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apostolosdt
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You asked for help. Now, in turn, you can help this Forum. Honestly, how much did this thread manage to illuminate the topic you started?Kashmir said:
Trying to understand space-time diagrams
- Context: Undergrad
- Thread starter Kashmir
- Start date
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- Tags
- Diagrams Space-time
Click For Summary
Discussion Overview
The discussion revolves around understanding space-time diagrams, particularly in the context of special relativity and Minkowski geometry. Participants explore the mathematical transformations between different inertial frames, the implications of these transformations on the geometry of space-time, and the interpretation of angles and distances within this framework.
Discussion Character
- Exploratory
- Technical explanation
- Debate/contested
- Mathematical reasoning
Main Points Raised
- One participant questions the correctness of calculating the time coordinate in a new frame as ##c t^{\prime}=\sqrt{a^2+b^2}##, suggesting it should be ##\sqrt{a^2-b^2}## instead.
- Another participant explains that Minkowski space geometry differs from Euclidean geometry, emphasizing that the Minkowski version of the Pythagorean theorem is ##s^2 = (ct)^2 - x^2##.
- There is a discussion about the terminology of scalar products, with some participants noting that while Minkowski geometry does not adhere to positive definiteness, it can still be referred to as a scalar product.
- Participants express caution regarding the application of Euclidean geometry to Minkowski diagrams, stressing the need for clarity in understanding the underlying geometry before drawing diagrams.
- One participant raises a question about the angle between the ##x## and ##x'## axes, leading to a discussion about the nature of hyperbolic angles versus Euclidean angles.
- Another participant points out that the angle ##\theta## is treated incorrectly when using the inverse tangent function, suggesting that hyperbolic functions should be used instead.
Areas of Agreement / Disagreement
Participants express differing views on the correct interpretation of distances and angles in Minkowski space, with no consensus reached on the proper application of Euclidean versus hyperbolic geometry in this context.
Contextual Notes
There are unresolved questions regarding the definitions and applications of scalar products in different geometrical contexts, as well as the implications of using Euclidean versus hyperbolic angles in calculations related to space-time diagrams.
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