Scope

Preceding chapters have dealt with relatively elementary applications of the EPI principle. These are problems whose answers are well-established within known experimental limits. Historically, such problems constituted ‘first tests’ of the principle. As we found, EPI agreed with the established answers, albeit with several extensions and refinements. The next step in the evolution of the theory is to apply it ‘in the large’, i.e., to more difficult problem areas, those of active, current research by the physics and engineering communities.

Two such are the phenomena of (i) quantum gravity and (ii) turbulence at low Mach number. We show, next, the current status of EPI work on these problems. Aspects of the approaches that are, as yet, uncertain are pointed out in the developments. It is hoped that, with time, rigorously correct EPI approaches to the problems will ensue. It is expected that final versions of the theory will closely resemble the first ‘tries’ given below.

Quantum gravity

Introduction

The central concept of gravitational theory is the metric tensor gμν(x). (For a review, see Exercise 6.2.5 and the material preceding it.) This defines the local distortion of space at a four-coordinate x. The Einstein field Eq. (6.68) permits the metric tensor to be computed from knowledge of the gravitational source ― the stress energy tensor Tμν(Sec. 6.3.4). This is a deterministic view of gravity. That is, for a given stress energy tensor and initial conditions, a given metric tensor results. This view holds over macroscopic distances x.