General Relativity For Teletubbies

Sir Kevin Aylward B.Sc., Warden of the Kings Ale


Apr 2020


Introduction

This set of papers forms an introduction to General Relativity, in as simple a manner as possible.

The goal of this approach is get to some sort of sensible comprehension of general relativity (G.R.) with out cluttering up the mind with all sorts of extraneous nonsense that’s not required, and only usually given in standard texts to try and impress one on how clever the author is.

To mathematicians this approach will be akin to fingernails on a blackboard, but I'm an EE, and see no need to complicate matters with such posh talk.

Its is assumed that the basic concepts of things such as why the grass is Greens, how to Div funds to offshore banking accounts, and how to Stoke a coal fire on a train has already been covered in other vector analysis courses. So, certain non essential goodies will be systematically ignored. For example, proving that such and such is really a tensor and that tensor equations are true in all coordinate systems and so forth is not particular illuminating, the goal is to achieve a good grip on G.R., not pure mathematics. What's much more of use to have step by step derivations that don’t jump about into hyperspace leaving you wondering why you seem so daft for not understanding something of real relevance. Usually the author was on drugs at the time and had no concept at all of what a logical argument was.

I have added some background math, just to get those of you punters who are more intellectually challenged up to relativistic speed

I do have some formal academic qualifications in Physics, although, I am er... and Analog ASIC design engineer..... .certificates


Simplified Summary

1 Its is experimentally observed that all masses, in the same gravitational field, fall with the same acceleration. 

2 Gravitational fields are generated by a mass.

3 There is a geometrical mathematical object, Gab, the contracted Riemann Tensor, that measures acceleration of geodesics (shortest distance between points on a curved surface).

4 There is a physical object, Tab, the energy-momentum tensor, that measures the motion of mass (and energy).

5 Both Gab and Tab satisfy the same mathematical identity, that is Gab;b = Tab;b = 0

6 Therefore if Tab is set equal to Gab, then mass motion will be described by a geometric object that determines acceleration of geodesics, which necessarily means that it satisfies the physical observation of mass generating accelerations if mass moves along a geodesic. 


Contents

The following papers should be read in sequence. The MathML versions have ctrl-+ & ctrl- proportional zooming support. MathML is directly supported in Firefox and Safari. The pdf versions also have proportional zooming support.

Calculus.xht - MathML
Calculus.html - gif
Calculus.pdf - pdf

Tensors - MathML
Tensors - gif
Tensors.pdf - pdf

Covariant Derivative.xht- MathML
Covariant Derivative.html - gif
Covariant Derivative.pdf - pdf

Calculus ofVariations.xht - MathML
Calculus of Variations.html - gif
Calculus of Variations.pdf - pdf
 
Geodesic - MathML
Geodesic - gif
Geodesic - pdf

Riemann Tensor - MathML
Riemann Tensor - gif
Riemann Tensor - pdf

Stress-Energy/Energy-Momentum Tensor.xht - MathML 
Stress-Energy/Energy-Momentum Tensor.html - gif
Stress-Energy/Energy-Momentum Tensor.pdf - pdf

Einstein Tensor & Einstein Field Equations.xht - MathML
Einstein Tensor & Einstein Field Equations.html - gif
Einstein Tensor & Einstein Field Equations.pdf - pdf


Misc. Stuff

Special Relativity.html - Special Relativity Refresher
Special Relativity.pdf -  Special Relativity Refresher - pdf

Special Relativity Background.html - Special Relativity Background
Special Relativity Background.pdf -  Special Relativity Background- pdf

E=MC2.xht - Direct derivation of relativistic mass without using Special Relativity - MathMl
E=MC2.html - gif
E=MC2.pdf - pdf

Twins Paradox.xht- A " correct" resolution to the twins paradox, as held by the SR model, without accelerations or General Relativity - MathML
Twins Paradox.htm - gif
Twins Paradox.pdf - pdf

Galilean Transformation Of Maxwell's Equations.xht - Without SR, Maxwell's predict a non invariant speed of light
Galilean Transformation Of Maxwell's Equations.html - gif
Galilean Transformation Of Maxwell's Equations.pdf - pdf

Geometry & Relativity - Geometry does not explain the physical results of Relativity
Geometry & Relativity - pdf

Fields & Aether - Are the Fields of QFT an Aether in disguise?
Fields & Aether - pdf

Axioms, Clocks & Relativity - “A clock always reads the correct time, and time is what a clock reads”. Oh dear... ahmmmm....
Axioms, Clocks & Relativity - pdf

Space-time & Quantum Mechanics - “Paths in space-time are imaginary” - to wit: "longer paths in space-time" contradicts Quantum Mechanics
Space-time & Quantum Mechanics - pdf

Space-Time Sanity - Space-time is only a mathematical, behavioral model that accounts for observations. 
Space-Time Sanity - pdf

POR - It isn't covariance - what the POR really means....


Other Authors

Ether And The Theory Of Relativity - An article by Einstein on the relationship between the Ether of Gravity and the Ether of Electromagnetism.

Covariance & Relativity - J. D Norton -  GR is not Covariance, GR contradicts Mach's Principle, and all accelerating frames are not equivalent.


Links

Kevin Aylward's Webs - Kevin's main web site


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