Well, after typing that title and writing out a longish post matching the title, I think I figured out a more sensible (i.e far less fantastic) way to ask what I think is substantively the same question.
So here’s the sensible version.
Check my intuitions here. If I’m on a platform accelerating at a rate that produces a 1g force on objects standing on that platform, and the platform at some point ceases its acceleration, then what happens to me is, I gently begin to float around (relative to the platform) and I do not suddenly shoot violently off into space. Right?
You’re standing atop a rocket that is accelerating at 1g in space, which to you feels like you’re standing on the ground on Earth (notwithstanding any vibration etc)
The motor shuts off abruptly, then yes, you and the rocket continue moving in a straight line together from there on, which to you feels like you become weightless with respect to the ground you thought you were standing on. (notwithstanding the elasticity of your body - which might result in you inadvertently jumping away from the ‘ground’ a little when the gravity from acceleration abruptly disappears)
Nitpick: you will be travelling along an elliptical path if there’s only one body nearby with a significant gravitational field, and along a more complex path if there are several such bodies (e.g., the Sun, Earth and Moon).
I originally wrote “in empty space away from all significant influence of other bodies”, but edited it back thinking it was unnecessary to qualify it that pedantically…
I think you could say “ignoring gravitational influences from other bodies” – I don’t think you’ll easily find a location outside a gravitational field. If you were anywhere inside the Milky Way Galaxy, you’ll be slowly orbiting around the galactic centre, for a start.
Mangetout had it right the first time: You’d be traveling in a straight line. If you don’t think that an elliptical orbit qualifies as a straight line, that just shows that you have a merely three-dimensional notion of “straight”.
You will shoot away. During the acceleration phase the platform will be flexed under your “weight”, the soles of your sneakers will be compressed, maybe your knees will be flexed. When acceleration stops everything will spring back and propel you away from the platform.
