Accelerating Body Creates Space-Time Curvature?

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Discussion Overview

The discussion centers around the effects of acceleration on space-time curvature, particularly whether an accelerating body creates local curvature or tidal effects similar to those experienced on the surface of a planet. The scope includes theoretical considerations of general relativity and the implications of acceleration in a spaceship context.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant suggests that accelerating at 1G in a spaceship creates a slight curvature of space-time, similar to that on Earth's surface.
  • Another participant counters that curvature is related to tidal gravity, which is absent in the scenario of a uniformly accelerating ship.
  • A different participant elaborates that while acceleration creates a gravity-equivalent effect, the space-time remains flat, and precise measurements would reveal differences from Earth's non-zero curvature.
  • One participant questions whether tidal effects are related to the convergence of vectors towards the center of mass of an attracting body, suggesting that proximity to a small planet would affect trajectory convergence differently than a larger planet.
  • Another participant agrees with the tidal effect explanation, indicating an understanding of the differences in measurements between the accelerating ship and a gravitational field.

Areas of Agreement / Disagreement

Participants express disagreement regarding the relationship between acceleration and space-time curvature, with some asserting that no local curvature occurs while others propose that effects akin to gravity are experienced. The discussion remains unresolved with competing views on the nature of tidal effects and their implications.

Contextual Notes

Participants reference the absence of tidal effects in the accelerating ship scenario, highlighting the importance of distinguishing between flat space-time and the curvature experienced in gravitational fields. The discussion does not resolve the implications of these differences on measurements.

DarkMattrHole
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TL;DR
Does an accelerating body cause a local curvature of space-time or gradient and wave-front?
If you are floating in space in your spaceship and you kick in the engines and accelerate at a comfortable 1G and you end up standing on the bottom of your ship, a slight curvature of space-time is formed, throughout the ship, perhaps immeasurable, such that without windows on the ship, you might think you were still on the ground, and with a God's eye view of the curvature throughout the ship (or real good equipment) you would measure it to be the same as found on the surface of earth, is that correct? Either way the answer is always interesting, often surprising. thanks.
 
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DarkMattrHole said:
Summary:: Does an accelerating body cause a local curvature of space-time or gradient and wave-front?

is that correct?
No. Curvature is related to tidal gravity and there is no tidal gravity in that scenario.
 
The
DarkMattrHole said:
and with a God's eye view of the curvature throughout the ship (or real good equipment) you would measure it to be the same as found on the surface of earth, is that correct?
Not correct. The gravity-equivalent effect produced by acceleration has nothing to do with spacetime curvature - the spacetime is still flat - and if your measuring instruments are sufficiently accurate they will detect differences from what you’d find on the surface of the earth, where the curvature really is non-zero.

The difference is the lack of tidal effects on the accelerating ship. On the accelerating ship, two objects dropped from the same height at the same time will be exactly as far apart when they hit the floor as when they were dropped, while on the Earth they will have moved a bit closer together. On the accelerating spaceship two objects released from different heights at the same time will maintain the same separation, while on the Earth they will move a bit farther apart. Both of these are tidal effects, present in the curved spacetime around the Earth but not present in the flat spacetime of the accelerating spaceship.
 
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Thanks guys. I think i can see the tidal difference you would measure.
Is the tidal effect the way all vectors point to the center of mass of an attracting body? If so, being close to the center of a small planet, one would measure trajectories or vectors converge more sharply, but strength of field may be less than large planet with more distant center of mass.
 
Yes, that is correct.
 

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