If empty space is something not nothing, then what is it? Quantum simulations describe spacetime as follows:
“…we think of empty spacetime as some immaterial substance, consisting of a very large number of minute, structureless pieces, and if we let these … interact with one another according to simple rules … they will spontaneously arrange themselves into a whole that in many ways looks like the observed universe.” (Ambjorn et al., 2008), p25.
This approach is compatible with the idea that space is a network of indivisible points that interact with each other according to simple rules, as proposed here. What then are the services that space provides in order to look like our space? The following are suggested:
- Locations. Points that define when objects are in the same locality and so interact.
- Directions. The neighbors a point can interact with define possible directions from that point.
- Dimensions. The number of independent degrees of freedom that the space can extend into.
Locations, directions, and dimensions are services that a space that looks like ours must provide. For example, in Wilson loop networks, each point is a volume of our space, and in Penrose spin networks, points interact in events that have input and output directions (Penrose, 1972). The need for dimensions is illustrated by their use in geometry. About two thousand years ago, the Greek Euclid created geometry by defining the structure of space as follows. He began with a point location of no dimensions that extended in one direction to make a line, that then extended at right angles to give a plane, that again extended to give a cube. This defined our space as having three linear dimensions, so every point could be represented by three number coordinates (x, y, z).
The resulting Cartesian System worked so well for geometry that it became the standard, but it doesn’t suit all cases. For example, war-gamers adapt Euclid’s space to the two dimensions of a game board by using hexagons not squares, as they give more directions of attack. Yet most simulations still assume a Cartesian or linear space, including loop quantum gravity (Smolin, 2001), cellular automata (Wolfram, 2002), and lattice simulations (Case, Rajan, & Shende, 2001), but to work on a network, a Cartesian space needs:
- A maximum size: The size of the space must be known in advance, to allocate coordinate memory.
- A zero-point origin: The space has to have absolute centre, or (0,0,0) point, within itself.
However, our space behaves in a way that satisfies neither of these requirements.
The maximum size requirement arises because the memory of linear coordinates depends on the network size. For example, a point stored as (2,9,8) in a 9-unit cube, must be stored as (002,009,008) in a 999-unit cube, so it needs more memory. This limit caused the Y2K bug that experts worried would crash our systems in the year 2000. The problem was that early computers stored years as two digits, to save memory, so 1949 was stored as “49”, but that meant that the year 2000 was stored as “00”, just as the year 1900 was. Even now, airline booking systems can mistake a 101-year-old woman for a baby for this reason.
If our space is a generated Cartesian space, its maximum size had to be set before the first event to avoid a Y2K bug. But our space has been expanding at the speed of light for billions of years and still is, with no end in sight, so its final size is undefined. A Cartesian space the size of our universe should have crashed by now, but it hasn’t, so our space can’t have linear dimensions.
The zero-point origin requirement arises because a Cartesian space needs a (0,0,0) point within itself, so when Hubble showed that every star and galaxy is receding from us, assuming a Cartesian space made our Earth the origin of the universe! But our planet only began recently, so it can’t be so! The discovery that our space is expanding everywhere at once wityhout an absolute center within itself also means it can’t have linear dimensions.
In general, linear coordinates work well for small, fixed spaces but not for a huge space like ours, that is expanding indefinitely from no point within itself.