Why is Tau-AB^2 not t^2 + x^2?

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Discussion Overview

The discussion revolves around the relationship between the expression for proper time, specifically why Tau-AB^2 is equal to t^2 - x^2 instead of t^2 + x^2. The context is rooted in the geometry of spacetime as described by special relativity.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • Some participants assert that Tau-AB^2 equals t^2 - x^2 based on the definition of the metric in an inertial frame in special relativity.
  • Others argue that it seems Tau-AB^2 should equal t^2 + x^2 according to the geometry depicted in a diagram.
  • A participant clarifies that the diagram represents Minkowskian geometry, which differs from Euclidean geometry, suggesting that interpretations of lines and angles should not follow Euclidean principles.

Areas of Agreement / Disagreement

Participants express differing views on whether Tau-AB^2 should be t^2 - x^2 or t^2 + x^2, indicating that multiple competing interpretations remain unresolved.

Contextual Notes

The discussion highlights the dependence on the definitions of metrics in different geometrical contexts and the implications of interpreting diagrams in special relativity.

BLevine1985
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TL;DR
question about proof page 21
why is Tau-AB^2 equal to t^2 - x^2 ?It seems it should be t^2 + x^2 according to the geometry of the diagram...
 

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BLevine1985 said:
why is Tau-AB^2 equal to t^2 - x^2 ?
Because that's how the metric is defined in an inertial frame in special relativity.

BLevine1985 said:
It seems it should be t^2 + x^2 according to the geometry of the diagram...
No, because the diagram is not depicting a Euclidean geometry. It's depicting a Minkowskian geoemetry. That means you cannot interpret lines and angles in the diagram as if they were Euclidean; they aren't.
 
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Thank you. That was very helpful!
 
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BLevine1985 said:
Thank you. That was very helpful!
You're welcome!

Also, welcome to PF!
 
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