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, G_{ab}, 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 G_{ab} and T_{ab} satisfy the same mathematical identity, that is
G_{ab;b} = T_{ab;b} = 0

6 Therefore if T_{ab} is set equal to G_{ab}, 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=MC^{2}.xht - Direct derivation of
relativistic mass without using Special Relativity - MathMl

E=MC^{2}.html - gif

E=MC^{2}.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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