How is the foregoing consistent with the statement that tensors are independent of coordinate systems? TY, AG
On Wednesday, September 4, 2024 at 10:39:33 PM UTC-6 Alan Grayson wrote: > No; you never posted any page numbers in your reference. Had you done > that, I would have immediately studied your specific reference. But I was > about to post something like what you wrote; namely, that *solving* for > the metric tensor *MEANS* solving for the 16 components defining its > function, given a stress-energy tensor and a coordinate system. The form of > the components must depend on the coordinates. And given a coordinate > system, the components will vary depending on location in spacetime, and > this is what's meant by the "metric tensor field". I thought the "field" > refers to a *unique* *real numbe*r at each point in spacetime, but it > must refer to the components of the matrix representing the tensor. Wiki's > definition seems misleading since it states that the metric tensor is a > bilinear function of two vectors on the tangent plane. Those vectors are > its arguments, but sort-of misleading. Is there anything in the foregoing > that I got wrong? AG > On Wednesday, September 4, 2024 at 8:09:07 PM UTC-6 Brent Meeker wrote: > >> The metric field is the set of metric tensors, one at each point. It's >> not some vector lengths. >> >> When are you gonna read "Relativity DeMystifie". I told you the page >> numbers and you can look up more in the index. >> >> Brent >> >> >> >> On 9/4/2024 5:59 PM, Alan Grayson wrote: >> >> But my point is therefore that the metric tensor field is ambiguous ! >> >> On Wednesday, September 4, 2024 at 6:40:38 PM UTC-6 Brent Meeker wrote: >> >>> It explains this "...and yields *different *real values for most >>> different pairs." >>> >>> Brent >>> >>> >>> >>> On 9/4/2024 1:03 PM, Alan Grayson wrote: >>> >>> and yields *different *real values for most different pairs. >>> >>> >>> -- >> You received this message because you are subscribed to the Google Groups >> "Everything List" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to [email protected]. >> >> To view this discussion on the web visit >> https://groups.google.com/d/msgid/everything-list/ae301a72-9969-4e60-a132-0c8fe6d6f16cn%40googlegroups.com >> >> <https://groups.google.com/d/msgid/everything-list/ae301a72-9969-4e60-a132-0c8fe6d6f16cn%40googlegroups.com?utm_medium=email&utm_source=footer> >> . >> >> >> -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/ddfc2b2c-28de-4338-b2eb-41d69bbcd58an%40googlegroups.com.
