If you're interested in the Tao instead of laughing at it, google "chakra'. AG
On Thursday, September 5, 2024 at 8:15:22 PM UTC-6 Alan Grayson wrote: > I know how they're defined but I never used them. AG > > On Thursday, September 5, 2024 at 5:26:36 PM UTC-6 Brent Meeker wrote: > >> Ever use cylindrical coordinates? >> >> Brent >> >> >> >> On 9/5/2024 2:07 PM, Alan Grayson wrote: >> >> Since the metric tensor is defined on the* flat *tangent space, will its >> matrix representation always be diagonal? TY, AG >> >> On Thursday, September 5, 2024 at 12:35:03 PM UTC-6 Brent Meeker wrote: >> >>> If you change coordinate systems the vectors and tensors transform in >>> such a way that the physics is unchanged. That's the defining property of >>> vectors and tensors and why they are not just the arrays used to represent >>> them. >>> >>> Brent >>> >>> >>> >>> On 9/4/2024 10:42 PM, Alan Grayson wrote: >>> >>> 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 >>> >>> <https://groups.google.com/d/msgid/everything-list/ddfc2b2c-28de-4338-b2eb-41d69bbcd58an%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/17a5202a-0dfd-4cfc-98fd-7e1e20e90f94n%40googlegroups.com >> >> <https://groups.google.com/d/msgid/everything-list/17a5202a-0dfd-4cfc-98fd-7e1e20e90f94n%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/b6aa3d37-0f8f-4883-9b30-b9f78a6a0c17n%40googlegroups.com.
