A Why is Tau-AB^2 not t^2 + x^2?

BLevine1985
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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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