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Old Nov 1st 2011, 05:21 PM   #1
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spacetime euclidean

Spacetime is described geometrically by the metric:
ds^2 = c^2dt^2 - dx^2 - dy^2 - dz^2
From where does it follow that space is still to be treated as euclidean?
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Old Dec 10th 2011, 07:01 AM   #2
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Originally Posted by aaaa202 View Post
Spacetime is described geometrically by the metric:
ds^2 = c^2dt^2 - dx^2 - dy^2 - dz^2
From where does it follow that space is still to be treated as euclidean?
That expression you wrote is called the "metric" the magnitude of ds is called the "interval". This is what makes spacetime non-euclidean. The expression ds^2 = dx^2 + dy^2 + dz^2 makes the space euclidean.
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