__The Background__: The hands of a clock are in motion relative to the observer’s rest frame yet they display the present time of the rest frame. The motion of the clock hands is identified with the time of the rest frame.

The speed of a body is its distance traversed per unit of time. The inverse of speed is called pace, which is the time of travel per unit of length. The vector version of speed is the displacement of a body per unit of time (velocity), but what is the vector version of pace? Call it *lenticity*, which would seem to be a kind of displacement in time per unit of length, but that implies there are three dimensions of time. The rest of this article defines time and shows that it has three dimensions, although two of its dimensions are usually latent.

The term *time* has many different meanings, but it is unavoidable because of the lack of alternatives. The main thing to remember is that time in physics is *duration*, Δ*t*, an interval or length of time (cf. Newton). Let us call this the *distime* because it is analogous to distance in space. Since time is homogeneous, in physics it makes no difference what the particular date and time are. It’s the same with space: only the *length*, Δ*x*, a distance, an interval or length of space that matters, not the particular coordinates.

__The Theory__: An *observer* is a device or person capable of making measurements relative to a frame of reference. An *inertial observer* is an observer in inertial motion, i.e., one that is not accelerated with respect to an inertial system. An observer here shall mean an inertial observer. An inertial frame is one that is not accelerating. A frame of reference here shall mean an inertial frame.

An observer P measures space coordinates relative to a frame K at rest relative to P. Call frame K a *space frame* for P. *Space* (3D space) is the R^{3} geometry of places and lengths in a space frame. A *place point* is a point in 3D space. The space origin is a reference place point. The location vector of a place point is the 3D space vector to it from the space origin. The coordinates of place points are called *locations* relative to the frame K of observer P and are measured in terms of length of space. Let the space axes in K be designated as *x*_{1}, *x*_{2}, and *x*_{3}.

An observer P measures time coordinates relative to a frame L in uniform motion at a standard rate relative to P. Call frame L a *time frame* for P. *Time* (3D time) is the R^{3} geometry of times and durations in a time frame. A *time point* is a point in 3D time. The time origin is a reference time point. The chronation vector of a time point is the 3D time vector to it from the time origin. The coordinates of time points are called *chronations* relative to the frame L of observer P and are measured in terms of length of time (duration). Let the time axes of L be designated *t*_{1}, *t*_{2}, and *t*_{3}.

Every observer has a space frame and a time frame, which together form a *complete frame of reference*. Let the direction of motion of the time frame relative to the space frame be the *x*_{1} axis, and let this axis be coincident with the *t*_{1} axis. In general, the coordinates of a point in space and time will then be ((*x*_{1}, *x*_{2}, *x*_{3}); (*t*_{1}, *t*_{2}, *t*_{3})).

Since uniform motion is one-dimensional, only one coordinate from either the space frame or time frame is required as the independent denominator for rates of motion. For rates of velocity, acceleration, etc., only one time coordinate is needed; the other two time coordinates are zero, so time (duration) is a scalar. For rates of lenticity, retardation, etc., only one space coordinate is needed; the other two space coordinates are zero, so space (stance) is a scalar.

If a time frame is moving at velocity **v**_{c} relative to its associated space frame, then the other time coordinates are zero: ((*x*_{1}, *x*_{2}, *x*_{3}); (*t*_{1}, 0, 0)). The time coordinate (*t*_{1}, 0, 0) may be expressed by a scalar; call it *t*. The result is the space coordinates (*x*_{1}, *x*_{2}, *x*_{3}) and a time scalar, *t*.

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