Science Forums

Members

3,690

Members

3,623

Members

30

## Popular Content

Showing content with the highest reputation on 04/17/2021 in all areas

1. ## Chtistoffel notation

I'm being asked by another poster at this site about this notation, how are the symbols used, probably also how they appear on physics. So I have decided to make this public so that its not a wasted discussion and so others will learn as well. I'll start it all in segments in good time.
1 point
2. ## Chtistoffel notation

I can't and will not, because I'd be laboring under a lie.
1 point
3. ## Chtistoffel notation

This following lecture is really good for the select few who have spouted a lot of nonsense concerning gravitons (;-) we all know who I'm talking about) because the lecture goes into talking about the gravitational waves. When asked how it is generated, Susskind clearly is careful not to say anything about gravitons. He states it's an analogue of how charges move. I made a quick post before, about how you can envision curvature much like how an electron circles round a proton. It's because it has an acceleration, what Susskind didn't mention though as I had before, some quantum effects does aw
1 point
4. ## Chtistoffel notation

Right heres the next lecture by Susskind, When I spoke about the relativitistic correction, ∇ = (∂ + Γ) It is also important to know how ot arises in general relativity for the Ricci curvature. It appears like R = ∂ Γ + ΓΓ because it has those essential space derivatives associated to the gradient with how geometry, more specifically curvature spreads through space with dimensions of inverse length squared . Again, to get the full relationship, you can simply expand (∂ + Γ)(∂ + Γ) with appropriate indices, and from it you find the parallel transp
1 point
5. ## Chtistoffel notation

If you want a more complicated look into it, you can follow my essay, where the torsion is non vanishing in bivector gravity theory. You'll find out how to expand the equation ∇·∇ = (∂ + Γ)(∂ + Γ) including how the gamma matrices (Pauli spin matrices) are involved as coefficients on the algebra. I don't expect everyone to be able to follow it as it a bit more difficult. https://bivector.quora.com/Final-Paper-for-Bivector-Gravity
1 point
6. ## Chtistoffel notation

Now, I know some of you really are interested in this, including the person who private messaged me, and while it is a complicated subject, and though I've given a very short rudimentary way for you to envision using them, they can be used in many different ways, such as replacing the acceleration with a Christoffel symbol, but then you need to start introducing the summation indices and from that you'd get the four force of gravity. Though it's not a force, it's just a notation symmetry to the which we think about the wat the force drops off 1/length^2. If you want to know more, here's Susski
1 point
7. ## Chtistoffel notation

Ivy, you'll find out soon, but a short answer is the derivatives of spacetime. when we speak of the operator, there is a correction term in the form of the Christoffel symbol. It is the Covariant derivative, which is the 1/length correction to the space derivatives. If you just have some patience, I would have got to this.
1 point
8. ## Chtistoffel notation

I distracted Dubbel however he will get to it.
1 point
9. ## Chtistoffel notation

What does any of this have to do with the Christoffel Symbols?
1 point
10. ## Chtistoffel notation

Ok, to understand the Christoffel symbol, I hope the notion of curved space and its unification with acceleration as the warping of gravity is also understood as a prerequisite because the aim of this post is not to teach the literal understandings of what you read in popular science books, but rather to break down what gravity is when it is manifestly spoke about in mathematical physics. Ok... So hopefully you will already know about basics of Euclidean space ie. The coordinates of ordinary flat space as x + y + z Algebraically speaking, this can also be written as the powers
1 point
×