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

  • Context: Undergrad 
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    1d Derivation
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Discussion Overview

The discussion revolves around the derivation of time dilation in special relativity (SR) specifically in one dimension. Participants explore various approaches to derive time dilation and related formulas, such as the Lorentz transformation and the invariance of the spacetime interval, while emphasizing the observer-independent nature of the speed of light.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant seeks a derivation of time dilation that does not rely on the conventional light-clock method, expressing dissatisfaction with existing approaches.
  • Another participant suggests using a longitudinal light clock, where light signals are parallel to the direction of motion, as a clearer derivation method.
  • Several participants provide mathematical derivations starting from the spacetime interval, leading to the time dilation formula, while others express a desire for alternative methods that do not assume perpendicular length contraction.
  • One participant references Bondi's work as a physically motivated approach using operational definitions, while others mention the algebraic derivation found in Einstein's writings.
  • There is a discussion about the linear nature of transformations in inertial frames and the implications of the invariance of the speed of light on the derivation of Lorentz transformations.
  • Some participants share links to external resources that provide derivations of Lorentz transformations and time dilation, noting their relative simplicity or complexity.
  • There is a contention regarding the completeness of certain derivations, with participants debating whether they fully incorporate the principles of relativity.

Areas of Agreement / Disagreement

Participants express a variety of approaches and preferences for deriving time dilation, with no clear consensus on a single method. Disagreements arise regarding the sufficiency of certain derivations and the assumptions made in different approaches.

Contextual Notes

Some participants note that existing derivations often rely on specific assumptions, such as the nature of light clocks or the treatment of perpendicular versus longitudinal motion, which may limit their applicability or clarity.

Who May Find This Useful

This discussion may be useful for those interested in the mathematical foundations of special relativity, alternative derivation methods for time dilation, and the conceptual underpinnings of 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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