Chtistoffel notation

[Vmedvil2]

1 hour ago, Dubbelosix said:

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

Ouch, I hate getting teeth pulled, I hope you get feeling better.

[HallsofIvy]

What does any of this have to do with the Christoffel Symbols?

[Vmedvil2]

13 hours ago, HallsofIvy said:

What does any of this have to do with the Christoffel Symbols?

I distracted Dubbel however he will get to it.

[Dubbelosix]

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.

Edited April 14, 2021 by Dubbelosix

[Dubbelosix]

And it takes a lit of time doing it from a phone, I'm not writing it out in latex if you've noticed, I'm copying and pasting symbols in an arduous way.

[Dubbelosix]

Let's ignore the box operator. I was going to do this thoroughly, but Ivy's response sort of doesn't want me to bother. It's nice people ask me about physics, but it's silly responses like that which makes me wonder why I bother sometimes. Anyway, to cut a long story, so much shorter,

The Christoffel symbol arises as, 

∇ = ∂ + Γ

Let's see if anyone's impatience serves them..  what if I wanted to take the square of this?

∇·∇  = (∂ + Γ)(∂ + Γ)

Can anyone work this out? It us just a matter of some algebra? I was going to get into longer posts about how you write the space operator in terms of general relativity, bit since I'm being rushed into explaining one thing, we might as well ignore all the subtleties I was going to explain. So long as you multiply through all the terms properly and cancel any relevant terms that repeat (cross terms), you'll find the curvature tensor that arises in general relativity. There, you can thank Ivy for me not being thorough enough.

 

Edited April 14, 2021 by Dubbelosix

[Dubbelosix]

If you can understand the ordinary Laplace operator, now we've literally brushed through the four spaces in the most direct and obnoxious way.

Edited April 14, 2021 by Dubbelosix

[Dubbelosix]

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 Susskind, he's pretty clear the way he does it. He has use of a white board and will glossary over the derivatives of space in terms of the Christoffel symbols when speaking about the curvature tensor.

 

Edited April 16, 2021 by Dubbelosix

[Dubbelosix]

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

Edited April 14, 2021 by Dubbelosix

[Dubbelosix]

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 transport from ordinary concepts of curvature and the geodesics that matter couples to. From it you find the antisymmetric part involving torsion. Again. In bivector theory, this part arises even more naturally than what you might expect I'm GR. I think personally, bivector theory is more intuitive in this matter as it avoids unnecessary debates as to whether torsion should vanish as a symmetry of ordinary general relativity. When I imposed the gamma Pauli spin to it, we see it preserves with it the generally accepted laws of Poincare spacetime symmetries. In other words, anything preserving the Poincare symmetries, we should in principle expect it to be a real facet of nature.

Edited April 29, 2021 by Dubbelosix

[Dubbelosix]

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 away with certain classical ideas of this acceleration when wave functions dominate inside an atom. How quickly took it to larger systems, like pulsars and was very clear about it, the waves come out of the gravitational theory, not as mediator particle but based on rapidly rotating binary systems which produce these ripples in spacetime. I just finished watching it there. I hope others have done so too, because he really knows his stuff. Even when scientists speak about h as the perturbation of the metric g he's cautious not speak of them in the extreme field interpretations where we have been misled into the notion it is a physical field. Gravity is a pseudoforce and until we abandon the enthusiastic and frankly, audacious let alone ambitious attempts of making it part of a mediator field, I feel like we won't be making much progress.

Edited April 17, 2021 by Dubbelosix

[Vmedvil2]

22 hours ago, Dubbelosix said:

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 away with certain classical ideas of this acceleration when wave functions dominate inside an atom. How quickly took it to larger systems, like pulsars and was very clear about it, the waves come out of the gravitational theory, not as mediator particle but based on rapidly rotating binary systems which produce these ripples in spacetime. I just finished watching it there. I hope others have done so too, because he really knows his stuff. Even when scientists speak about h as the perturbation of the metric g he's cautious not speak of them in the extreme field interpretations where we have been misled into the notion it is a physical field. Gravity is a pseudoforce and until we abandon the enthusiastic and frankly, audacious let alone ambitious attempts of making it part of a mediator field, I feel like we won't be making much progress.

Accept the gravitons into your heart dubbel! You speak heresy against the gravitational pull. There must be a wave-particle mediator of gravity. I am not going to debate it with you.

Edited April 17, 2021 by VictorMedvil

[Anchovyforestbane]

4 minutes ago, VictorMedvil said:

Accept the gravitons into your heart dubbel! You speak heresy against the gravitational pull. There must be a wave-particle mediator of gravity. I am not going to debate it with you.

Why must there be? From what I understand, gravity isn't a force in the same sense that the other essential forces are.

[Dubbelosix]

I can't and will not, because I'd be laboring under a lie. 

[Dubbelosix]

Yes. Gravity isn't a force, and Susskind says this around two or three times as well from his lecture. I've been saying it for years as well. You don't ever quantize fields,  that are not actually fields. It's a wrong turn amd has led us to a wrong path, as the Idea butcheres the first principles of relativity, that is. That gravity is and always will be a pseudoforce from the curvature and distortion of the metric from contribution of these stress energies that are known as contributed from the real particles of the standard model. If you want gravitons, you'd have to say GR is wrong, and doing that youll figuratively be cutting off the same foot to which we hold all our models on, in good faith.

Edited April 17, 2021 by Dubbelosix