The last couple of years were very difficult times for me as a researcher, but also as a mere human being. I actually reached the limits of mental sanity while I was finishing the work I had undertaken almost 10 years earlier, when I published the first version of the paper that became the massive book which is entitled Negative-Energy Matter and the Direction of Time. It all began when a few significant problems emerged as I was reviewing the research report on which this book is based, in order to produce an abridged version of it.
First of all, I realized that there was a problem with my description of voids in a uniform matter distribution and for a while I believed that this difficulty was jeopardizing the validity of my original proposal that voids in the positive or negative portions of vacuum energy are equivalent to the presence negative- and positive-energy matter, respectively. It took me a sizeable amount of time and efforts to realize that this was not the case and that my basic postulate was still valid. It took me nearly as much time to explain in words why that was an appropriate conclusion and to adapt other portions of the report to reflect those changes and other less crucial developments.
As I was putting the final touch on those corrections and a few others, however, I realized that there was something else I had done that was not fully satisfactory. As I began to dig the issue of black hole information and entropy, it became clear that my early proposal for a description of the fundamental degrees of freedom of particles caught inside a black hole event horizon was at best incomplete and maybe somewhat incorrect. I had to re-examine this whole issue, which is the subject of nearly an entire chapter of the book. I wrestled with that problem very intensely, as I had the strong intuition that its solution would bring about significant progress in our understanding the state of elementary particles on the quantum-gravitational scale.
But every step forward I was making seemed to only make things worse and at some point I began to think that this is a problem I would never be able to solve and that it might be preferable to simply remove the whole portion of the book that dealt with discrete symmetries and black hole entropy and forget about the whole thing. But given that this would have affected the validity of key results discussed in other parts of the book, as well as the whole structure of the document, I had no choice but to keep going. At some point I realized that my understanding of the semi-classical theory of black hole thermodynamics was incomplete. But as I was progressing in my research career I had developed a tendency to work with a minimum input of information and was reluctant to go back studying what had been achieved in the field since I first explored the subject, many years ago. Now, however, I had no choice, so I took a whole summer reluctantly studying black hole thermodynamics.
Yet, once I completed my crash course on this research topic, at the boundary of relativity theory and quantum theory, I found myself even more confused. Things I had assumed were right turned out to be incompatible with some very basic theoretical constraints. At some point I really thought I would go crazy. But I never abandoned. I had no choice, I needed to make sense of this whole situation, especially since I realized that the specific problem I was working on was actually one of the last remaining unsolved issues which researchers in the field had identified as affecting the semi-classical theory of black hole thermodynamics. This is the most difficult problem I was ever faced with while working to integrate a consistent concept of negative-energy to physical theory. The miracle is that, just as I was about to abandon everything, I finally found out, nearly by chance, what I had failed to understand concerning the formula that provides the entropy of a black hole as a function of its various macroscopic parameters. But this particular aspect of the relationship between the area of a black hole and its mass, charge, and angular momentum is precisely what the generalized gravitation theory I had previously developed allowed to explain.
From this mentally exhausting work resulted a very elegant model that allowed to account for the degrees of freedom of matter whose state is encoded in the discrete quantum gravitational units of area on the event horizon of macroscopic black holes, such as those at the center of our galaxy. But the most surprising aspect of those developments is that they also allow one to describe, with complete precision, what the discrete degrees of freedom are for the elementary particles which are present on the Planck scale. This is an outcome of recognizing that matter particles are actually always subjected to the gravitational field of the smallest possible black holes, which must be present on the quantum gravitational scale as a result of quantum fluctuations in energy and spacetime curvature.
This is how my journey in fundamental theoretical physics came to its satisfactory completion. It is with enormous relief that I can now go back to write for the pleasure of it, without having to consistently watch for the possible mistake or inconsistency that may invalidate the whole framework I have, with great pain, been allowed to elaborate. Of course, not everybody will ever agree that those developments are valid or appropriate. Given the progress I have been able to achieve, though, I sincerely believe that at the present moment this can only be a matter of ignorance and not the outcome of any rational argument based on empirical evidence. Yet only time and careful astronomical observations will tell if rationality with regard to the matters involved was, in effect, the appropriate path to follow, or if presuppositions must endure.