Is dt/ds always positive in General Relativity?

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SUMMARY

In General Relativity, the relationship between coordinate time (t) and proper time (s) is defined by the equation dt² - dx² = ds². It is established that dt/ds is not always positive, as one can reverse the coordinate time by applying the transformation t -> -t. This indicates that the sign of dt/ds can change based on the chosen coordinate system, confirming that it is not a universal constant.

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  • Understanding of General Relativity principles
  • Familiarity with coordinate transformations
  • Knowledge of proper time and coordinate time concepts
  • Basic grasp of differential geometry
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deadringer
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Is it always true that dt/ds is always positive, where t is the coordinate time and s is the proper time? I suspect his is the case, but am not sure why.
 
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No, it's not true. dt^2-dx^2=ds^2. You can reverse coordinate time freely t->-t. After all, it's just a coordinate.
 

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