What Gives a Motionless Meteorite Shard Momentum in the Curvature of the Sun?

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Discussion Overview

The discussion revolves around the concept of momentum and motion in the context of General Relativity (GR), specifically addressing what causes a motionless meteorite shard to gain momentum when placed in the curvature created by the Sun. Participants explore the implications of spacetime curvature on the movement of objects, the nature of momentum, and the relationship between mass and curvature.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants assert that the curvature of spacetime directs the movement of objects, implying that even a stationary object has a trajectory through spacetime that can be influenced by curvature.
  • Others argue that the Sun and the meteorite move toward each other due to their mutual gravitational attraction, raising questions about the initial conditions of their motion.
  • There is a distinction made between kinematic and dynamic views of momentum, with some suggesting that momentum cannot be defined in a coordinate-independent way in GR.
  • Participants discuss the philosophical implications of how spacetime "tells" particles how to move, with some proposing that particles follow paths based on probabilistic reasoning or feedback from their environment.
  • Some contributions suggest that spacetime can be likened to a field that influences the movement of particles, with analogies drawn to a ball rolling down a hillside.
  • There are claims that distances in curved spacetime can change without the need for particles to move or accelerate, leading to a discussion about the nature of movement and distance in GR.

Areas of Agreement / Disagreement

Participants express a range of views on the relationship between spacetime curvature, mass, and momentum. There is no consensus on the exact mechanisms that cause a motionless meteorite shard to gain momentum or how to interpret the implications of spacetime curvature on motion.

Contextual Notes

Some discussions highlight the limitations of defining momentum in a coordinate-independent manner and the challenges in reconciling kinematic and dynamic perspectives within the framework of General Relativity.

  • #31
tiny-tim said:
ah … but the ball doesn't feel the bumps, it looks at them …

so it's using eyesight to calculate gravity! :wink:

How long does the ball take to calculate gravity?
 
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  • #32
DaleSpam said:
Hi Chaste,

This is best understood in geometrical terms. Do you understand (in SR) how the worldline of an inertially moving object is a straight line? If two inertially moving objects are at rest wrt each other then their worldlines are two parallel lines. In a flat space the distance between two parallel lines is constant and they never intersect.

Now, consider geometry on a sphere. On a sphere a "straight" line is a great circle. Longitude lines are examples of great circles. If you consider two nearby longitude lines at the equator they are parallel, and yet at the poles they intersect and the distance between the two lines is not constant.

So, on a sphere two lines can be parallel at one point and intersect at another point despite the fact that both lines are straight at all points. Translating back to physics, in a curved spacetime two observers can be at rest wrt each other at one point and their paths can intersect despite the fact that neither accelerates at any point (they are each inertial at all points).

Isn't that called geodesic deviation and shows that the tidal forces of a gravitational field (which cause trajectories of neighboring particles to converge/diverge) can be represented by curvature of a spacetime in which particles follow geodesics
 
  • #33
Yes, but I would add the qualifier "inertial" so that it is "trajectories of neighboring inertial particles to converge/diverge" and "a spacetime in which inertial particles follow geodesics".
 

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