On 4/24/2019 6:36 PM, [email protected] wrote:
They are some glitch in my email program which puts in extra ??? It is mysteriously inconsistent.On Wednesday, April 24, 2019 at 6:46:49 PM UTC-6, Brent wrote: On 4/24/2019 4:17 PM, [email protected] <javascript:> wrote:On Wednesday, April 24, 2019 at 5:11:13 PM UTC-6, [email protected] wrote: On Wednesday, April 24, 2019 at 3:34:28 PM UTC-6, Brent wrote: On 4/21/2019 7:35 PM, [email protected] wrote:On Sunday, April 21, 2019 at 8:07:28 PM UTC-6, Brent wrote: On 4/21/2019 6:31 PM, [email protected] wrote:*Here's something odd. At 9:45 in Susskind's Lecture 2 on GR, he says the metric tensor is a Kronecker delta function. But I could swear that the diagonal of -1,1,1,1 represents flat space in SR. AG??*What's odd about that??? Flat space is just special case of curved space in which the curvature is zero. Brent *Sure, but he seems to be saying that the Kronecker delta is the metric tensor for curved space. Isn't that how you interpret his comment?*No.?? After he goes thru the derivation with delta function in it, then he says it's different for a curve?? space. Brent *I just reviewed it again. That's not my reading. In any event, it's not clear what he means, and using Bruno's suggestion, t' --> it,?? doesn't really help either since you end up with the Lorentz metric which is far from Euclidean intuition for demonstrating deviations from flatness. Further, there are transformations that keep spacetime flat with NON-zero off diagonal elements, such as a simple rotation. AG??* *Using the Lorentz metric, how is "flat" spacetime defined mathematically? AG *The general definition is that the Riemann tensor is zero.?? This is independent of what coordinate system is used.?? https://en.wikipedia.org/wiki/Riemann_curvature_tensor <https://en.wikipedia.org/wiki/Riemann_curvature_tensor> If the Lorentz metric applies globally the space is flat. Brent Are the double question marks significant in some way, or typos? AG
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