# Tag Info

### Complex coordinates $ds^2 = dzdz̄$ in 2d

It helps to notationally distinguish between skew-symmetric exterior products and ordinary tensor products: $$dz \wedge d\bar z= (dx+idy)\wedge (dx-idy) = -2i dx\wedge dy$$ for the volume element, ...
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### How do we interpret measurements of Mercury's position?

This is a good question. The 3D space part of a 3+1D flat Minkowski spacetime is a Euclidean space. We can make an identification when it is so. You are correct that the coördinates that we are using ...

• 11
1 vote

### Whether nonlinear coordinate transformations are symmetries of flat spacetime

"The laws of physics must have the same form under transformations from one inertial frame to another inertial frame". … nonlinear transformations from Cartesian to curvilinear coordinate ...
• 102k
1 vote

### Whether nonlinear coordinate transformations are symmetries of flat spacetime

Poincaire invariance in special relativity is a global symmetry that relates one physical state to another, different physical state. By Noether's theorem, the existence of this symmetry implies the ...
• 49.6k
1 vote

### Whether nonlinear coordinate transformations are symmetries of flat spacetime

My one cent. A rotating frame or accelerating frame or other non-inertial frame is not inertial frame of reference. On the other hand, merely a different choice of coordinates description (eg ...
• 5,202

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