Derivation of SR's time-dilatation in 1d?

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    1d Derivation
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SUMMARY

The forum discussion centers on deriving time dilation and related formulas, specifically in one dimension, using the invariance of the speed of light (c). The user seeks alternatives to the conventional light-clock method, expressing dissatisfaction with the perpendicular approach. Key equations presented include the spacetime interval and the Lorentz transformation, with references to Bondi's derivation as a more physically motivated method. The discussion emphasizes the need for a longitudinal light clock and the operational definitions involved in radar measurements.

PREREQUISITES
  • Understanding of spacetime intervals in special relativity
  • Familiarity with Lorentz transformations and their derivation
  • Knowledge of the concept of time dilation and its mathematical representation
  • Basic grasp of operational definitions in physics, particularly in relativity
NEXT STEPS
  • Study the derivation of time dilation using longitudinal light clocks
  • Explore Bondi's method for deriving Lorentz transformations
  • Investigate the algebraic derivation of Lorentz transformations in Einstein’s "Relativity: The Special and General Theory"
  • Learn about the Doppler effect and its implications in special relativity
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Physicists, students of relativity, and anyone interested in the mathematical foundations of time dilation and Lorentz transformations.

  • #61
Pony said:
Who's clock shows, where, what do you mean 'shows'?
See posting #40. That definition of time separates for example SR from Lorentz ether theory.

Pony said:
What does the first equation mean, and how do I conclude that?
I copied the first equation from your posting #58.
 

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