I am fighting to reach the next level of math, the one used by Einstein general relativity. It is said that noone really understands the equation. But I want at least to have a basic understanding of the language used in the equation. I understand it is about multidimensional tensors. I have to let my brain get used to it. And it takes time, having to listen several times to the same lesson
Tibees explains vectors and reference frames with space time diagrams in one of her youtube but you have to pay to read the text in your own pace in brilliant.org.
“the facts of the universe” (Lillian Liebherr)
I have seen this video where Dan Fleisch gives a very good explanation about tensors. You need to know about vectors as I do but Dan explains vectors to in case you forgot about these. Vectors is just one type (rank 1) of tensors in the tensor family. It has to be seen several times to understand the indexing system.
“A student guide to vectors and tensors” is available as a ebook at books.google.it/books
There is a kind of tensor called metric tensor. I like the definition shared in mathworld.wolfram.com/MetricTensor.html
How you can understand the rank of a tensor is well explained by eigenchris in the video below. In his channel you find a serie of tensor calculus videos.
When he continues with calculus it become very difficult if you never have done vector calculus. I must repeat that.
I decided to move this part about tensors to a (and develope it fiurther in) a separate page that will be placed in my menu under learning -math
general relativity field equation
As is correctly explained in Wikipedia
- Rμν is the Ricci curvature tensor,
the Ricci tensor is the part of the curvature of spacetime that determines the degree to which matter will tend to converge or diverge in time
- R is the scalar curvature,
the scalar curvature (or the Ricci scalar) is the simplest curvature invariant of a Riemannian manifold.
- gμν is the metric tensor,
- Λ is the cosmological constant,
- G is Newton’s gravitational constant,
- c is the speed of light in vacuum, and
- Tμν is the stress–energy tensor.
I found this yotube that explains the general relativity field equation. I like it because of the good graphic representations.
As with the tensor youtube made by Dan Fleisch, this made by Eugene Khutoryansky show graphically how a tensor change depending on curvature of space. Very well done video.
Eugene Khutoryansky shares another youtube with amazing graphics.
Einstein followed his friends Grossamans advice 1912 to study Riemann geometry (“Albert Einstein” written by Vincenzo Barone, page 61) studied It looks like I have to deal with Rieman geomtry and math too to get closer to the math in the field equation. I must doe it now and will document this work in a separate page.