Einstein's Field Equations – A Simple Derivation
Having assembled all the ideas in the previous videos (GR - 01 to GR - 17), this video (GR - 18) sets out to give a simplified derivation of Einstein’s Field Equations.
It starts with some Newtonian Equations from earlier videos (GR - 01 and GR - 02), and uses the ‘pattern’ seen in them (the space-time connection with mass) to formulate a rank two tensor equation which uses the ‘Stress-Energy-Momentum Tensor’ instead of simply mas or mass density. Possibilities for the spatial side of the equation are discussed and tested using the ‘Continuity Equation’, until an equation is found which seems to fit the bill - and which reduces to Newtonian mechanics when the speed of light is taken to be infinite.
Towards the end of this video, there is a short discussion of gravitational waves, and a mention that these ‘bare’ Einstein Equations obviously do not contain any mention of the cosmological constant (they are not yet applied to the cosmos). The issue of the Cosmological Constant will be discussed in the final video in this series (GR - 20).
This video is part of a series of videos on General Relativity (GR-01 to GR-20), which has been created to help someone who knows a little bit about “Newtonian Gravity” and “Special Relativity” to appreciate both the need for “General Relativity”, and for the way in which the ‘modelling’ of General Relativity helps to satisfy that need – in the physics sense.
The production of these videos has been very much a ‘one man band’ from start to finish (‘blank paper’ to ‘final videos’), and so there are bound to be a number of errors which have slipped through. It has not been possible, for example, to have them “proof-watched” by a second person. In that sense, I would be glad of any comments for corrections ……. though it may be some time before I get around to making any changes.
By ‘corrections and changes’ I clearly do not mean changes of approach. The approach is fixed – though some mistakes in formulae may have been missed in my reviewing of the final videos, or indeed some ‘approximate explanations’ may have been made which were not given sufficient ‘qualification’. Such changes (in formulae, equations and ‘qualifying statements’) could be made at some later date if they were felt to be necessary.
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