In Newtonian mechanics inertial frames of reference are related by a *Galilean* transformation and *time* is absolute. In the special theory of relativity (STR) inertial frames of reference are related by a *Lorentz* transformation and the *speed of light* is absolute. By taking account of the three dimensions of time with a single dimension of space, we may derive a dual mechanics to each of these: (1) a Newtonian dual with a single dimension of absolute space and three dimensions of relative time, and (2) an STR dual with a single dimension of relative space and three dimensions of relative time.

In the usual exposition there is a reference frame S’ moving with constant velocity *v* in the direction of the *x _{1}* space coordinate (with no movement in the

*x*and

_{2}*x*directions) and absolute time

_{3}*t*. That changes to constant

*legerity*(inverse of velocity)

*w*in the direction of the

*t*

_{1}*time coordinate*(with no movement in the

*t*and

_{2}*t*directions) and absolute space

_{3}*r*, the travel length. The dual Galilean transformations are then

*t _{1}‘ = t_{1} – wr*

*t _{2}‘ = t_{2}*

*t _{3}‘ = t_{3}*

*r’ = r*

What does this mean? It means that there is a constant movement measured by legerity so that as the travel length increases, the duration changes from *t* to *t _{1}‘* such that

*t – t*, which is a constant ratio of duration over length multiplied times the travel length.

_{1}‘ = wrThe Lorentz transformation is analogous to this with the absolute *time speed* of light, c, replaced by the absolute *space speed* of light, which is the inverse of c, or 1/c.

*t _{1}‘ = γ (t_{1} – wr)*

*t _{2}‘ = t_{2}*

*t _{3}‘ = t_{3}*

*r’ = γ (r – t _{1}wc²)
*

in which

*γ = 1* / sqrt(*1 – w²c²*)

What does this mean? It means that time (duration) appears dilated and length appears contracted, which is the same as the standard Lorentz transformation (known as a Lorentz *boost*). The laws of physics remain the same despite changing to a space reference from a time reference.