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criticisms of the einstein field equation - Alpha Institute for Advanced ...

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all <strong>the</strong> Christ<strong>of</strong>fel symbols and all elements <strong>of</strong> <strong>the</strong> Riemann, Ricci and Einstein<br />

tensors. Each line element is checked <strong>for</strong> metric compatibility, and each line<br />

element is checked to see if it obeys <strong>the</strong> fundamental Ricci cyclic <strong>equation</strong>,<br />

known in <strong>the</strong> standard literature as <strong>the</strong> first Bianchi identity. This appellation<br />

<strong>of</strong> <strong>the</strong> standard physics is a misnomer, because it is nei<strong>the</strong>r a true identity<br />

nor was it given by Bianchi. It was first given by Ricci and Levi-Civita. The<br />

rigorously correct Bianchi identity in geometry was first given by Cartan as is<br />

well known, and as is equally well known, must include <strong>the</strong> torsion ineluctably.<br />

Finally in this chapter by Eckardt, <strong>the</strong> line element solutions are tested against<br />

<strong>the</strong> dual identity proven in chapter two. The results are given in tables and<br />

graphs. They are exceedingly intricate, so <strong>the</strong> computer is used to build up <strong>the</strong><br />

tables without manual transcription error. The results show clearly that <strong>the</strong><br />

Einstein <strong>field</strong> <strong>equation</strong> is incorrect geometrically - meaning that <strong>the</strong> standard<br />

<strong>the</strong>ory <strong>of</strong> relativity must be revised fundamentally to place torsion as a central<br />

feature <strong>of</strong> <strong>the</strong> natural and engineering sciences. This is what ECE <strong>the</strong>ory does.<br />

In <strong>the</strong> fifth chapter, Kerry Pendergast uses his skills as an educator and<br />

writer to put <strong>the</strong>se results in historical and scientific context. In so doing he<br />

uses some <strong>of</strong> <strong>the</strong> material from his "virtual best seller" on www.aias.us, called<br />

"Crystal Spheres" to give a historically accurate description <strong>of</strong> <strong>the</strong> evolution <strong>of</strong><br />

<strong>the</strong> <strong>the</strong>ory <strong>of</strong> relativity.<br />

In <strong>the</strong> remainder <strong>of</strong> this introductory chapter a brief account is given <strong>of</strong><br />

<strong>the</strong> evolution <strong>of</strong> space-time torsion in geometry and ECE <strong>the</strong>ory. The latter is<br />

reviewed in detail in chapter two <strong>of</strong> this book, (paper 100 <strong>of</strong> www.aias.us). The<br />

fundamental idea <strong>of</strong> <strong>the</strong> <strong>the</strong>ory <strong>of</strong> relativity is that physics must be an objective<br />

subject independent <strong>of</strong> anthropomorphic bias.<br />

This philosophy was given <strong>for</strong> example by High Renaissance thinkers such<br />

as Bernardino Telesio and Francis Bacon, but goes back to classical times. Its<br />

most well known manifestation appears in <strong>the</strong> Idol <strong>of</strong> <strong>the</strong> Cave philosophy <strong>of</strong><br />

Bacon. By this he means <strong>the</strong> fantasies <strong>of</strong> <strong>the</strong> human mind, <strong>the</strong> word "idol"<br />

being used in its original classical Greek meaning <strong>of</strong> "dream". Bacon asserts<br />

that <strong>the</strong> workings <strong>of</strong> nature must be manifest through empirical testing <strong>of</strong> human<br />

ideas, in our times "experimental data". Contemporary science is based on this<br />

philosophy combined with <strong>the</strong> earlier philosophy <strong>of</strong> William <strong>of</strong> Ockham, that<br />

<strong>the</strong> simpler <strong>of</strong> two <strong>the</strong>ories is preferred in natural philosophy or physics. The<br />

invisible college <strong>of</strong> Francis Bacon later developed into <strong>the</strong> Royal Society, which<br />

espouses <strong>the</strong> Baconian philosophy.<br />

In Newtonian times <strong>the</strong> idea <strong>of</strong> absolute space and <strong>of</strong> absolute time was predominant,<br />

and <strong>the</strong> whole <strong>of</strong> Newtonian mechanics is based on <strong>the</strong> separation<br />

<strong>of</strong> space and time. The anthropomorphic bias <strong>of</strong> <strong>the</strong> human mind makes this<br />

separation seem entirely natural from everyday experience. Time seems to be<br />

moving in one way, in space we can move <strong>for</strong>wards an backwards, and <strong>the</strong> two<br />

concepts appeared to be described by Newtonian mechanics with <strong>the</strong> later addition<br />

<strong>of</strong> <strong>the</strong> Euler, Laplace and Hamilton <strong>equation</strong>s and so <strong>for</strong>th in classical<br />

dynamics. In <strong>the</strong> nineteenth century <strong>the</strong>se well known concepts <strong>of</strong> dynamics<br />

were challenged by <strong>the</strong> <strong>the</strong>n new classical electrodynamics, notably <strong>the</strong> vector<br />

<strong>equation</strong>s <strong>of</strong> Heaviside. These are <strong>the</strong> well known <strong>equation</strong>s <strong>of</strong> classical electro-<br />

6

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