On 9/2/2024 9:06 PM, Alan Grayson wrote:


On Monday, September 2, 2024 at 7:58:04 PM UTC-6 Brent Meeker wrote:

    I should think it was obvious that the metric tensor, M, at a
    point g*Mg gives the length of g.


It's not obvious and I don't see how it's relevant. At each point the metric tensor can be evaluated on an uncountable set of pairs of vectors. So which pair does one choose? AG
Don't pick a pair.  Pick one and it's conjugate.

Brent


    I generally ignore these questions because you're asking questions
    that take some exposition which is found in any text book and many
    online sites.  I also recommend "Relativity Demystified" by David
    McMahon.


TY for the reference. I'll check if it has the issue I need addressing. It's not on any of the sites I checked, so far. AG

    Bretn



    On 9/2/2024 5:25 PM, Alan Grayson wrote:
    Brent; do me a small favor. If you are unable to answer my
    question, just say so. OK? AG

    On Saturday, August 31, 2024 at 8:48:13 PM UTC-6 Alan Grayson wrote:

        You seem to know a lot about relativity, so please explain
        how the metric tensor can be defined unambiguously at some
        point P on the underlying manifold, spacetime, if there is an
        uncountable set of pairs on a vector space on the tangent
        space at some point P on which the metric tensor is defined
        (as a bilinear function which maps to the real numbers.) TY, AG

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