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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
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- Diagrams Space-time
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SUMMARY
This discussion focuses on understanding space-time diagrams, specifically the transformation of coordinates in Minkowski space. The key equations provided are the Lorentz transformations, which include hyperbolic functions: \( ct' = \cosh(\theta) ct - \sinh(\theta) x \) and \( x' = -\sinh(\theta) ct + \cosh(\theta) x \). Participants emphasize that Minkowski geometry differs fundamentally from Euclidean geometry, particularly in how distances and angles are defined, leading to the conclusion that the time coordinate in the new frame is given by \( ct' = \sqrt{a^2 - b^2} \). The discussion also clarifies the distinction between hyperbolic angles and Euclidean angles.
PREREQUISITES- Understanding of Minkowski space geometry
- Familiarity with Lorentz transformations
- Knowledge of hyperbolic functions and their properties
- Basic concepts of special relativity
- Study the derivation and implications of Lorentz transformations in special relativity
- Learn about hyperbolic geometry and its applications in physics
- Explore the differences between Euclidean and Minkowski geometries
- Investigate the concept of rapidity and its relation to velocity in special relativity
Students and educators in physics, particularly those studying special relativity and space-time concepts, as well as mathematicians interested in hyperbolic geometry.
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