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Originally Posted by tusenfem
That does not make sense, why would the result for -x be different from +x. That would mean that if we see an eclips in summer the beding would be different from what we would see in winter.
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Depending on which variable is x, y and z, there is no differences for x- and x+. It is the z- and z+ (the vertical) that is different. The 6 directions are simply representing the whole sphere of directions. As we agreed, it needs to be proven over the whole sphere, but the average is going to be somewhere between 1 and 3 and probably near 5/3.
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you keep on mentioning Birkhoff, care to say what paper or book?
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I got the information on G D Birkhoff from a book caleld "The Measure of the Universe" by J D North. He states that Birkhoff produced an explanation of GR from Schroedinger's equations in 1927. Birkhoff was a respected American Mathematician. I am not sure what journal he published his ideas in, but other people continued on with his idea of explaining GR from Schroedinger's equations. However this is a little different. He also gave some GR equivalent equations in vector form (which I find much easier to understand) and these show that relativistic matter is also affected additionally in the same way as light, so that matter at v~=c has a 2x factor and I think the form is (1+v^2/c^2).
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This is even more woolly than before! You need, FROM THE START, to come up with correct equations to describe what you are envisioning. Your "new" term pull, which is basically force per unit mass, is nice but does not do very much. It is totally unclear what you want to do here, redifining gravitational interactions and such.
If you don't think you can do the math, then say so, and I will drop out of this thread and let you muddle on by yourself.
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I think that the required thing is time rate of change of momentum per unit mass which I called b. Yes, force per unit mass is the same thing I suppose. As long as it is understood that a gravitational field is having a force on radiation and that for horizontal radiation it results in double the acceleration.