My understanding is that extra space dimensions are added in a way such that the line element in flat spacetime is calculated by the Pythagorean theorem:


Now I know that the all space dimensions are linked to time, that's why it is called spacetime. But I'm wondering about a case when the change in a space dimension is equal to the change in time. Let's say a change of 1m in $dx_4$ would mean a change of 1s in $dt$. How would you add such a dimension to the metric? And is there any logic to adding such a dimension?

If I just replace $dx_4$ with $cdt$ then I have removed time from my metric and have suddenly a 4+0 metric instead of 3+1. But I can also go back if I want. Does this make sense?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.