Thread: Convention of n_(i,j) View Single Post


Andy Y wrote: > Hi Physicists, > I'm a chemist studying relativity. I have two references that use > opposite conventions for $\Eta n_(i,j):$ [...] The mostly minuses'' metric is sometimes called the west coast'' metric; the mostly pluses'' is te east coast'' metric. > Three questions: > 1. Does that reverse the convention of which vectors are time like and > which vectors are space like? No. The definition of timelike depends on the signature of the metric; it's defined so that the vector (1,0,0,0), which has only a time component, is timelikew. > 2. Which convention is the modern one (i.e. which one is found in > current literature)? Both appear in the literature, about equally often. Which one is used depends largely on which one an author learned in school, but each has its advantages. If you're looking at a canonical (Hamiltonian) formulation of gravity, for example, in which a spacelike hypersurface evolves in time, it's natural to want the induced spatial metric to be positive, so you are likely to prefer the east coast convention. If you're working on Euclidean quantum gravity, it's easiest to have the imaginary time'' metric positive definite rather than negative definite, so you're again likely to prefer the east coast convention. On the other hand, if you're looking at motion of observers in a spacetime, it's easiest to have the interval ds be proper time, which means you'll use the west coast convention. And particle physicists usually, though not always, use the west coast metric, in part because it means that physical (timelike) four-momenta have positive squares. In the end it's an arbitrary choice, and the textbooks are split almost evenly. The only place it makes a difference is if you aren't careful about matching your definition of spinors to your choice of metric signature; then the sign of the metric can matter. (See S. Carlip and C. DeWitt-Morette, Where the Sign of the Metric Makes a Difference,'' Phys. Rev. Lett.60 (1988) 1599.) > 3. Why didn't you folks "standardize" this? History. The usage is too evenly split; standardizing would require that some very large group of people change their convention, and no one will agree to that. > I am aware that the results will be the same either way, but it seems > to be something that might cause continual annoyance. After a while, you get used to it, and it becomes less annoying (though I've actually seen published papers that were wrong because their authors accidentally mixed two conventions). Steve Carlip