What's being curved, when mass bends the spacetime continuum?

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Discussion Overview

The discussion revolves around the nature of spacetime and what is being curved when mass influences the spacetime continuum. Participants explore theoretical and conceptual aspects of spacetime, questioning its fundamental nature and the implications of its curvature as described by General Relativity.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions what exactly is being curved in spacetime, suggesting that if there is nothing present, there is nothing to curve.
  • Another participant explains that spacetime geometry is described by a mathematical tool known as a metric, which organizes numbers for calculations, but this does not directly answer the question of what spacetime is.
  • A different viewpoint suggests that spacetime can be thought of as an underlying structure that is curved, but whether spacetime is "something" remains uncertain.
  • One participant uses a two-dimensional analogy of a triangle on graph paper to illustrate the concept of curvature, but acknowledges it does not address the essence of spacetime.
  • Another participant emphasizes that spacetime is a mathematical coordinate system that yields correct results, questioning the usefulness of discussing it as "curved" when it may not be distinguishable from flat spacetime without measurements.
  • One participant argues that while a coordinate system is useful for calculations, it does not explain what spacetime is, asserting that mathematical constructs do not equate to physical reality.
  • Another participant raises the question of whether spacetime must be considered as something beyond just geometry.
  • One participant speculates that for space to be warped, it must be made of something or influenced by something that prevents it from being warped in the absence of mass.

Areas of Agreement / Disagreement

Participants express a range of views on the nature of spacetime, with no consensus reached on what constitutes spacetime or whether it is merely a mathematical construct. The discussion remains unresolved with multiple competing perspectives.

Contextual Notes

Participants acknowledge the limitations of current understanding and the abstract nature of spacetime, highlighting the challenges in defining its essence beyond mathematical descriptions.

  • #61


Hi.

Oh, we have very good definition for that. All of 64 Riemann curvature tensor components vanish simultaneously? Then space is flat at that point. Some of Riemann curvature tensor components are different than zero? Sorry, not flat. Einstein was poetic that day. Too much gulash, I guess. Heh, gulash is cooked with - wine!

Cheers.
 
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  • #62
A.T. said:
But the geometry of spacetime is also described by a field. Newtons gravitation is a vector field. Einsteins gravitation is a tensor field:
http://en.wikipedia.org/wiki/Field_(physics )

Which tensor field in GR would you call the gravitational field?
 
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  • #63


Hi.

Heh, it depends on nomenclature... For instance, in metric \delta s^2 = \left(1+2V(r)\right)\delta t^2-\frac{\delta r^2}{1+2V(r)}-r^2 \delta \Omega^2 metric tensor components are fields describing gravity... Strictly speaking, there is no exterior field for gravity. This is the very condition for gravity: E_{\mu \nu}=0. Nothing on the right-hand side. On the other hand... What is 1+2V(r) then?... It's some field, right? So... I'm becoming a bit bored of this now.

Cheers.
 
  • #64


My simplistic understanding is that to get from Hither to Yon, you have to go a certain way. The rule for light is it has to get there the fastest way, not the straightest path. Since almost always they are the same, it's confusing when they diverge.

Another is like saying - how come the way to Mecca is off to the northeast for local Muslim folks? Mecca's actually at a slightly lower latitude to where I live, but not much. Ought to be SOUTHeast, by my guess. What is the thing that causes the Qibla (the way to Mecca) to curve? That's a fallacious question.
 

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