Two key expressions for space-time dynamics are the momentum and the kinetic energy. Here we derive the corresponding expressions for time-space, which are called the *celentum* and the *kinetic co-energy*.

The momentum and kinetic energy are the force through time or space:

momentum = *mv* = *F* Δ*t*, an

kinetic energy = *mv²*/2 = *F* Δ*s*,

where *m* = mass, *v* = velocity, *F* = force, *t* = duration, and *s* = distance.

Since *F* = *ma*, these formulae come from the related kinematic formulae without mass:

*v* = *a* Δ*t* and *v²*/2 = *a* Δ*s*,

where *a* = acceleration, with initial distance and velocity zero.

For time-space the corresponding kinematic formulae are these:

ℓ = *b* Δ*s* and ℓ*²*/2 = *b* Δ*t*,

where ℓ = celerity and *b* = prestination, with initial duration and celerity zero.

These formulae may be multiplied or divided by mass to get the desired result. Since velocity and celerity are inversely related, the form of mass should also be inversely related. Thus these formulae should be divided by the mass, or multiplied by the inverse of the mass, which I’m calling the *vass*.

Since *Γ* = *b*/*m* = *nb*, the corresponding dynamic formulae for time-space are:

*celentum* = ℓ/*m* = *n*ℓ = *Γ* Δ*s*, and

*kinetic co-energy* = ℓ*²*/2*m* = *n*ℓ*²*/2 = *Γ* Δ*t*,

where *Γ* = *gorce*, the time-space form of force and *n* = *vass*, the inverse of mass.

The kinetic energy and kinetic co-energy are related:

1/kinetic energy = 2/*mv²* = 2*n*ℓ*²* = 4(*n*ℓ*²*/2) = 4 × kinetic co-energy.