โ Scribed by Karlheinz E Woehler
No coin nor oath required. For personal study only.
Based on Wheeler's conjecture that the quantum fluctuations of the metric create a multiple connected foam-like structure of the vacuum with a structure constant of II* = (hC/c")'i* w 1O-33 cm and large virtual energy densities of the order c"/GL*" Q 1O115 erg/cm3 and that elementary particles are exciton-like weak coherent perturbations in the violent vacuum physics, a mode1 theory is constructed in which real turbulent fluctuations are superimposed on the average metric with the fluctuating metric satisfying the free space Einstein equations.
A stationary turbulent field of "mixing length" L* represents the vacuum fluctuations, long-range coherent fluctuations the exciton-like particles. Averaging gives the Einstein equations for the average metric which because of the nonlinear terms contains a vacuum term associated with the small-scale fluctuations and a term associated with the coherent part which is interpreted as the energy momentum tensor. Estimate of the leading terms in the energy momentum tensor gives for the size L of the excitons the relation L -L*2/3Rk'3 with the average universal curvature radius R,. For R0 -10mz8 cm, L is of the correct order of magnitude lo-l3 cm. Further relations between microscopic and cosmologic quantities are derived which appear to be Eddington's relations. The vacuum terms give a modification of Einstein's equations which act as mass production terms and are proportional to the average curvature with an estimated rate of 1O-4L g/cm3 sec. Possible consequences due to time dependence of R are briefly discussed.
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