Diagrammatic Tensor Notation from the Beginning

LukeD
Messages
354
Reaction score
3
I've posted this in the Geometry & Topology section, but I believe it will get many more views here, so I'm posting a link

Pictures here:
https://www.physicsforums.com/showthread.php?t=407776

---

I really liked Penrose's diagrammatic way of writing tensor algebra, so I spent a while learning the basic notation. Unfortunately, it took a very long time for me to learn this because there is so little info on it to begin with. I also didn't see much mention of how to use the notation for doing numerical computations.

So since I want to be able to use the notation for everything that I should be able to do with tensors, I figured that I'd start at the very beginning of algebra and use the notation. My plan is to write a little tutorial that teaches everything from how to write numbers, vectors & covectors to how to take integrals.

The notation for adding tensors is mine as far as I know, and I've changed some other notation here and there.

I have 14 pages done, but they are very rough. So far they are very basic ideas. Should I continue with this? Any suggestions for cleaning it up? I want to make it as short & simple as possible while still getting the point across.
 
Physics news on Phys.org
Can you teach me how to konw it
 
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...
Does the speed of light change in a gravitational field depending on whether the direction of travel is parallel to the field, or perpendicular to the field? And is it the same in both directions at each orientation? This question could be answered experimentally to some degree of accuracy. Experiment design: Place two identical clocks A and B on the circumference of a wheel at opposite ends of the diameter of length L. The wheel is positioned upright, i.e., perpendicular to the ground...
According to the General Theory of Relativity, time does not pass on a black hole, which means that processes they don't work either. As the object becomes heavier, the speed of matter falling on it for an observer on Earth will first increase, and then slow down, due to the effect of time dilation. And then it will stop altogether. As a result, we will not get a black hole, since the critical mass will not be reached. Although the object will continue to attract matter, it will not be a...
Back
Top