He also got angry when I told him I believed spacetime is positively 
curved. He said I should calculate the curvature tensor, since it would be 
zero if spacetime is flat. I responded, asking him why I should do that, 
since whatever I calculated, assuming I knew how to do it, wouldn't prove 
anything since the result would depend on my assumptions. He never replied 
-- a sad ending for me, for what I considered a friendship. AG
On Sunday, February 16, 2025 at 10:07:58 PM UTC-7 Alan Grayson wrote:

> I'm sure you know him. RW. AG
>
> On Sunday, February 16, 2025 at 9:14:42 PM UTC-7 Brent Meeker wrote:
>
> What's his name?  I still know a few people there.
>
> Brent
>
>
> On 2/16/2025 6:07 PM, Alan Grayson wrote:
>
>
>
> On Sunday, February 16, 2025 at 3:33:29 PM UTC-7 Alan Grayson wrote:
>
> I got into a fairly heated argument with a Ph'D in physics from Brent's 
> alma mater, the University of Texas at Austin, concerning the construction 
> of the tangent vector space in GR. For this and other reasons we are no 
> longer in communication. He insisted on including particle paths of all 
> velocities passing through a point P on the spacetime manifold, aiming to 
> construct the tangent vector space at P. I objected since this would 
> violate one of the basic postulates of GR, which preclude particles assumed 
> to be exceeding light speed. I was berated for making such a criticism. 
> Initially I thought these faster than light speed particles were needed to 
> form a *vector space*, in order to satisfy the linear additive property 
> of a vector space under the field of real numbers. But suppose these 
> vectors are constrained to be added relativistically, so no pair when 
> added, can exceed light speed. Will this be sufficient to satisfy the 
> linear additive property of vectors in a vector space, without violating 
> the postulate of GR precluding faster than light speed particles? TY, AG 
>
>
> Since the LT is linear, I think it will work to restrict the velocities on 
> the tangent space to less than light speed. I'm puzzled why the physics 
> guru from the U of Tx adamently objected to my criticism and implied simple 
> fix for his obvious error. AG 
>
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