acts upon them to alter that.
Einstein then showed that gravity works by curving space to alter the geodesic, so arrows actually still move in straight lines. Equally, the earth’s gravity keeps the moon in orbit by curving space around it, so that becomes its straight line. Gravity then isn’t a force acting on an object, but a change in space itself that alters what a straight line is.
Space as a network that transmits waves supports this view, as waves move based on how they are passed on. Light should then move in a straight line, not by itself, but because it is passed on that way by the network. In this view, space naturally transmits things in straight lines, unless something alters space.
Let us now suppose that.
“A point in spacetime is … represented by the set of light rays that passes through it.” (S. Hawking & Penrose, 1996) p110.
In network terms, the neighbors around a point define its possible transfer directions as a sphere around it. But for a given photon, those directions are a circle because a transverse wave must move at right angles to its vibration. This is why every photon has a polarization plane, perpendicular to its transverse vibration, in which it moves, so the directions available to a photon passing through a point are a planar circle (Figure 2.8).
The points of this circle limit how a photon can pass through a point, so it enters from and exits to a planar circle. Planar circles simplify how photons pass through a point, just as planar anyons simplify the quantum Hall effect (Collins, 2006)
Why then does light move in straight lines? For a network, the shortest path between any two points is the one with the fewest transfers, which is also the fastest path. Light will then move in a straight line to any destination if it always takes the fastest route, which it does. Chapter 3 gives more details but essentially light waves travel in straight lines because they take every path to a destination and the first to arrive triggers a physical event. Chapter 4 establishes that matter is also a wave so the same principle applies. Chapter 5 can then explain gravity as matter altering the network of space, just as Einstein said.
If the geometry of the universe is rotational, based on circles not squares, then for a point in space, planar circles specify how light is passed on and transverse circles specify how it vibrates (Figure 2.9). In the next section, transverse circles define time, just as planar circles define space.
