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Other than the fact that one may move in only one direction in time but can move in two directions in each spacial dimension (e.g. arrow of time), are there any other physical characteristics that distinguish between the time and space directions?

As a follow-up question: If I write a line element $ds^2 = -dt^2 -dw^2 + dx_1^2 + dx_2^2 + dx_3^2$, does the negative sign on the $w$ direction automatically imply the existence of an arrow of time associated with the w-dimension (or vice versa)?

(I admit that models containing more than one time dimension typically have many problems and are automatically considered unphysical by almost everybody, Itzhak Bars possibly being the most famous exception. The purpose of the follow-up question is more of a 'what if' to have a better understanding of the difference between spacial and temporal directions.)

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