Statistical Relativity Elections
A mathematical physics text-book on Relativity theory by a nearly fifty-year amateur student. By far, my most specialist and difficult work. Not that the mathematics is advanced by professional standards but that the original, or unorthodox, ideas are unfamiliar and therefore inaccessible to layman and expert alike. More
Physics, the romance of how the world works (with perhaps a clue to why we are here) interpreted by a long-time reader of popular expositions, without benefit of class instructions or personal tuition. (It was left to my intuition.) Like Don Quixote, whose head was turned by reading too many romances, I developed unconventional ideas. I never thought that I would write a book on physics. I was well aware, from the start, that the professionals are authoritative on conventional physics, which I generally accept.
My background is in social science. I did not take much to the presentation of the social part of the course, as to the lesser part, the science, especially the statistics, which is the approach I take to both relativity theory and electoral method. These two subjects have received my amateur attentions thru-out a working life-time (and beyond).
Basically, on one quite simple point do I disagree with physics tradition, the Michelson-Morley calculation, contradicted, by the famous experiment -- and by my own use of a different average.
The calculation was patched-up with the so-called Fitzgerald-Lorentz contraction (read: correction) factor or gamma factor. (Corrections are inevitable. I must have made scores of errors in my own working. This book is open to corrections, criticisms and comments. Only the caldera chapter has been independently checked.)
To replace the ad hoc gamma factor, I invoked the principle of Least Action. All local reference frames in high energy physics are unprivileged. They amount to a random distribution, which forms the graphical area under the path of least action as a normal curve.
Special relativity is based on a symmetry principle (so-called rotational symmetry of the Minkowski Interval) that there is no privileged view-point of events. Local observations, of a given event, take particular measures of space and time, but ultimately they are the same metric of a unified space-time.
A theme, by this amateur or naive physicist, is to extend the symmetry principle. By adding a damping factor to the Interval, and comparing the new result with the old, magnitude symmetry is added to rotational symmetry, to create vector symmetry, with an extension to its corresponding conservation law, from angular momentum to vector momentum.
Another extension, from the Michelson-Morley experiment (MMX), for instance, to the LISA project, is a sine-generalised Interval to non-perpendicular frames of reference.
The Minkowski Interval correctly predicts the Michelson-Morley experiment result of equal times, taken by the perpendicular light beams. It is conjectured that this equality of times is formally similar to the Einstein Equivalence principle of the equality of masses, gravitational and inertial. Hence, he Minkowski Michelson-Morley clock of the universe (M3) only shows absolute time in perpendicular frames of reference. Likewise for absolute mass.
In special relativity, kinematics, as of time, and dynamics, as of mass, are formally the same. Hence, the sine-generalised (All-angles) Interval should apply to an Extra Einstein Equivalence principle (E3), where non-perpendicular reference frames do not give equality of gravitational and inertial masses, just as they do not give equality of times.
A comprehensive comparison between special relativity and electoral method is enabled, once two-dimensional voting is introduced (FAB STV 2-D), because then both sciences, Physics and Electics, are on the same footing of using complex variables. A formal similarity of kinematics and dynamics, in special relativity, can be elucidated by a formal similarity between voting with ones hands, on the ballot paper, and voting with ones feet, by moving between electoral districts or constituencies.