On 1/18/2025 5:12 AM, John Clark wrote:
On Fri, Jan 17, 2025 at 1:41 PM Alan Grayson <agrayson2...@gmail.com>
wrote:
/> IMO SR can handle curved spacetime. _All one has to do_ is make
the partitions very fine, so we're approximating inertial motion
along very short paths. AG /
*All one has to do? Well yes but that's easier said than done, it took
Einstein 10 years of grueling work to figure out exactly how to do it,
and the effort nearly killed him, he got sick, lost 50 pounds and
figured he would die soon. Fortunately he did not. One of the most
difficult things he had to figure out was how to measure distance in
4D non-Euclidean spacetime that was curved in any given way that was
useful and never produced self-contradictory results. Mathematicians
insist that distance must have the following properties:*
*1) Non-negativity: d(x,y) ≥ 0
2) Identity of indiscernibles: d(x,y) = 0 if and only if x = y
3) Symmetry: d(x,y) = d(y,x)
4) Triangle inequality: d(x,z) ≤ d(x,y) + d(y,z)*
*
*
*After years of false starts and dead ends Einstein eventually found a
measuring stick that worked, it's called the Metric Tensor.
*
Well he didn't discover it. Bernard Riemann did many years earlier.
Einstein's friend Marcel Grossman put Einstein onto it. Most of those
years of trial and error were spent trying figure out how to represent
gravity in the equation and what function of the metric corresponded to
what representation of gravity.
Brent
*
*
*John K Clark See what's on my new list at Extropolis
<https://groups.google.com/g/extropolis>*
tg1
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