I feel like I am now entering the end game, which probably just means my troubles are just beginning. For a while now I've had a theoretical goal that can be boiled down to two things:
1) Reproduce the bending of light by the Sun, just like general relativity.
2) Retain the ability of quantised inertia to predict MoND-like behaviour in galaxies.
It was Alex Unzicker's books (especially "Einstein's Lost Key") that convinced me that the best way to do this would be to focus on a curious path followed by Einstein in 1911-1912 just before he was persuaded away into untestable geometry by Marcel Grossman. While in Prague Einstein devised a version of GR that treated space as if it had a refractive index. The idea was that the speed of light c=fL reduces close to masses because relativity reduces both f (frequency) and L (wavelength) there, and so light beams bend around the Sun twice as much as Newton would have predicted. Unfortunately, at the time he forgot the reduction in L and predicted only half the correct bending of light. This error was corrected by Dicke in 1957 but by then it was too late and the later geometrical-tensor GR had taken over because it was not stymied by the factor of two error.
To agree with the data on light bending by the Sun (data: the only important consideration), the correct theory must predict this equation for the speed of light c a distance r away from a mass M:
For a lot of last year, on and off, and for several weeks this year I have been trying to get this relation from QI. I did it last year and rejected it for various intuitive reasons. Last week I did it again and realised that it was the right way! The solution is obvious and beautiful in a way that cannot be explained until you actually see it, but it's not published yet so I can't tell you the whole story.
What quantised inertia says is that the zero point field (and its energised version: Unruh radiation) close to matter is damped (reduced) so light bends towards the matter, sliding down the zpf gradient. This gives Newtonian gravity (see my 2013 paper), but in QI we also have to consider the cosmic horizon of the light which reduces the inertial mass of the photons even more than expected so they bend towards the Sun twice as much as expected. It all works out nicely and gives the equation above. The great advantages of the new QI dynamics are that it gets rid of dark matter, it predicts cosmic acceleration and practical thrust and, unlike bent space which cannot be directly tested, it could be directly tested by measuring the zpf in different places with, say, a Casimir probe.
Given the lab results that are starting to come in (see my blog last month) and this latest theoretical result I expect breathless requests for zoom presentations will come flooding in from physics departments all over the globe! (I always like to end on a humorous note).
References
McCulloch, M.E., 2013. Gravity from the uncertainty principle. Astrophys & Space Science, 349, 957-959. Link to Pdf
Unzicker, A., 2015. Einstein's Lost Key.
