APPENDIX A: REFLECTIONS ON HISTORY
Strange as it might seem, I believe Einstein is the hero of this story. Einstein was the first (and possibly the last) researcher to understand that there was something seriously awry with GR—pathological exact solutions. Both the Friedmann metric tensor and the Schwarzschild metric tensor give rise to troubling infinities. Einstein tried to save general relativity by eliminating the most troubling pathology through the introduction of a cosmological constant (the opposite sign from what we call dark energy today). A few years later, Hubble’s observations (and their erroneous interpretation as a doppler shift) would wreck Einstein’s repair job and perversely tarnish his reputation.
Decades later (when it became clear that GR by itself could not agree with observations), there was a reversal of fortune. Two fudge factors (dark matter and dark energy) were added to physics so that we could pretend that GR is a correct theory—posthumous reputation restored.
There followed decades of research developing GRLCDM, and the pathologies became entrenched. Einstein and the researchers who followed cannot be blamed for following this sterile path. Their toolbox was nearly empty.
GR is based on nineteenth-century math and physics. Since GR is a geometric theory, it has more in common with the axiomatic theories of the ancient Greeks than with modern physics, e.g., the standard model of particle physics.
Since my teens, I have been very interested in attempts to eliminate the expanding universe pathology. As a freshman at Cal Tech (class of 1960), I attended a luncheon featuring Fred Hoyle. His steady-state universe model was an addition to the Einstein attempt—a (dubious) explanation for cosmological redshift. This attempt failed also for lack of a mechanism to steadily create the hydrogen required for stellar fusion. There were other ideas that failed, e.g., the unit of electric charge is a function of time. Without realization, my interest left a seed. Mechanisms (for control of nucleosynthesis and the draining of energy from photons in flight) would be necessary for a successful attempt.
Some years later as a graduate student at Harvard, my thesis advisor was Walter Gilbert. Walter did pioneer work on Higgs fields (considered to be a rabbit hole at that time). He also taught a course on Quantum Field Theory which I audited. That was the first time that I saw a self-supporting (scalar) field. At that time there was a research associate (several offices away from Walter) that I recognized from Cal Tech, Sydney Coleman. Sydney tutored me about the eight-fold way one summer, and I recognized that he would be important in the future.
At Harvard one was expected to do field theory using Green’s functions, but at Cal Tech one used Feynman’s path-integral method. Green’s functions are poorly suited for finding a successful attempt, but Feynman’s method could be applied to many different problems (including classical fields). Years later, [3] and [4] would provide tools for another path toward a successful attempt. My toolbox was no longer empty, but I was no longer interested in attempts. I went down a different rabbit hole.
I would return to the quest forty years later. During that period, I had developed an interest in the recurring ice ages. I found a chaos theory model that featured sudden transitions between lengthy stable climates (ice or no ice). Furthermore, propagating disturbances in the neutral Higgs field had been observed (Higgs bosons). Thus, the idea (of a self-supporting field pervading all of space and time could exist) was solidified. Sydney Coleman’s idea of sudden vacuum transitions was the final tool required. My toolbox was full, and section II in NCNG followed. The idea of relativity died on the day that the Higgs boson was observed.
I followed a path that was akin to a Forrest Gump adventure—at the right place at the right time. The final irony is that Einstein could have eliminated the pathologies only by destroying general and special relativity.