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

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SUMMARY

Tau-AB2 is defined as t2 - x2 due to the principles of special relativity, specifically within the context of Minkowskian geometry. Unlike Euclidean geometry, Minkowskian geometry alters the interpretation of distances and intervals, leading to the conclusion that the proper time interval is calculated using the difference of squares rather than their sum. This distinction is crucial for understanding spacetime metrics in inertial frames.

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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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