Properties of Mass in Curved Space-Time

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Discussion Overview

The discussion revolves around the properties of mass in curved space-time, particularly focusing on gravitational time dilation and the behavior of massive bodies in relation to areas of varying time rates. Participants explore theoretical implications and analogies related to general relativity (GR) and the nature of space-time.

Discussion Character

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

Main Points Raised

  • Some participants suggest that time dilates due to the gravity of massive bodies, leading to a distortion of space-time that affects how mass interacts with time.
  • There is a proposal that bodies of mass fall towards areas of greater time dilation, likening this to a two-dimensional model where mass moves to the "lowest" point created by a massive body.
  • One participant introduces the idea of intrinsic curvature as a distortion of distances, comparing it to a variable density medium that influences the movement of objects.
  • Another participant asserts that bodies of mass are moved by the curvature of space-time, questioning why they wouldn't move towards areas where time travels faster.
  • Some participants discuss the Principle of Least Activity, suggesting it may relate to how objects move through curved space-time.
  • There is a clarification that space itself does not travel through time, but rather serves as a dimension through which other entities move.
  • Analogies are used, such as comparing gravitational effects to driving on different surfaces, to illustrate how mass interacts with curved space-time.

Areas of Agreement / Disagreement

Participants express various viewpoints on the relationship between mass, time dilation, and the curvature of space-time. There is no consensus on the underlying reasons for the behavior of mass in this context, and multiple competing views remain present.

Contextual Notes

Some discussions involve assumptions about the nature of space and time, as well as the applicability of analogies used to explain complex concepts. The discussion does not resolve these assumptions or the implications of the proposed models.

danielatha4
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From what I understand of GR, time dilates due to the gravity of massive bodies. I like to think of it as the three coordinates of space drag, or lag, through time at a slower rate resulting in distortion of space-time. Correct me if my logic is flawed.

But my question is this; why do bodies of mass fall towards areas of greater time dilation? or I guess in a 2 dimensional model of space it falls to the "lowest" point, the dip caused by the massive body? Does mass long to travel through time at slower rates?
 
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danielatha4 said:
From what I understand of GR, time dilates due to the gravity of massive bodies. I like to think of it as the three coordinates of space drag, or lag, through time at a slower rate resulting in distortion of space-time. Correct me if my logic is flawed.
Intrinsic curvature means a distortion of distances, but you can alternatively visualize it as variable density of a medium, that slows down the advance trough it.

danielatha4 said:
But my question is this; why do bodies of mass fall towards areas of greater time dilation?
Speaking in the "variable density" metaphor: For the same reason light rays bend towards the denser region in a medium. Note that the light ray represents a world line (space-time path) of an object, in this analogy.

danielatha4 said:
or I guess in a 2 dimensional model of space it falls to the "lowest" point, the dip caused by the massive body? Does mass long to travel through time at slower rates?
There is no "lowest point" because there is no "down direction", but there is a point with the locally lowest potential, where the gravitational time dilation is maximal as well.

To understand why everything tends toward that point in terms of geodesics in curved space-time I recommend these links:
http://www.physics.ucla.edu/demoweb..._and_general_relativity/curved_spacetime.html
http://www.relativitet.se/spacetime1.html
http://www.adamtoons.de/physics/gravitation.swf
 
why do bodies of mass fall towards areas of greater time dilation?

Because that's where curved spacetime moves them.
 
Naty1 said:
Because that's where curved spacetime moves them.

Why not towards areas of space that travel through time at a faster rate?

Does the Principle of Least Activity have anything to do with this?
 
danielatha4 said:
Why not towards areas of space that travel through time at a faster rate?
Space doesn't travel trough time. Space and time are dimensions other stuff can travel trough. This picture explains how gravitational time dilation and gravitational pull are connected:

http://www.physics.ucla.edu/demoweb/demomanual/modern_physics/principal_of_equivalence_and_general_relativity/curved_time.gif

danielatha4 said:
Does the Principle of Least Activity have anything to do with this?
In a way, yes. Moving locally straight ahead on a distorted grid, leads you towards the area with more 'stretched' distances.

In the alternative 'variable density' analogy you are pulled towards the denser area which breaks you more. Imagine driving a car with two wheels on the road, and two on the grass.
 
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