Is Spacetime Linear? - The Universe in a Nutshell

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    Linear Spacetime
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Discussion Overview

The discussion revolves around the nature of spacetime, particularly whether it can be accurately represented as a linear fabric. Participants explore the implications of spacetime curvature in relation to gravitational effects, as inspired by Stephen Hawking's book "The Universe in a Nutshell." The scope includes conceptual clarifications and metaphorical representations of spacetime.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions the depiction of spacetime as a linear fabric, noting the spherical gravitational pull of the sun and the implications for objects above and below it.
  • Another participant suggests that the term "linear" may be misleading and proposes a more complex metaphor involving a 3D net to better represent spacetime curvature.
  • A later reply emphasizes that spacetime is not a simple 2D fabric, but rather a 3D construct that curves in the presence of mass, arguing that simplified diagrams may not capture this complexity.

Areas of Agreement / Disagreement

Participants express differing views on the appropriateness of the fabric metaphor for spacetime, with some advocating for a more nuanced representation while others acknowledge the limitations of simpler analogies. The discussion remains unresolved regarding the best way to conceptualize spacetime.

Contextual Notes

Participants highlight the limitations of metaphors used to describe spacetime, noting that a 2D representation may not adequately convey the complexities of a 3D model. There is also uncertainty regarding the implications of curvature on gravitational interactions.

Justinmcg67
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I was wondering about this question when I was reading my new book The Universe in a Nutshell by Stephen Hawking and the images in the book depict space time as a linear fabric. I don't understand how this could be if the sun has a spherical gravitational pull, as we see at the very outermost reaches of our solar system. So if space time is curved down on a linear fabric, how are objects gravitattionally bound below and on top of the Sun?

I'm sure there is an explanation, I however can not seem to find it. So any light shed on this subject is very much appreciated.
 
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What do you mean by a "linear" fabric? Functions can be linear. Operators can be linear.

The fabric metaphor is an easy way for people to understand spacetime curvature by analogy to stretching. It's not the most precise metaphor, though. Instead of the single sheet curving downwards due to gravity, imagine instead a net lying flat on a table. Pretend this net can be stretched any way you like without breaking. This net represents spacetime, and any stretching gives rise to "curvature".

To complete the metaphor, imagine instead of a flat net you have a grid of connected ropes in 3d space which can stretch like the net.
 
The 3D net makes a lot more sense to be honest. And by linear I mean flat, straight, like a line. Thank you for the answer though as it does shed some light on the topic for me.
 
Just repeating the above, the metaphor isn't quite exact. Space time ISNT a 2D "fabric" that curves in the presence of mass. We must add another dimension so it is now a 3D "fabric" that curves in the presence of mass. For simplicity diagrams show a 2D fabric because a 3D fabric would be too complicated.
 

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