| sufficiently rigid
Three necessary and sufficient conditions for rigidity of a particle are the following: (r2-r1)(v2-v1) = 0, (r3-r2)(v3-v2) = 0, and (r3-r1)(v3-v1) = 0. Applying the mass-time operator (p/v)(d/dt) to either the left or the right factors give the following: (p2-p1)(v2-v1) = 0, (p3-p2)(v3-v2) = 0, and (p3-p1)(v3-v1) = 0, and (r2-r1)(f2-f1) = 0, (r3-r2)(f3-f2) = 0, and (r3-r1)(f3-f1) = 0. The factors containing forces and space-time displacements could be used to describe the rigidity of the quantum vacuum. The following properties are necessary for reducing some of the factors: f1 ^ f2, f1 ^ r1, f1 ^ r2, f1 || f2, f1 || r1, f1 || r2, f2 ^ r1, f2 ^ r2, f2 || r1, f1 || r2, r1 || r2, r1 ^ r2 . Note that not all of these properties can be simultaneously satisfied.
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Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: ¶a(t)·¶r(t)=c²
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