How Does General Relativity Explain Gravity's Conundrum?

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Discussion Overview

The discussion revolves around the explanation of gravity through general relativity, focusing on the conceptual understanding of spacetime curvature and its implications for the motion of objects. Participants explore the nature of spacetime, the analogy of cones, and the mathematical framework necessary to describe these phenomena.

Discussion Character

  • Conceptual clarification
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant questions the analogy of a cone used to describe spacetime, noting that it leads to confusion about the motion of objects and their relationship to mass.
  • Another participant emphasizes that spacetime is curved rather than bent, suggesting that popular illustrations may oversimplify complex concepts.
  • A different participant argues that the terms "curving" and "bending" are not interchangeable in the context of spacetime, indicating a need for precise mathematical definitions.
  • Concerns are raised about the application of Euclidean geometry to spacetime, with a suggestion that Riemann geometry is more appropriate for these discussions.
  • One participant expresses uncertainty about the concept of "relativity of simultaneity," indicating a gap in understanding that may affect their grasp of the overall topic.

Areas of Agreement / Disagreement

Participants exhibit disagreement regarding the interpretation of spacetime curvature and the appropriateness of analogies used to explain it. There is no consensus on the validity of the cone analogy or the terminology used to describe spacetime.

Contextual Notes

Participants highlight limitations in understanding due to the complexity of four-dimensional spacetime and the challenges of visualizing these concepts through two-dimensional analogies. The discussion reflects a variety of interpretations and assumptions about the mathematical frameworks involved.

Mohammad Hunter
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So the other day I saw a YouTube video on how gravity works according to general relativity.
From what I understand, objects bend space_time with their mass and create a shape which is close to a cone. Since objects only move forward in time through a straight line, the bent space_time makes the objects fall on each other.
But my question is: when you create a cone and draw a straight line on it, the line starts from a lower level, goes up and down again( I'm talking about the lines Einstein had in mind) which creates a problem... In the model, all objects start from what looks like the peak and descend down.
I don't understand two things:
1. The heavy object is located on the peak of the cone( right?) And when the straight line is followed, it does get close to the massive object but passes through and starts wandering away( to make it easier I assumed one object is not massive enough to effect the other here)
2. Don't both objects travel with the same speed through time?( Specially when the two objects have the same mass) If so, they should be staying still from each other's perspective.( Their relative velocity is zero) So while the objects are moving forward in time, the cone is moving forward with them. So no fall should be expected.
 
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You are taking popular animations and illustrations a bit too seriously here.

Energy, momentum, and stress act as sources of spacetime curvature. (Note that the technical word is that spacetime is curved, not bent.) Spacetime is four-dimensional and that cannot be easily illustrated so popularisers make do with analogies and do what they can.
 
Orodruin said:
You are taking popular animations and illustrations a bit too seriously here.

Energy, momentum, and stress act as sources of spacetime curvature. (Note that the technical word is that spacetime is curved, not bent.) Spacetime is four-dimensional and that cannot be easily illustrated so popularisers make do with analogies and do what they can.

So many questions, I don't know if they're actually scientific but if I'm correct, curving should not be possible without bending... I've forgotten the term but it has to do with the shape of the object, you can't cover a ball with a piece of flat paper without creating overlaps. If the same rule applies to space-time, then some bending is expected maybe?
Also this is clearly out of my area of knowledge cause I don't know what "relativity of simultaneity" is.
Thanks for the answer, I'll read about relativity of simultaneity.
 
Mohammad Hunter said:
you can't cover a ball with a piece of flat paper without creating overlaps
This is neither curving nor bending. "Bending" has no well defined meaning in this context and "curved" has a very precise mathematical meaning. It requires no external space to be curved in as you are likely imagining it.
 
Mohammad Hunter said:
... curving should not be possible without bending
You are using Euclidean Geometry terms. This is not the proper math to use for spacetime (you need Riemann Geometry) and as Orodruin pointed out the terms as applied to space-time do not mean what you think they mean.
 
Mohammad Hunter said:
So the other day I saw a YouTube video...
How about a link, so we know which one you mean.
 

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