Hyperbolic Co-ordinates – The ‘Accelerating Frame of Reference’
From the hyperbolic co-ordinates of the last video (GR - 11) which can essentially measure ‘position’ in flat Minkowski space-time, a corresponding ‘time’ measurement is introduced which comes from the hyperbolic equations. Once this new space and time measuring system of ‘accelerating co-ordinates’ is established, it is then used to try to ‘mimic’ gravity - via a simplistic application of the Equivalence Principle. We then look at the Equation of a Geodesic in a region of this ‘mimicked’ gravity, and find that it essentially boils down to the measurement of a Newtonian force of gravity. This is our first glimpse at the ideas of General Relativity (Geodesic Motion) giving rise to ‘measured’ forces. This is all without any ‘mass’ being present, and in the next video (GR - 13), mass will be introduced in such a way that its size and position will produce the same effect as that of the above acceleration. This will lead to a discussion of the Schwarzschild Metric.
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.
This video (and channel) is NOT monetised
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