Unraveling the Mystery of Warped 4D Spacetime

  • Context: Graduate 
  • Thread starter Thread starter daniel_i_l
  • Start date Start date
  • Tags Tags
    4d Mystery Spacetime
Click For Summary

Discussion Overview

The discussion revolves around the concept of warped 4D spacetime, particularly in the context of general relativity (GR). Participants explore the implications of curvature in spacetime and whether a fifth dimension is necessary for understanding this warping. The conversation includes theoretical considerations and visualizations of dimensionality.

Discussion Character

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

Main Points Raised

  • One participant questions the necessity of a fifth dimension for the warping of 4D spacetime, suggesting that the effects might be due to a distortion in the coordinate system rather than a physical bending into another dimension.
  • Another participant argues that a fifth dimension is not required for defining spacetime curvature, emphasizing that curvature can be understood through the intrinsic geometry of the manifold.
  • A participant uses the analogy of an ant on the Earth's surface to illustrate how curvature can be experienced in a lower-dimensional space without needing to perceive higher dimensions.
  • There is a discussion about how warped space might affect the perception of coordinates, with one participant suggesting that points in a warped 2D grid would be unevenly spaced, leading to a "messed up" coordinate system.
  • Another participant elaborates on the idea of local straight lines appearing non-straight when viewed from a distance, indicating that the perception of geometry can change based on the curvature of the space.

Areas of Agreement / Disagreement

Participants express differing views on the necessity of a fifth dimension for understanding warped spacetime. Some agree on the intrinsic nature of curvature, while others maintain that higher-dimensional visualization is helpful. The discussion remains unresolved with multiple competing perspectives.

Contextual Notes

Participants reference various geometric properties and analogies to illustrate their points, but there are unresolved assumptions regarding the nature of dimensionality and curvature. The discussion does not reach a consensus on the implications of these concepts.

daniel_i_l
Gold Member
Messages
864
Reaction score
0
In 2D for example, warping it only makes sense in a 3D enviorment. In a 2D world, bending 2D would be meaningless. So in GR when we talk about bending 4D ST, is a fifth dimension needed to give ST something to "bend into"? If not, in what sense can we talk about warped ST? I suspect that maybe it warps not in a physical (dimensional - into another dimension) way, but rather the cooardinite system gets messed up and those effects are noticable in 3D. Can someone clarify this please?
 
Physics news on Phys.org
No daniel_i_l, you do not need a fifth dimension for space-time curvature. The curvature can be defined and described in terms of the intrinsic geometry of the manifold: do the internal angels of a triangle sum to 2[itex]\pi[/itex]? do parallel lines meet? does a vector, such as the axis of a Gravity Probe B gyroscope, still point in the same direction when you have parallel transported it around a closed circuit?

However in order to visualise the situation, and Einstein himself said that he needed to be able to visualise his theories to understand them, as a mental exercise you do need the higher dimension in which to embed the 4D manifold of space-time.

Garth
 
Last edited:
daniel_i_l said:
In a 2D world, bending 2D would be meaningless.

Consider an ant walking on the surface of the earth. If there were no hills or mountains, to him, the existence of the 3rd spatial (height) dimension would be non-existent as he would never experience it. However, he could still experience the curvature of the Earth's surface, which is purely a 2D space. As Garth has pointed out, he could walk a giant triangle (with a vertex at the North pole, and 2 at the equator, for example) and see that the triange has a total internal angle of [itex]3\pi[/itex].
 
Thanks, so if I understand correctly (please correct me if I'm wrong) if for example 2D space was represented as a grid with eavenly spaced intersection points, in warped space the poits would be closer in some places and further is others ("messed up cooardinates")?
 
daniel_i_l said:
Thanks, so if I understand correctly (please correct me if I'm wrong) if for example 2D space was represented as a grid with eavenly spaced intersection points, in warped space the poits would be closer in some places and further is others ("messed up cooardinates")?

Well, you could always consider whatever the co-ordinates are around you as "straight lines intersecting perpendicularly". But the point is that co-ordinate lines far away from you wouldn't necessarily look "straight and perpendicular" compared to the ones around you.
 

Similar threads

  • · Replies 19 ·
Replies
19
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 2 ·
Replies
2
Views
3K
Replies
9
Views
4K
  • · Replies 11 ·
Replies
11
Views
4K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 25 ·
Replies
25
Views
7K
  • · Replies 0 ·
Replies
0
Views
4K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 4 ·
Replies
4
Views
4K