Dear Alan
Thanks for your reply. I understand that the quest for a unify theory is a titanic task. What you have achieved so far is a great headway. Indeed, I agree that there is still work to be done in order to deprive QM from its "mysteries", but I believe it is just a matter of time. Some other people are working in the same direction.
You :such as the nonlinear self-interaction that turn a continuous field into a discrete particle with quantized spin.
do you mean the process of creation and annihilation of particles within the context of NQP?
You: A gravitational potential pervades the universe, and this reduces the natural frequencies of all quantum oscillators...
In the cosmological model of the universe applying Newtonian gravity, it is assumed that the universe has a gravitational potential which leads to the a simplified version of the Friedman equations. Are you referring to this?
You: This in turn slows time locally, and also reduces the speed of light.
In 1911 Einstein knew that the bending of light was due to a change in the speed of light. Actually, he derived the equation (1) that you show for weak gravitational potentials. I agree with this, the speed of light is not really a constant.
You: I have not yet carried out a complete formal derivation, but I believe that this will reproduce conventional GR to first order.
Well, Edwin Klingman has also worked out something similar and he also claims that he could get GR to first order. But as I mentioned before, I think GR is not compatible with QFT nor with the notion of particles as solitons. If you could derive it, that would be great but I wouldn't worry about it.
You: leads to the surprising conclusion that event horizons and gravitational singularities are mathematical artifacts of an incomplete theory, and do not exist in nature.
This is a very important observation, although, I must confess that I don't fully understand why you conclude that. Are you saying that the Schwarzschild metric is not correct. What do yo mean b "an incomplete theory"? What theory are you referring to, GR? In what sense do you mean is incomplete? I think it is difficult (I would say impossible) to persuade the mainstream that black holes doesn't exist. Most people now believe that almost every galaxy has a black hole in its core.
You: I cannot, as yet, explain these results, but I will be working on that.
It would be remarkable if you could find an explanation.
As you can see from my bio, my main field of study is condensed matter, and at this moment I'm spending more time doing research in my official field than in the foundations of physics. So, I think that I cannot make a lot of progress in this field for the following months. However, I'll be glad to add you to my list of contacts and keep you in mind for future discussions on these topics.
Best Regards
Israel