ittiandro

Yes, I now see this acceleration, but it is relative to the other body , because the two geodesics come closer and closer at an accelerating rate and so do the two bodies moving along them. However if we have only one body, instead of two, moving along its geodesic, its acceleration (= change of velocity) is in relation to what? AlI I can see is a steeper curvature towards the end of the path, where it would intersect the geodesic of the other moving body, IF IT WAS THERE. But it is not there. So, again what does acceleration mean in this case?What is its point of reference? This would answer my original question only if we posit TWO bodies moving parallel to one another along their curved spacetime geodesics, but not in the case there was only one body, as already queried in the preceding section.

Elfmotat’s comment is right on : parallel lines drawn on a flat space seem to converge when drawn on a curved surface. Similarly, I have to infer, the paths of two bodies falling in a curved space along their geodesics seem to converge towards the center of the Earth, but in reality this convergence is only apparent and there is really no deviation from straight line motion caused by a “force” of gravity. It is only a question of different geometries of space. I fully agree on this. This explanation seems, however, to address only one aspect of acceleration, i.e. the change in direction. It does not address the other aspect I referred to in my initial thread: the change in velocity. Indeed, in this regard, my question still remains : if there is no longer a " force" of gravity acting on bodies and making them deviate from the straight line of uniform motion, what explains that( falling) bodies when moving towards the Earth along the geodesics still undergo an acceleration (they change their velocity) at a rate of 9.8 m/s^2 ? G.R. holds that gravity is stronger near the Earth . Since it is not a force, but is due to the curvature of spacetime, do we have to conclude that the acceleration of a falling body as it approaches the Earth is due perhaps to a steeper curve in the space near the Earth? But why so? Such a notion would reintroduce gravity as a force, wouldn’it? Can anybody cast some more light on this? Thanks Ittiandro

Elfmotat’s comment is right on : parallel lines drawn on a flat space seem to converge when drawn on a curved surface. Similarly, I have to infer, the paths of two bodies falling in a curved space along their geodesics seem to converge towards the center of the Earth, but in reality this convergence is only apparent and there is really no deviation from straight line motion caused by a “force” of gravity. It is only a question of different geometries of space. I fully agree on this. This explanation seems, however, to address only one aspect of acceleration, i.e. the change in direction. It does not address the other aspect I referred to in my initial thread: the change in velocity. Indeed, in this regard, my question still remains : if there is no longer a " force" of gravity acting on bodies and making them deviate from the straight line of uniform motion, what explains that( falling) bodies when moving towards the Earth along the geodesics still undergo an acceleration (they change their velocity) at a rate of 9.8 m/s^2 ? G.R. holds that gravity is stronger near the Earth . Since it is not a force, but is due to the curvature of spacetime, do we have to conclude that the acceleration of a falling body as it approaches the Earth is due perhaps to a steeper curve in the space near the Earth? But why so? Such a notion would reintroduce gravity as a force, wouldn’it? Can anybody cast some more light on this? Thanks Ittiandro

1. Hi ! , tI If, according to General Relativity, bodiesfall ( or,rather,move ) towards the Earth not due to a “ force” of gravity pulling down on them but simply because they naturally follow the geodesics of curved space-time and can therefore be viewed( I suppose) as moving in uniform motion, how come they are still seen as moving ( falling) at an acceleratingrate? Indeed their acceleration rate ( in the sense of an increase in velocity) is accurately measured at 9.8 m/s/s. My question may sound naïve to some, but may be I have reached the limits of conceptual understanding, without using maths, in which I have little familiarity beyond college algebra, long time ago ( I am 71 years old and my background is in philosophy). Thank you for what you can do to dispel my ignorance. iiiiiiiiIttiandro ItI T T T