- #1

dodo

- 697

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- TL;DR Summary
- TL;DR: why the spacetime deformation that bends the trajectory of a ball tossed up and coming down is not bending my own body the same way?

Hi,

apologies if questions of the same form have been asked by laymen multiple times. (You must all be tired of this!) I tried to search on the forum, but I did not find my exact question answered. For context, I have some university math background, but when it comes to physics I am pretty much a layman.

If I toss a ball from my hand and catch it back (let's say the trajectory is not exactly vertical, so I have to move my hand a little to catch the ball back), it describes a very narrow arc of ellipse (the focus is at Earth's center of mass, so modelling it with the focus at infinity as an arc of parabola is not much of a relative error). Imagine now that I take a piece of paper, and draw vertical parallel lines representing inertial lines under the spacetime deformation; the ball would follow one straight line segment in this diagram, but my hand would have to be drawn simultaneously at both ends of that line segment. Ultimately my question is, then, why is my body not torn by this extreme deformation.

I understand (I think) how, in classical mechanics terms, a tidal force moves the water much more than it moves the land, as the latter is held by cohesion forces stronger than the water's. But I fail to see how this would apply to the ball's inertial trajectory bending to such narrow curve (which would be a straight line away from me, if I were in interstellar space away from big masses), and that bending being the result of spacetime deformation (and hence as much an imaginary artifact as a force as "centrifugal force" is), while not apparently affecting my own body (and my apartment) the same way.

A drawing of my body on that paper with straight lines would help. As we determined, my hand is at two places. I am ignoring the time dimension on this drawing (plus mapping 3 spatial dimension onto 2) but that "mapping" would need to be multivalued, in order to take the same 3D point to 2 different positions on the paper! So please feel free to imagine how the missing dimensions would illustrate (if at all) the issue.

Thanks again for your patience.

apologies if questions of the same form have been asked by laymen multiple times. (You must all be tired of this!) I tried to search on the forum, but I did not find my exact question answered. For context, I have some university math background, but when it comes to physics I am pretty much a layman.

If I toss a ball from my hand and catch it back (let's say the trajectory is not exactly vertical, so I have to move my hand a little to catch the ball back), it describes a very narrow arc of ellipse (the focus is at Earth's center of mass, so modelling it with the focus at infinity as an arc of parabola is not much of a relative error). Imagine now that I take a piece of paper, and draw vertical parallel lines representing inertial lines under the spacetime deformation; the ball would follow one straight line segment in this diagram, but my hand would have to be drawn simultaneously at both ends of that line segment. Ultimately my question is, then, why is my body not torn by this extreme deformation.

I understand (I think) how, in classical mechanics terms, a tidal force moves the water much more than it moves the land, as the latter is held by cohesion forces stronger than the water's. But I fail to see how this would apply to the ball's inertial trajectory bending to such narrow curve (which would be a straight line away from me, if I were in interstellar space away from big masses), and that bending being the result of spacetime deformation (and hence as much an imaginary artifact as a force as "centrifugal force" is), while not apparently affecting my own body (and my apartment) the same way.

A drawing of my body on that paper with straight lines would help. As we determined, my hand is at two places. I am ignoring the time dimension on this drawing (plus mapping 3 spatial dimension onto 2) but that "mapping" would need to be multivalued, in order to take the same 3D point to 2 different positions on the paper! So please feel free to imagine how the missing dimensions would illustrate (if at all) the issue.

Thanks again for your patience.