Rotational solutions under the new theory of motion

Abstract

The author recently introduced a new theory of motion which resolves several problems in the philosophy of physics and mathematics by replacing the continuum with nonvanishing time. Nonvanishing time means that the magnitude of an instant does not have the functional properties of zero, even though it may be very small. As a result, joint functions of time, such ass=vt, vary as the other terms even when time is instantaneous. Hence size (vdt or instantaneous position) is increasing as velocity. This paper presents some quantitative solutions to the above for the case in which a point of massm is resolving in a perfect circle with uniform speedv=ωr. The magnitude of an instantdt — the minimum time for real events—is found by obtaining the magnitude of the arcds along which the rotating point is distributed overdt time. Under the Heisenberg uncertainty principle this turns out to beds ²=h(mω)⁻¹. If the de Broglie equation and Einstein's two equations for photon energy are introduced, then in generalds ²=λr. Under the quantum mechanical definition of orbital angular momentum λr ⁻¹=2πn ⁻¹, wheren is the integral scalar forħ. Hence there is an asymmetry on the right side of the last expression fords, and the ratio ofds to the circumference of the circle is (2πn)^−1/2.