Converse physics

Velocity is defined as:

$\mathbf{v}(\mathbf{x},t)=\frac{\mathrm{d} \mathbf{x}}{\mathrm{d} t}$

where x is the displacement and t = ‖t‖ is the independent time interval, the distime of a parallel reference motion. The inverse of v is the function defined by the reciprocal of this derivative:

$\mathbf{v}^{-1}(\mathbf{x},t)=\left ({\frac{\mathrm{d} \mathbf{x}} {\mathrm{d} t}}\right )^{-1}$

The converse of v is w, the lenticity, which is defined as:

$\mathbf{w}(\mathbf{z},s)=\frac{\mathrm{d} \mathbf{z}}{\mathrm{d} s}$

where t is the dischronment and s = ‖s‖ is the independent distance, the distance of a parallel reference motion. The inverse of v is the function defined by the reciprocal of this derivative:

$\mathbf{w}^{-1}(\mathbf{z},s)=\left ({\frac{\mathrm{d} \mathbf{z}} {\mathrm{d} s}}\right )^{-1}$

If s were always the dependent variable and t were always the independent variable, then v and w would be inverses of each other. But that is not the case here. The dependency of s and t changes between v and w.

Since x and z are symmetric, so are v and w. Interchange x and z and then s and t to get the corresponding equation for v and w, or other pairs of symmetric variables such as a and b, the acceleration and the relentation.

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