How Does 3D Distortion Affect the Space-Time Fabric?

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Discussion Overview

The discussion revolves around the concept of the space-time fabric and how it may be distorted, particularly in relation to dimensions beyond the familiar three. Participants explore the implications of such distortions in both theoretical and conceptual contexts, referencing general relativity and topology.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants question how a 3D fabric of space-time would be distorted and whether it requires an additional dimension for such distortions.
  • One viewpoint suggests that distortions can be understood without invoking an extra dimension, emphasizing that the properties of a surface can be intrinsic and independent of embedding in higher dimensions.
  • Another participant proposes that distortions occur in the 4th dimension, which is time, referencing general relativity's implications regarding gravitational fields affecting time.
  • There is a discussion about the nature of curvature, with some participants noting that the example of a torus may not adequately illustrate the concept due to its flat Gaussian curvature.
  • Humorous exchanges occur regarding fictional dimensions and references to pop culture, which do not contribute to the technical aspects of the discussion.

Areas of Agreement / Disagreement

Participants express differing views on whether additional dimensions are necessary to explain distortions in the space-time fabric. The discussion remains unresolved, with multiple competing perspectives presented.

Contextual Notes

Some participants acknowledge limitations in their examples, particularly regarding the distinction between topological and geometric properties, and the implications of curvature in the context of the discussion.

sreekant
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hey guys,

i jus got a question regarding space time fabric...if we take an example of a 2d fabric...it is distorted in the third dimension...now if it is a 3d fabric ( which is what it is supposed to be ) then in which dimension will it get distorted??
 
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sreekant said:
hey guys,

i jus got a question regarding space time fabric...if we take an example of a 2d fabric...it is distorted in the third dimension...now if it is a 3d fabric ( which is what it is supposed to be ) then in which dimension will it get distorted??
Good question. You don't actually need to have an 'extra' dimension to accommodate the distortion. In your 2D example, sure, we are accustomed to thinking of a 2D surface embedded in 3D space. However, the surface is still 2D, and we can geometrically encode the bending and warping of the surface by data on the surface, without the need for a higher dimensional ambient space within witch to place our 2D surface. For example, a torus (donut) has a well known form when its 2D surface is embedded in 3D space. However, I can equivalently represent a torus as a 2D sheet, with 'rules' for how to connect opposing edges of the sheet -- specifically, glue together opposite edges. The old Atari game 'Asteroids' is an example of toroidal topology even though the surface (screen) is only 2D!
 
Yeah that's a very good question. In my opinion, it will get distorted in the 4th dimension - time. As well all know from the general theory of relativity, times run slower for objects in a strong gravitational field compared to other objects that are not in such a field.
 
silentbob14 said:
In my opinion, it will get distorted in the 4th dimension - time.

Also possible - but bapowell's explanation is better because it shows that you don't need to introduce any new elements for its explanation (elements that might or might not get one into trouble later on). It is not necessary to invoke another dimension to have distortions.
 
DaveC426913 said:
It is not necessary to invoke another dimension to have distortions.
Right. This is key. The Ricci curvature is intrinsic to the surface, and completely independent of the (unnecessary) embedding. Silentbob -- the OP's 2D example helps visualize the problem, but really we have a 4D curved manifold in GR. The question the OP is asking then is...what is the 5th dimension? Time is already included in the 4D.
 
Ahh, the 5th dimension is where the String Theorists hide their extra Gravity. :biggrin:
 
Frame Dragger said:
Ahh, the 5th dimension is where the String Theorists hide their extra Gravity. :biggrin:
Dude, you're not helping :wink:
 
bapowell said:
Dude, you're not helping :wink:

Look, it was that or a reference to Buckaroo Bonzai. I think I made the right choice. :smile: Now, the 6th dimension is where lost ballpoints go... and the 7th is all marmalade.
 
I don't think the example works quite well though? Although identifying opposite edges of a square gives a quotient topology of a torus, this torus is flat - it's gaussian curvature is zero.
 
  • #10
yenchin said:
I don't think the example works quite well though? Although identifying opposite edges of a square gives a quotient topology of a torus, this torus is flat - it's gaussian curvature is zero.
Right, sorry. I gave a topological example instead a geometric one! However, the point of the example was meant to convey that fact that you don't need to embed a manifold in order for it to have nontrivial properties. Of course, one could just say that the Ricci curvature (or the fundamental form, or whatever) is intrinsic to the surface and is independent of any embedding. But point taken, sorry.
 
  • #11
Frame Dragger said:
Look, it was that or a reference to Buckaroo Bonzai.
Nicely done John FrameDragger. :biggrin:
 
  • #12
DaveC426913 said:
Nicely done John FrameDragger. :biggrin:

You are too kind monsieur! Too kind! Nah... just right. :wink: Glad someone got the reference though... classic movie, absolutely classic. Lithgow is an AMAZING actor, and the rest... well.. rofl. just rofl! :smile:

EDIT: @bapowell: No need to apologize to anyone. Hell, if we had to say "sorry" every time we're wrong about spacetime... um... have you ever seen a western businessman try to "bow" properly in Japan? I can only describe the resulting series of bows as a kind of "bowing war", or maybe a bit like those rocking-birds that use surface tension as a spring. Anyway, that's what it would look like around here!
 
  • #13
Frame Dragger said:
You are too kind monsieur! Too kind! Nah... just right. :wink: Glad someone got the reference though... classic movie, absolutely classic. Lithgow is an AMAZING actor, and the rest... well.. rofl. just rofl! :smile:
It is one of my top ten. And Lithgow was indeed a shining star.
 
  • #14
DaveC426913 said:
It is one of my top ten. And Lithgow was indeed a shining star.

You are clearly a man of substance. :smile:

Are you a fan of 'Dexter'? Lithgow played the villain this season, and he was TERRIFYING. I'm normally unmoved by simulated violence, but... wow. He has an amazing range.
 
  • #15
Frame Dragger said:
You are clearly a man of substance. :smile:

Are you a fan of 'Dexter'? Lithgow played the villain this season, and he was TERRIFYING.
Huh. Did not know that.
 
  • #16
DaveC426913 said:
Huh. Did not know that.

He is amazing, but it is VERY graphic. Frankly he's not the most violent in the show, or on tv/movies, but... well, the opening has him killing a woman and using a mirror to see her die. His acting makes it utterly convincing, and deeply DEEPLY frightning. For this, he won an emmy, I should add.

So... it may not be for everyone (I found it difficult at times... a first for me), but to see a master at his craft, it's worth it.
 

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