Physics Major's Questions on Geodesics

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Discussion Overview

The discussion revolves around the conceptual understanding of geodesics as experienced by a hypothetical "point-like creature" in a one-dimensional space. Participants explore the implications of curvature on visibility and line-of-sight, particularly in flat and positively curved geometries, while also touching on the relevance of these ideas to General and Special Relativity.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions what a "point-like creature" can see on different geodesics, suggesting that in a flat line, it can see everything, while in a positively curved line, visibility may be limited.
  • Another participant proposes that the creature's line-of-sight is determined by its position and the curvature of the space, noting that in a circular 1D world, the creature could see itself if it is the only object present.
  • There is a discussion about whether the curvature of the space (positive or negative) affects visibility in one-dimensional space, with one participant arguing that it does not significantly matter in 1D.
  • A later reply raises the question of how light behaves in this context, particularly if it follows geodesics, and how visibility is affected by non-differentiable parts of the line.

Areas of Agreement / Disagreement

Participants express differing views on the implications of curvature for visibility in one-dimensional space, with no consensus reached on how these concepts apply to the creature's perception or the behavior of light.

Contextual Notes

Participants do not fully resolve the implications of curvature on visibility, nor do they clarify how light behaves in relation to geodesics in one-dimensional spaces.

ArielGenesis
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I am sorry with the bad title and I am physics major with very weak math. So I come to the forum to rescue me.

Basically I have one question, what does a "point-like creature" on a one dimensional line "sees" on different geodesics?

if the line is flat, then the creature can sees everything on the line, right?

If the line has a positive curvature, can the creature sees anything beyond itself? I mean we can see the horizon because we have non-zero height, as we get shorter, the horizon gets smaller and if we have zero height, then the horizon would suddenly collapse to just the immediate proximity. am I right, but these seems strange.

More over I want to confirm one thing. A positive geodesic is essentially a negative geodesic if it does not matter on which side of the line the creature is. Then my point would be, does which side of the line matters?

Can such creature see beyond the (a kink) non-differentiable parts of the line?

Last but not least, sooner or later I will study Special Relativity and General Relativity where geodesic become a main topic. I just want to have a good intuition about the nature of space and dimension before coming to class.

Thank You,
Regards,
A
 
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Since you are imagining a one-dimensional creature on a circle, what are you imagining about its sight? Does light move in a straight line or around its circle? That's pretty much up to you- it your imagination!
 
It's usually understood to mean the creature can see anything it has line-of-sight to.

In a flat 1D world, a creature on a line would be able to see the next closest object to it on the line.

In a circular 1D world, the creature would be able to see the next closet object too... unless it's the ONLY object in the world. Then it would see itself. No height required. It's line-of-sight is from one end of the creature, all the way around the circle, and back to its butt.

I don't think in 1D space it matters whether a space is positively or negatively curved. There's only so much you can do with 1D space. It's a line. Or it's a circle. Or it's a disjoint combination of those two. Once you move up to 2D and above, you have angles to work with, and there's a lot more variety.
 
so, combining the two response, the light curve and follow the geodesic? (I mean how would it is understood so as to be able to be applied to GR and SR )

how about if there is a kink in the circle?

thank you.
 

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