Non-Euclidean Physics & Straight Lines: Can They Coexist?

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Discussion Overview

The discussion revolves around the relationship between non-Euclidean physics and the concept of straight lines in our universe. Participants explore whether non-Euclidean geometries imply the absence of straight lines and how these concepts relate to modern physics, particularly in the context of space-time geometries.

Discussion Character

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

Main Points Raised

  • One participant questions if non-Euclidean modern physics implies the non-existence of straight lines in the universe and seeks clarification on this concept.
  • Another participant asks for a definition of "non-Euclidean modern physics" and emphasizes the need to clarify what is meant by "straight line," suggesting that the criteria for determining straightness may vary.
  • A participant asserts that non-Euclidean geometries refer to straight lines as 'geodesics,' which do not share all properties of straight lines in Euclidean geometry, highlighting differences in parallel line behavior.
  • There is a suggestion that non-Euclidean ideas are built upon Euclidean concepts, prompting further exploration of their relationship.
  • A later reply proposes that Riemannian Geometry may be a more accurate term than Non-Euclidean Geometry, as it encompasses both types of geometries.

Areas of Agreement / Disagreement

Participants express differing views on the implications of non-Euclidean geometries for the concept of straight lines, with no consensus reached on whether straight lines can coexist within non-Euclidean frameworks.

Contextual Notes

Participants have not fully defined the terms used, such as "non-Euclidean modern physics" and "straight line," which may affect the clarity of the discussion. The relationship between Euclidean and non-Euclidean geometries remains somewhat ambiguous.

thinkandmull
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Here's something I've been wondering about: does non-Euclidean modern physics imply that there are no straight lines in our universe? If so, how is this possible? With any circular object or space, one can always draw a straight line through it, right? Thanks.
 
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What exactly do you mean by "non-Euclidean modern physics"? If you're thinking about the non-Euclidean space-time geometries of relativity, these allow straight lines.

It's also worth taking a few moments to crisply define what you mean by "straight line". If I present you with a path between points... What standards will you use to determine whether that path is a straight line?
 
No. It just means that straight lines - which are called 'geodesics' in Non-Euclidean geometries - don't necessarily have all the same properties that they have in Euclidean geometry.

For instance, in Euclidean geometry there is only one straight line through a point that is parallel to a line that doesn't pass through the point. In some non-Euclidean geometries there will be multiple such straight lines and in others there will be none.
 
Oh, so non-Euclidean ideas build of Euclidean ones?
 
In a sense. They are generalisations of them. Riemannian Geometry might be a better word than Non-Euclidean Geometry though, because Riemannian Geometries include both Euclidean and Non-Euclidean Geometries.
 

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