iSoul In the beginning is reality

Relativity at any speed

This is a summary of posts (such as here and here) about the application of relativity theory to transportation. This is different from applying theories of physics to other subjects such as economics since here it is real relativity, not some analogy. However, the application is an approximation, but that is the nature of transportation, which has both physical and social aspects.

Transportation (or transport) modes are means of transporting goods and/or people. The common modes are roads (including motorized and non-motorized modes), railroad (passenger and freight), pipeline, maritime (ferry and shipping modes), air (aviation), etc. One can consider information a good and the telecommunication of information as a form of transportation. In that sense any signal or high-speed particle can be considered a mode of transportation.

Transportation is subject to a variety of obstacles, including excess volume per available capacity (called congestion) and stoppages caused by crashes, storms, construction, or other disruptions (which may also cause congestion). There may be complicating factors such as the mixing of modes (e.g., bike and pedestrian traffic).

The minimum, maximum (free-flow), or typical speeds of a transportation mode are characteristic of the transportation mode as a system, rather than the speed of a particular vehicle or particle (even though a particular vehicle or particle might have this value in a particular context). As such, these characteristic or modal speeds are constants within the transportation system under consideration.

There are contexts in which a speed characteristic of a transportation mode (perhaps under congestion) is a constant, at least for a certain period of time. In these contexts relativity theory plays a role similar to high-speed physics with the speed of light in a vacuum. Such characteristic speeds are constants that are independent of the speed of particular objects (vehicles) in that mode.

So, for example, a free-flow highway speed may be considered a constant over a region or transportation network. Then in this context such a constant speed would play the role of c, the speed of light in a vacuum. This speed would relate space and time. The Lorentz transform would be needed to determine relative speeds.

The characteristic speed may be a maximum speed within the mode or it may be less than the maximum, such as a typical speed, in which case some vehicle speeds greater than the typical speed would be expected. This may be different from physics, in which tachyons may not exist. In any case, relativity theory can cover these cases, which would arise in transportation.

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