Natural Science Forum / Physics / General Physics / April 2007

If we take x or y in dy/dt = A(t) + B(t)y + C(t)y^2, the Riccati
Differential Equation, equal to spin, then since spin in Quantum
Mechanics "measures" angular momentum, which classically is based upon
angular velocity w = d(theta)/dt for angle theta, it follows that
changing y to y = dw/dt measures angular acceleration classically via
dy/dt.   QM spin is still not the classical angular momentum, but we
can plausibly approximate it by the classical case in various
scenarios.

But this acceleration in its linear analog is dv/dt, so in considering
the acceleration of the Universe, setting y = v = velocity yields dy/
dt = a = linear acceleration.

So both classical linear velocity and angular velocity and their
associated accelerations are plausibly expressed by the Riccati
Differential Equation, and the Quantum Mechanical analogs are
approximated by the former two in various scenarios in linear and
angular momentum, etc.

Osher Doctorow