What is the path of earth in 4-d space?

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Discussion Overview

The discussion revolves around the concept of Earth's path in four-dimensional space, particularly in relation to general relativity and the curvature of spacetime. Participants explore analogies, such as the trampoline model, to understand how mass affects the geometry of space and the movement of celestial bodies.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions how a curved path can be perceived in a two-dimensional representation, specifically regarding the analogy of a plane moving over a mountain.
  • Another participant agrees with the idea that mass curves four-dimensional space, likening the sun's effect to a paper weight on a trampoline, but notes that this analogy is often criticized for being overly simplistic.
  • A different participant emphasizes that the concept of "path" is relative and requires a reference point, prompting a discussion about the necessity of a coordinate system.
  • Some participants express uncertainty about the clarity of the analogy and its implications for understanding spacetime curvature.

Areas of Agreement / Disagreement

Participants express differing views on the appropriateness of the trampoline analogy for explaining spacetime curvature. While some find it helpful, others argue it oversimplifies the complexities of four-dimensional spacetime. There is no consensus on the best way to visualize or understand these concepts.

Contextual Notes

Limitations include the potential misunderstanding of analogies used to explain complex concepts in general relativity, as well as the varying interpretations of what constitutes a "path" in four-dimensional space.

Who May Find This Useful

This discussion may be of interest to those exploring concepts in general relativity, spacetime curvature, and the challenges of visualizing higher-dimensional physics.

Rishavutkarsh
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what is the path of Earth in 4-d space??

as i read in the brief history of time "let a plane be moving straight in 3-d world but we see it in a curved path on a 2-d Earth surface (mountain). can any1 tell how can we see the space curve as 2-d has not elevation??
moreover i used to think that bodies with mass curve the 4-d space like a paper weight (sun) curves a trampoline and object like Table tennis ball (earth) which try to move in straight path in 4-d space will be disturbed by their path and revolve around the center (as the Earth to sun) and will get closer and closer and will reach the center in some time (millions of year when talking about sun and earth) and in secs in our model (trampoline) .

Am i having a misconception?
 
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Rishavutkarsh said:
as i read in the brief history of time "let a plane be moving straight in 3-d world but we see it in a curved path on a 2-d Earth surface (mountain). can any1 tell how can we see the space curve as 2-d has not elevation??
I am not familiar with this analogy, so I cannot comment.

Rishavutkarsh said:
moreover i used to think that bodies with mass curve the 4-d space like a paper weight (sun) curves a trampoline and object like Table tennis ball (earth) which try to move in straight path in 4-d space will be disturbed by their path and revolve around the center (as the Earth to sun) and will get closer and closer and will reach the center in some time (millions of year when talking about sun and earth) and in secs in our model (trampoline) .
Yes, this is correct. Most people on this forum do not like the trampoline analogy since it is a 2D spatial example whereas GR deals with curvature in 4D spacetime (3D space and 1D time). However, it seems that you understand that key difference and understand that it is an analogy for spacetime.
 


"path" I think has meaning only RELATIVE to something. That is, you have to have point of origin for a coordinate system. What reference point did you have in mind?
 


DaleSpam said:
I am not familiar with this analogy, so I cannot comment.

it literally means that an plane for example moves straight above the mountain (3-d space) but is seen to move in curve according to 2-d because of up's and down's of mountain . my question is that how can the elevation of the mountain be seen in 2-d?
 


Rishavutkarsh said:
it literally means that an plane for example moves straight above the mountain (3-d space) but is seen to move in curve according to 2-d because of up's and down's of mountain . my question is that how can the elevation of the mountain be seen in 2-d?
It cannot, but the curvature of the 2D surface of the mountain can be measured purely within the 2D surface without ever referring to the altitude.
 

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