A Why is Tau-AB^2 not t^2 + x^2?

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Tau-AB^2 is equal to t^2 - x^2 due to the definition of the metric in an inertial frame of special relativity. The confusion arises from interpreting the diagram as Euclidean geometry, but it actually represents Minkowskian geometry. In Minkowski space, the relationships between time and space differ from those in Euclidean space, leading to the subtraction rather than addition of the squared terms. Understanding this distinction is crucial for grasping the principles of special relativity. The discussion emphasizes the importance of recognizing the geometric framework when analyzing such equations.
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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