In this video (GR - 04), we take the idea of one-dimensional Contravariant and Covariant vectors, and move to thinking about TWO dimensional space, and the vectors in that space having two types of components - again called ‘Contravariant’ and ‘Covariant’. This leads on to a simple introduction to the ‘Metric Tensor’. On the way to this, the Einstein Summation Convention is introduced, which will be used from now on to reduce long equations to a much simpler-looking form.
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.
56:51 Correction - The column vector on the left hand side should read (downwards) V1, V2, V3
This video (and channel) is NOT monetised
12 янв 2023
