In What Frame Is (t2 - t1)^2 Measured?

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Discussion Overview

The discussion revolves around the measurement of the time interval (t2 - t1)^2 in the context of special relativity, specifically questioning in which inertial frame this time interval is measured. The scope includes theoretical considerations of proper time and spacetime intervals.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant states that T represents proper time as measured in an inertial frame, questioning the frame in which (t2 - t1)^2 is measured.
  • Another participant asserts that t1, x1, t2, and x2 can be measured in any inertial frame, and that the result T will remain invariant regardless of the chosen frame.
  • A later post reiterates the equation for T and emphasizes that the sign of \Deltas2 can indicate whether it represents proper time or proper distance, suggesting a nuanced understanding of the spacetime interval.

Areas of Agreement / Disagreement

Participants express differing views on the measurement frame for (t2 - t1)^2, with some asserting invariance across frames while others raise questions about the implications of the sign of \Deltas2. The discussion remains unresolved with multiple competing perspectives.

Contextual Notes

Participants highlight the dependence on definitions of proper time and distance, as well as the implications of the sign of \Deltas2, which remain unresolved in the discussion.

Best of the Worst
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T = root((t2 - t1)^2 - (x2 - x1)^2)

As I understand it, T is proper time as measured in someone's intertial frame, and (x2 - x1)^2 is their movement through space... but in what frame is (t2 - t1)^2 measured?
 
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t1,x1 and t2,x2 are both measured in somenone (anyone's) inertial frame.

Regardless of which inertial frame you chose to measure t1,x1,t2, and x2, the result T will be the same - it will be invariant.
 
Awesome. Thank you kindly ;).
 
Best of the Worst said:
T = root((t2 - t1)^2 - (x2 - x1)^2)

As I understand it, T is proper time as measured in someone's intertial frame, and (x2 - x1)^2 is their movement through space... but in what frame is (t2 - t1)^2 measured?
Please note that

[itex]\Delta[/itex]s2 = (t2 - t1)2 - (x2 - x1)2

may be either positive, negative or zero. [itex]\Delta[/itex]s2 may be either a proper time or a proper distance according to its sign.

Pete
 
Last edited:

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