Physics is an unusual science. In most of the rest of science, one is exposed to explanations that make intuitive sense to the initiate. In contrast, understanding the foundations of physics requires a certain suspension of disbelief. Most of the standard heresies of physics come, one way or another, from refusing to suspend disbelief.
When I was a young man, I suspended disbelief and I learned physics. I was a physics graduate student at the University of California at Irvine. I was in the PhD program. I passed the comprehensive examination, and for this the university awarded me the MS in Physics. I didn’t find a thesis adviser I wanted to work for so I left to make a living doing engineering. But I left believing in the foundations of physics. I was curious to see how the remaining problems would be solved, but I was confident in the foundations.
When I was a grad student in physics, I briefly considered doing work in lattice gauge theory. In this theory, one replaces the continuum of spacetime with a discrete (and finite) lattice of points. This is intended as an approximation of spacetime. It can be shown that the limit as the lattice size goes to zero gives the same results as a continuous spacetime calculation.
Our understanding of spacetime can come only from observations of particles; we cannot observe spacetime itself. Even Einstein used light, that is, photons, to define spacetime. So lattice gauge theory (and perhaps an obvious generalization of the infinite resistor array problem) got me to wondering whether it was possible that spacetime could be built from a discrete lattice. Not a lattice with a constantly changing topology (as in loop quantum gravity, but a fixed lattice that would only appear to have translational, rotational and Lorentz symmetries at low energies (large distances). If such a lattice existed, it would be in contradiction to the philosophy of Einstein’s special relativity. But the same critique could be made of lattice gauge theory. At least as a fig leaf, one could suppose that such a lattice were only a computational convenience. And lattice models of the particles do appear in the literature from time to time. For example, see hep-th/0006212 and citations.
At the time I was in physics grad school, string theory was only just getting started. So I was not exposed to the possibility of large numbers of hidden dimensions, but in one class, a professor, probably Dennis Silverman did give one lecture on the Kaluza-Klein method of unifying gravity with electricity and magnetism. In this form, one adds a small, curled up, spatial dimension to the usual Minkowski spacetime. The result can be split into Einstein’s gravitation equations plus electricity and magnetism.
So I had these sorts of things in mind. One day I realized that if I started with Newtonian space-time, that is, three Cartesian spatial coordinates and one time coordinate, and added a single small, curled up, spatial dimension as is done in Kaluza-Klein, I would end up with a geometry that would naturally support special relativity. Particles moving in these four dimensions with speed c would have motion similar to particles moving in Minkowski spacetime. The proper time experienced by a particle would be proportional to the number of circuits made in the hidden dimension. I wrote up the details showing how this would give classical special relativity in a short paper.
It was only by being away from physics for nearly 20 years that I could have sinned so badly. I figured that with a few weeks of work I could knit this idea into the rest of physics and would quickly come up with some new and interesting results in quantum mechanics. Of course nothing of the sort happened.
I had forgotten completely how the foundations of physics are so carefully woven together, and how long the strands are. It is impossible to make a small change to one part of the foundations of physics without that change propagating into all the other assumptions built into all the other foundation stones. I would never have tried this scheme if I had known then what I knew when I was a grad student. So the Kaluza-Klein version of Newtonian spacetime was only my first heresy. To continue exploring this idea required that I reconfigure more and more of what I had once believed to be theory settled by careful experiment that as in no need of correction or modification.
The first problem came up when I realized that waves in this version of spacetime would interfere with themselves around the hidden dimension. This would cause speeds to be quantized. Okay, I said to myself, it is impossible to experimentally measure speeds exactly so this is possible. But this led to further problems the nature of which escapes me at the moment. Perhaps it was that stationary particles would have to have the shortest wave lengths in the hidden dimension, and therefore have the highest energies.
So I concluded that while speeds would be quantized, only particles with the smallest possible speeds in the hidden dimension (and therefore the maximum possible speed in the visible dimensions) would be possible. This implies that the visible particles must all travel at the same speed, c, or perhaps one infinitesimal notch below c. And this fits in better with what is known from elementary particles because the chiral wave states seem to be more fundamental than the particles, and they are massless and so travel at speed c.
But this was only the beginning of my many heresies. About a year ago, I wrote down all the things I now believe about physics that are incompatible with the standard way of looking at things. I came up with a list of more than a dozen. It is possible to have a few heretical beliefs and still get along with the rest of the physics community. But when you end up with as many as I have, and when they are as deep in the foundations as my beliefs are, it becomes almost impossible to communicate with physicists. I hardly try any more. Instead, I simply try to better understand the consequences of the assumptions that I prefer.
Every now and then I chance upon a simple equation that can be understood outside of my heretical beliefs. And it might happen that such an equation is similar to something that someone else has worked upon from inside the physics establishment. In that case, I can send them a letter with the simple equation on it, and they may see that I have written something that extends what they have found. As I get closer to an understanding of mass I am less and less inclined to go to these efforts. Why should I look for assistance when I am close to the goal? But a year ago I sent a letter to Yoshio Koide pointing out that his formula for the charged lepton masses could be extended to the neutrinos by changing the sign of the mass of the lightest lepton. The paper I wrote up describing how I found the formula (with most of the heresy removed) is here, Yoshio Koide’s attempt to obtain the new formula from standard physics is written up as hep-ph/0605074 and in hep-ph/0607.2534, also mentioned in Mohapatra and Smirnov’s paper Neutrino Mass and New Physics, Ann.Rev.Nucl.Part.Sci. 56 (2006) 569-628.