Understanding Tensors & General Relativity

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I enjoyed this video about tensors very much. I would recommend it to anyone seeking to understand the concept in general and general relativity specifically.

https://vimeo.com/32413024

You can fast forward through the repetitive parts and try to place yourself in the role of beginner as you watch.

Do you think anything essential is missing in this presentation?
 
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I forgot to mention I found the emphasis on the association between basis vectors and components to be powerful. It leads to moving beyond thinking of a vector as an arrow to thinking of it as one of many possible associations between basis vectors and components. This generalized association is a good conceptual definition of a tensor in my opinion. It's a good way to find your footing as you explore.
 
Thread 'Can this experiment break Lorentz symmetry?'

Thread 'Can this experiment break Lorentz symmetry?'

1. The Big Idea: According to Einstein’s relativity, all motion is relative. You can’t tell if you’re moving at a constant velocity without looking outside. But what if there is a universal “rest frame” (like the old idea of the “ether”)? This experiment tries to find out by looking for tiny, directional differences in how objects move inside a sealed box. 2. How It Works: The Two-Stage Process Imagine a perfectly isolated spacecraft (our lab) moving through space at some unknown speed V...
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Thread 'Relativator (Circular Slide-Rule): Simulated with Desmos - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. The Relativator was sold by (as printed) Atomic Laboratories, Inc. 3086 Claremont Ave, Berkeley 5, California , which seems to be a division of Cenco Instruments (Central Scientific Company)... Source: https://www.physicsforums.com/insights/relativator-circular-slide-rule-simulated-with-desmos/ by @robphy
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Thread 'A sufficient condition for integrability of equation ##\nabla g=0##'

In Philippe G. Ciarlet's book 'An introduction to differential geometry', He gives the integrability conditions of the differential equations like this: $$ \partial_{i} F_{lj}=L^p_{ij} F_{lp},\,\,\,F_{ij}(x_0)=F^0_{ij}. $$ The integrability conditions for the existence of a global solution ##F_{lj}## is: $$ R^i_{jkl}\equiv\partial_k L^i_{jl}-\partial_l L^i_{jk}+L^h_{jl} L^i_{hk}-L^h_{jk} L^i_{hl}=0 $$ Then from the equation: $$\nabla_b e_a= \Gamma^c_{ab} e_c$$ Using cartesian basis ## e_I...
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