Chtistoffel notation

[Dubbelosix]

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.

[Dubbelosix]

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 of amy arbitrary notation 

x and x^2 and x^3. This won't be important for our discussions though. What is important us that to have a four dimensional space, where time is a coordinate, you can write

s^2 = x^2 + y^2 + z^2 - t^2

Why is the last leg of this four dimensional Pythagorean taken away? It doesn't need to be, its a sign convention with notation (+,+,+,-), it can also be (-,-,-,+) it's only that the former is seen more often than the latter. The symbol "s" is the conventional notation describing a metric. By introducing the extra space dimension as a leg of the Pythagorean triangle, we have entered what us called Minkowski space.

General relativity is not easier for newcomers to understand, but let's try and break it down, as simple as we can. In special relativity, the space which things can move in is described by an operator, called the Laplace operator and has the appearance of the derivatives with inverse length squared, and is a differential notation for the divergence 

∇·∇ 

Or simply as

∇² 

In short it describes, acting on a function "f", we write it  as

∇² f = ∂²f/ ∂x²  

⁺  ∂²f/ ∂y^{2  +}  ∂²f/ ∂z²  

For three space dimensions, so what about the forth? While we are talking about a forth soon, we still have not degressed into the issue of curvature because operators can speak of a forth dimension and still not really talk about curvature, we'll get into that in good time. The next lesson will be about operators in four dimensions. I'll let this post be digested properly first.

 

Edited April 10, 2021 by Dubbelosix

[Vmedvil2]

37 minutes ago, Dubbelosix said:

 

General relativity is not easier for newcomers to understand, but let's try and break it down, as simple as we can. In special relativity, the space which things can move in is described by an operator, called the Laplace operator and has the appearance of the derivatives with inverse length squared, and is a differential notation for the divergence 

∇·∇ 

Or simply as

∇² 

In short it describes, acting on a function "f", we write it  as

∇² f = ∂²f/ ∂x²  

⁺  ∂²f/ ∂y^{2  +}  ∂²f/ ∂z²  

For three space dimensions, so what about the forth? While we are talking about a forth soon, we still have not degressed into the issue of curvature because operators can speak of a forth dimension and still not really talk about curvature, we'll get into that in good time. The next lesson will be about operators in four dimensions. I'll let this post be digested properly first.

 

You are talking about my favorite operator!, *Gets Excited*

[Dubbelosix]

3 hours ago, VictorMedvil said:

You are talking about my favorite operator!, *Gets Excited*

Well you're in for a ride so to speak. 

[Dubbelosix]

By the way, there is a relativistic operator - but that's for a much later discussion.

Edited April 10, 2021 by Dubbelosix

[Vmedvil2]

27 minutes ago, Dubbelosix said:

By the way, there is a relativistic operator - but that's for a much later discussion.

Ya, i know , link = https://en.wikipedia.org/wiki/D'Alembert_operator

[Dubbelosix]

Except that was for later, I was speaking about the Newton Poisson equation. 

Edited April 10, 2021 by Dubbelosix

[Dubbelosix]

https://en.m.wikipedia.org/wiki/Schrödinger–Newton_equation#:~:text=The Schrödinger–Newton equation%2C sometimes,function as a mass density%2C

 

 

But anyway, this was for much later

[Vmedvil2]

27 minutes ago, Dubbelosix said:

https://en.m.wikipedia.org/wiki/Schrödinger–Newton_equation#:~:text=The Schrödinger–Newton equation%2C sometimes,function as a mass density%2C

 

 

But anyway, this was for much later

Okay, whatever I have disrupted your lectures now continue it, I wonder sometimes what happens in the alternate universes I am not here in. I have significantly altered the timeline of the scienceforums.com, did I have the right?

Edited April 10, 2021 by VictorMedvil

[Dubbelosix]

Maybe. Who knows? Personally I think there is only two.

Edited April 10, 2021 by Dubbelosix

[Vmedvil2]

2 minutes ago, Dubbelosix said:

Maybe. Who knows? Personally I think there is only two.

Well see I even thought about saying nothing for a solid 30 seconds but decided to say something but continue your lecture on Christoffel notation.

[Vmedvil2]

7 minutes ago, Dubbelosix said:

Maybe. Who knows? Personally I think there is only two.

So what you believe that there is a right handed and left handed probability dimension one where you always pick the opposite of this universe for every decision over and over again?

Edited April 10, 2021 by VictorMedvil

[Dubbelosix]

Got baked potatoes in the oven be right back

 

[Dubbelosix]

Yes sorry, there is only two further reason. Somthing determined it very early on in my opinion.

[Dubbelosix]

And it's humble, because once I thought this universe was all there was! 

Edited April 10, 2021 by Dubbelosix

[Vmedvil2]

30 minutes ago, Dubbelosix said:

And it's humble, but cause once I thought this universe was all there was! 

well see I think i comes to more decisions than that because there are 3 dimensions of space so for every action you can choose a 0 state which is not to move or move 1 planck length in +X,+Y,+Z, or -X,-Y,-Z. So I believe it splits at every Planck length moved or whatever the smallest unit of movement is 7 times per planck time, also splitting when others move too in their own "Choice" Bubble. So NSingle Point  = 7^(1/tp)*dt , NMultiple Points = 7^(1/tp)*dt ^ (1/lp^3) * (4/3)*π*Runiverse^3.  But ya I'll let you get back to Christoffel symbols.

Edited April 10, 2021 by VictorMedvil

[Dubbelosix]

I was going to get back to this today but recovering from a tooth extraction, so will be back soon.