Quote:
Originally Posted by Ken G
The dimensionality is the number of independent coordinates you need to specify a location. That's a coordinate-dependent approach to dimensionality, there are probably more abstract coordinate-free approaches but I always prefer what seems concrete and physical, so I like to choose a coordinate approach.
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I want to take issue with this statement as I feel that GR leaves some ambiguity if you only define a point with 3 coordinates.
We know from GR and from astronomy that light is bent around massive objects. We also know that the speed of light is constant. From this we can infer that the light following the Curve around a massive object is a bit longer than the distance between the viewer and the object.
So if the light were exactly 300,000 km away the light should take 1 second to reach us however just off to the left of the straight path lies a massive planet, it bends the light and so the light takes 1.00001 seconds to reach us. We know that the speed of light is constant and so we know that the spatial distance between us and the light source is 300,003 km. Now if you imagine a 3D point on that curve which position is given by (x,y,z) I believe you would find some ambiguity as to its actual position as there is 3km of unaccounted for 3D space. Add in a forth coordinate however and the ambiguity disappears the actual position can be calculated. (on the curved spacetime)