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Is Gravity Complex?


Dubbelosix

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You said previously you started with a conclusion, which I must have missed, now you say you have no such direction.

My conclusion is:- you are are just groping mathematically in the dark learning your own theory for the first time, ie you dont even have a theory yet, you are just waffling mathematically. ? You do not even have a plausible theory yet.

 

Why not read some extant theories before making one up  :sherlock:  which your own contrivances will agree with more or less. If they are not close then you will most likely be a long way and maybe have been over imbibing.  :beer-fresh:

 

I posted you a noddy's guide to general relativity which you said was "standard gravity". You havent even presented a none standard version of gravity yet, or even an incline of where you are headed with your mathematical waffling  :shocked:  

Just in case you have not yet come across it, here http://www.scienceforums.com/topic/30787-dubbelosix-supersock/. is the thread in which I have started recording the bans Dubbelosix (Gareth Lee Meredith) gets, on the forums I have subscribed to. 

 

The conclusion you are reaching about his incontinent mathematical scribbling (a lot of it cut and pasted from other people's books or papers) is shared by just about everyone else. A Walter Mitty character, who has been doing this for about a decade, apparently: http://www.sciforums.com/threads/sonoluninscence.161108/#post-3551523

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I wasnt running my mouth of.You havent developed even a none standard theory of gravity yet. You have not even demonstrated you are close.

 

The quick link I posted was more informative than anything you have posted to date, it is however dated. 

 

Perhaps with a little prodding you might decide to prove/derive something, that can be tested. What you have done so far is directionless waffle, are you telling us all that you are going to come up single handed with a new theory of gravity that is going to shake the world. :) or are you deluding your self ? 

Crossed with my post 77.....

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I wasnt running my mouth of.You havent developed even a none standard theory of gravity yet. You have not even demonstrated you are close.

 

The quick link I posted was more informative than anything you have posted to date, it is however dated. 

 

Perhaps with a little prodding you might decide to prove/derive something, that can be tested. What you have done so far is directionless waffle, are you telling us all that you are going to come up single handed with a new theory of gravity that is going to shake the world. :) or are you deluding your self ? 

 

The only waffle here is you. When have I ever said this theory will ''shake the world.'' Piss literally comes out of your mouth.

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I don't know what you mean by ''you have me,'' this isn't some competition, I am a creative thinker and writer, this has nothing to do with ''getting anyone.''

 

 

 

Back to the topic, I was able to find, not a gravitational theory with this idea, but there is a spacetime model for electromagnetism of the form:

 

[math]F = (\mathbf{E} + i c\mathbf{B})\gamma_0[/math]

 

see https://en.wikipedia.org/wiki/Geometric_algebra

 

As some will know, I studied the concept of gravielectromagnetism, which is in fact a linearized theory of gravity - and it makes some very good predictions to boot. But more importantly from those investigations we found that gravity mimicked the electromagnetic force in mathematical structure, so attempting to find an analogue is a natural thing to do.

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Let's propose the four dimensional covariant case then explain what it means geometrically:

 

[math]\mathbf{G}_{\mu \nu \rho \sigma} = g_{\rho \eta} \mathbf{T}^{\eta}_{\sigma \mu \nu} = \mathbf{T}(A_{\mu \nu} \cdot B_{\rho \sigma} + A_{\mu \nu} \times B_{\rho \sigma} + A_{\mu \nu} \wedge B_{\rho \sigma})[/math]

 

This solution is of course obtained from identifying the metric with [math](\gamma_{\mu} \cdot \gamma_{\nu})[/math]. Because I found a case within electromagnetism, I sought for the case in gravielectromagnetism. I obtain the derivation:

We can form something similar using a gravitational four potential [math]\mathbf{D}_{\mu}[/math] the product of two covariant derivatives is

 

[math]\Phi_{\mu \nu} = \nabla_{nu}\mathbf{D}_{\nu} - \nabla_{\nu}\mathbf{D}_{\mu}[/math]

 

In terms of geometric algebra for D=4 this would become

 

[math]\nabla_{\mu \nu}\mathbf{D}_{\rho \epsilon} = \nabla_{\mu \nu} \cdot \mathbf{D}_{\rho \epsilon} + \nabla_{\mu \nu} \wedge \mathbf{D}_{\rho \epsilon}[/math]

 

This forms a product of bivectors in [math]\Phi_{\mu \nu}[/math]. It shares a relationship that we already know about, that concerns the cross product which is involved with the space of rotations - this features in a slightly modified version of the last equation that more suits general relativity ~

 

[math]\nabla_{\mu} \mathbf{D}_{\nu} = \partial_{\mu} \cdot \mathbf{D}_{\nu} + i \sigma \cdot (\Gamma_{\mu} \times \mathbf{D}_{\nu})[/math]

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Adding a spin feature to spacetime itself will give rise to polarizability of the gravitational fields. It could answer for the chirality problem in early cosmology and it might have consequence for alternatives to dark matter models. Being in the space of rotations now, it belongs to the full Poincare group, which will also involve torsion.

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Some extra identities:

 

[math]\nabla_{\mu} \mathbf{D}_{\nu} = \partial_{\mu} \cdot \mathbf{D}_{\nu} + i \sigma (\Gamma_{\mu} \times \mathbf{D}_{\nu})[/math]

[math]\Box = \gamma^{\mu}\partial_{\mu}[/math]

[math]\Box \mathbf{D}_{\nu} = (\gamma^{\mu} \partial_{\mu}) \cdot \mathbf{D}_{\nu} + i (\sigma \gamma^{\mu} \Gamma_{\mu}) \times \mathbf{D}_{\nu}[/math]

The continuity equation for the mass current comes as:

[math]\nabla^{\mu} \nabla^{\nu} \phi_{\mu \nu} = \nabla^{\mu} \partial_{\mu} \cdot \nabla^{\nu} \mathbf{D}_{\nu} + i \sigma (\nabla^{\mu} \Gamma_{\mu} \times \nabla^{\nu} \mathbf{D}_{\nu}) = \frac{4 \pi G}{c^2}\nabla^{\mu \nu}\mathbf{J}_{\mu \nu} = -\mathbf{R}^{\mu \nu} \phi_{\mu \nu}[/math]

 

Where it features the Ricci tensor and the current [math]J[/math]

Edited by Dubbelosix
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