The tangent space and the metric tensor field are used in GR. I fail to see 
how your comments relate to the possibly ambiguous concept of the latter. 
The metric tensor field seems ambiguously defined. AG

On Tuesday, September 3, 2024 at 2:31:50 PM UTC-6 John Clark wrote:

> On Tue, Sep 3, 2024 at 3:58 PM Alan Grayson <[email protected]> wrote:
>
> *> I don't think you understand the issue. Velocities greater than c in 
>> the underlying spacetime manifold are allowed in the construction of the 
>> tangent plane,*
>
>
> I don't think you understand that the things that mathematics allows and 
> the things that the laws of physics allow are not necessarily the same 
> thing. Mathematics allows for the existence of Newtonian physics, and 
> Newton allows objects to travel much faster than the speed of light, but 
> Einstein taught us that the laws of physics forbid it.  
>
> Nearly all new theories in physics are mathematically consistent, but 
> nearly all new theories in physics are also eventually proven to be wrong.  
>
>  John K Clark    See what's on my new list at  Extropolis 
> <https://groups.google.com/g/extropolis>
> wpb
>
>  
>

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