What Determines the Straightness of a Line?

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Discussion Overview

The discussion revolves around the criteria for defining a straight line, exploring concepts from physics and mathematics, including the behavior of light, inertia, and the geometry of space-time. Participants consider both theoretical and conceptual aspects of straight lines in different contexts.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants suggest that a straight line could be defined by the path of a beam of light, while others challenge this by noting that light can be bent by gravitational lensing and other mediums.
  • One participant proposes that an object in motion without forces acting on it could be considered to move in a straight line, raising questions about the implications of this in different contexts, such as orbital motion.
  • Another participant introduces the concept of geodesics in space-time, indicating that these are the true "straight lines" in a non-Euclidean framework, as opposed to Euclidean straight lines.
  • A question is raised about whether the inquiry into straight lines is more mathematical than physical, suggesting a distinction between the two fields.
  • Participants discuss the mathematical background required to understand non-Euclidean geometry and geodesics, mentioning topics such as calculus, vector and tensor analysis, and differential geometry.

Areas of Agreement / Disagreement

Participants express differing views on the definition of a straight line, with some emphasizing physical interpretations and others focusing on mathematical definitions. The discussion remains unresolved regarding the criteria for straightness and the relationship between physics and mathematics.

Contextual Notes

The discussion highlights the complexity of defining a straight line, particularly in the context of different geometrical frameworks and physical interpretations. There are unresolved questions about the implications of orbital motion and the nature of light paths.

mkristof
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I was wondering what should be used as the criteria for a straight line? One suggestion would be the path that a beam of light would take. Another criteria would be that based on inertia. An object in motion that experiences no forces could be considered to be moving in a straight line. This almost seems too simple, but I had considered that if one were in a capsule in orbit around the earth, and did not have a window, force measuring devices, like an accelerometer, could not distinguish an orbit from motion between stars.
Could a gyroscope help?
Could an "inertial" straight line be what is meant by gravity being "bent" space.
This is my first post. I like to think about fundamental questions and not take anything for granted. I hope this post makes sense.

Mark
 
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The path a beam of light takes isn't always a straight line. Gravitational lensing can bend a beam of light as can mirrors or prisms.
 
In flat space, a Euclidean "straight line" is quite reasonable and it is in fact the basis for our understanding that space-time is NOT Euclidean. The "straight lines" in space-time are more properly called "geodesics" and yes, they are the path that light follows due to what in Euclidean geometry would be considered "bent". We CALL space-time "bent" and similar phrases and that is in reference to Euclidean space. This was shown by the "bent light" around the sun that confirmed the theory of relativity about 100 years ago.
 
"What is a straight line?"

Isn't this a mathematics question and not physics? Physics does not define the shape and geometry.

Zz.
 
What level of mathematical training and subject area would be needed to understand non-Euclidian geometry and geodesics?
 
mkristof said:
What level of mathematical training and subject area would be needed to understand non-Euclidian geometry and geodesics?
Calculus (including partial differential equations), Vector and Tensor Analysis, Differential Geometry
 

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