In order to keep things as simple as possible, I’m starting to name the dual to standard physics with the qualifier “dual”, so that dual physics, dual mechanics, dual speed (not two speeds), dual velocity, etc. refer to their dual terms. Like tangent and cotangent, there is an inverse relationship between physics and dual physics. Here is the beginning to a systematic presentation of this dual physics, starting with classical mechanics.

The simplest mechanics concerns a point object with finite but negligible mass, called a *particle*. A particle is described by its position in space, which may vary in a time series. A *dual particle* is described by its position in time, which may vary over a series of places, i.e., over a path or route. A particle might not change its position in space but it must exist over multiple positions in a time series. Similarly, a dual particle might not change its position in time but it must exist over multiple positions in a series of places.

Note: This is an unusual perspective, but it will make more sense as we go along. Have patience.

The definition of *speed* is, “The time rate of change of position of a body in space without regard to direction; in other words, the magnitude of the velocity vector.” (*McGraw-Hill Dictionary of Physics*, 3rd edition, used throughout with slight modification). Implicit in this definition is that there must be a non-zero change in a time series, which is nominally the unit in the denominator, e.g., “metres per second” refers to the spatial change in metres over one second of a time series.

The definition of *dual speed* or *pace* then is “The space rate of change of position of a body in time without regard to direction; in other words, the magnitude of the dual velocity vector.” Implicit in this definition is that there must be a non-zero change in a place series, which is nominally the unit in the denominator, e.g., “seconds per metre” refers to the temporal change in seconds over one metre of a place series.

The definition of *velocity* is, “The time rate of change of position of a body in space; it is a vector quantity, having direction as well as magnitude.” The definition of *dual velocity* is, “The space rate of change of position of a body; it is a vector quantity, having *dual direction* as well as magnitude.”

Direction in space is based on distance and dual direction is based on duration using triangles and trigonometry. If light or anything with a constant speed is used to measure both distance and duration, then these directions will be equivalent. But otherwise they may be different, for example with travel on city streets.

The definition of *acceleration* is, “The rate of change of velocity with respect to a time series.” The units are, e.g., metres per second per second. Similarly, the definition of *dual acceleration* is, “The rate of change of dual velocity with respect to a place series.” The units are, e.g., seconds per metre per metre.