Hi, I'm doing a first course in GR and have just found out that(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\eta_{ab} = g(\vec{e}_{a}, \vec{e}_{b}) = \vec{e}_{a} \cdot \vec{e}_{b}[/itex]

where g is a tensor, here taking the basis vectors of the space as arguments. I haven't seen this written explicitly anywhere but does this mean that

[itex]\vec{e}_{0} = (i, 0, 0, 0)[/itex]?

Isn't this strange? And does it have any particular significance or is it just an oddity? Apologies if this is asked before or just plain wrong.

EDIT: I should say that I know this preserves the time component in the spacetime metric, but it still seems weird to think of imaginary basis components that describe a physical space. Or is it wrong to think of spacetime as anything other than purely mathematical?

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# Basis vectors of Minkowski space

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