iSoul In the beginning is reality

# Transportation and physics

Theoretical physics has been applied to a variety of disciplines such as economics and traffic flow theory. Here we are returning the favor by considering transportation as a model for physics; in other words, physics is like a transportation system.

Consider the space-time continuum as an infinitely dense transportation network. The spatial extent of the network is the union of the lengths traveled by all light rays. The temporal extent of the network is the union of the durations taken by all light rays.

We begin with the minimal assumptions that space is 3-dimensional, homogeneous, isotropic, and locally Euclidean. The space-time network is self-contained; there is no external space or time in which it exists. So measures of space and time are measures of travel on the space-time network.

Network regularities, called laws, are the same for every trip in which the speed is constant (the principle of relativity). We will focus for now on the special case in which each trip has a constant speed (special relativity).

There exists a speed that is constant for all travelers (also called observers). For transportation this is usually an average or typical speed. For physics this speed is the speed of light in a vacuum, c (the principle of invariant light speed).

The speed that is constant for all travelers enables a conversion between space (travel length) and time (travel duration). In physics this means that for any length, x, the corresponding duration is x/c and for any duration, t, the corresponding length is ct, i.e., x = ct. Since space is linearly related to time (and vice versa), time possesses all the properties of space as well: time is 3-dimensional, homogeneous, isotropic, and locally Euclidean.

As is well known, from these assumptions the Lorentz transformation may be derived. If time is reduced to its magnitude only, spacetime may be represented by the 4-dimensional Minkowski space. If space is reduced to its magnitude only, spacetime may be represented by a 4-dimensional space that is isomorphic to Minkowski’s.

From this we know that Δr2 = Δx2 + Δy2 + Δz2 and Δt2 = Δx12+ Δx22+ Δx32 with the convention that Δx2 = (Δx)2. Then Δr2 = c2Δt2 or equivalently c2 Δt2 – Δr2 = 0 so that is an invariant of spacetime. This means that there is a kind of conservation of spacetime; the network remains the same no matter what people do.