Ebook: Once upon a time there was a pendulum

This book is the result of a search that began in 1968, when a very old universal atlas fell in my hands. The first pages caught my attention, for they described the knowledge about the universe at the beginning of the 20th century, how the 19th century idea of the existence of the ether had been discarded by the Michelson-Morley experiment and the theory of relativity. I thought the idea of the ether was beautiful, some fixed spacetime structure to hold, sort of platonic, and I got convinced that there had to be a way to make the existence of the ether compatible with relativity. Somehow, somehow, perhaps making the structure flexible…, its flexibility conspiring to make the speed of light an invariant and to allow relativity.
In the following decades, whenever I found a lattice -a honeycomb, the structure of graphite, cubes in playgrounds- I wondered whether that might be the structure of the ether.
The answer came as a surprise in 2009, after having spent many months playing with the geometry that appears in Escher´s Waterfall, modifying it so as to turn that impossible fascinating object into something possible.
When I realized I had found a special geometry I tried to contrive it to match the ideas described in Sean Carroll´s From Eternity to Here, but the fit was not perfect. Then I turned to the very small, to David Griffiths´ Introduction to Elementary Particles and, to my astonishment, everything seemed to find its right place in the structure, which is not the ether but the structure of the Higgs field, spacetime quantified.
Geometry beyond the standard model and relativity:
The first part of the book describes how the main questions in particle physics fit in this proposed geometric structure for the ether, built from a modification of that structure that appears in Escher´s Waterfall. There is a geometric representation of quarks, leptons, the four types of gauge bosons, the weak isospin and the geometry and algebra of many interactions and decays. It is explained how to calculate the values of the Weinberg angle and the Cabibbo angle, the parameters in the CKM matrix. Simple formulas for the calculation of the masses of the six quarks are also given.
After that a geometric representation of CPT symmetry is described in the structure to give accommodation to:
• Special relativity.
• The tensors of general relativity.
• The geometry of the measurement problem.
• The geometry of the uncertainty principle.
• The second law of thermodynamics.
• Neutrino oscillations and the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix.
• The gravitational constant, the dielectric constant, Boltzmann constant and Planck´s constant.
• The process of formation of a black hole.
• The four fundamental interactions: gravitation, electromagnetism, the strong interaction and the weak interaction.
• All the free parameters of the standard model find their precise values in the proposed structure. The fundamental constants -the gravitational constant, Boltzmann constant, Planck´s constant and the vacuum permittivity- are related by the golden ratio.
The primes:
The link between the distribution of prime numbers and symmetry.
I had always thought that there was a hidden rule governing the distribution of the prime numbers among the natural numbers. There is a very simple program that controls that distribution, it is described in the second part of the book.
Does this idea and the geometric structure described in the first part of the book mean that we live in a gigantic computing machine? I think so. It is not boring, though.