iSoul In the beginning is reality

Conservation of celentum

Note: prolentum was changed to celentum, lenticity was changed to celerity, and mollence/visity/elaphrence was changed to gorce, June 2017.

In a recent post, I defined celentum as the celerity divided by the mass. Here I show that celentum is conserved, as momentum is. I will do this in 1D with a result that may be generalized to 3D time.

Consider the equation of motion for a particle:

(1/m) dℓ/dr = M,

where M is the gorce. Multiply both sides by dr:

(1/m) dℓ = dq = M dr,

where dq is a differential of the particle’s celentum, q = ℓ/m.

In integral form:

q2q1 = Δq = ∫ M dr.

Consider two interacting particles. For particle 1 we have

dq1/dr = M12,

where M12 is the alowance exerted on particle 1 by particle 2. For particle 2 we have

dq2/dr = M21,

where M21 is the gorce exerted on particle 2 by particle 1. By addition,

d(q1 + q2)/dr = M12 + M21 = 0,

using Newton’s third law applied to gorce. After integration, we find

q = q1 + q2 = constant,

so that the total celentum of the system is a constant of the motion. That is, celentum is conserved.

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