GR: Inertial Systems & Direction Changes of Motion

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Discussion Overview

The discussion revolves around the concept of inertial frames in General Relativity (GR) as it relates to a cannon shooting a ball straight up. Participants explore the nature of motion, acceleration, and the perception of direction changes in different frames of reference, addressing both theoretical and conceptual aspects of GR.

Discussion Character

  • Conceptual clarification
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant suggests that both the freely falling body and the upmoving ball at its turning point can be considered inertial frames in GR, as no non-gravitational forces act on them.
  • Another participant clarifies that in GR, inertial frames involve particles following geodesics, implying that the ball's trajectory is a geodesic.
  • A later reply reiterates the initial point about the cannon ball being in free fall and feeling no acceleration, while the cannon itself is in a non-inertial frame due to gravitational effects.
  • It is proposed that the cannon would not notice the change in direction of the ball's motion unless it had an altimeter to measure the maximum height reached.

Areas of Agreement / Disagreement

Participants express differing views on the nature of inertial frames in GR, with some asserting that multiple inertial frames exist while others argue for a singular local inertial frame for the cannon ball. The discussion remains unresolved regarding the implications of direction changes in motion and the perception of acceleration.

Contextual Notes

There are assumptions regarding the ideal conditions of no air resistance and the definitions of inertial frames in the context of GR that are not fully explored. The discussion also highlights the complexity of distinguishing between inertial and non-inertial frames.

Ratzinger
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When a canon shoots a ball straight up (one dimension), the ball only accelerates as long as the nongravitational force of the canon acts on it. After that, the ball decelerates in the gravity field until the point it turns back and accelerates in the opposite direction as it falls back on earth.

So is it right to say that according to GR, not only the freely falling body, but also the upmoving and 'turning point' frame are inertial, since no non-gravitational force acts on them?

But doesn't the ball notice the direction change of its motion? Is that because there are (at least) three local inertial systems?
 
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I'm pretty sure you're confusing special relativity's inertial frames with GR's inertial frames. In GR, in an inertial frame, particles don't go in straight lines, they go in geodesics. In this case, the ball's trajectory is a geodesic.
 
Ratzinger said:
When a canon shoots a ball straight up (one dimension), the ball only accelerates as long as the nongravitational force of the canon acts on it. After that, the ball decelerates in the gravity field until the point it turns back and accelerates in the opposite direction as it falls back on earth.
So is it right to say that according to GR, not only the freely falling body, but also the upmoving and 'turning point' frame are inertial, since no non-gravitational force acts on them?
But doesn't the ball notice the direction change of its motion? Is that because there are (at least) three local inertial systems?
In the ideal case of no air resistance: in GR there is only one locally inertial frame of reference in this case: that of the cannon ball.

The cannon ball's acceleration w.r.t. the supported cannon's non-inertial frame of reference is always negative - 'downwards', whereas, initially, the cannon ball's velocity is 'upwards'.

That 'upwards' velocity is first reduced to zero by the negative acceleration before becoming a 'downwards' velocity and then eventually it would fall straight back down the cannon's mouth. [Well you did say: "a canon shoots a ball straight up (one dimension)"!]

In the cannon ball's frame of reference it is in free fall and feels no acceleration.

Therefore the cannon would not notice the change of direction unless it had an altimeter on board, when the reading would reach a maximum, the cannon ball is in free fall all the time. It is the ground and the cannon that are not in an inertial frame of reference, that is why the cannon weighs so much!

I hope this helps.

Garth
 
Last edited:
I hope this helps.
It did. No it looks easy. Thanks, Garth.
 

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