# Robert W. Spekkens

Perimeter Institute for Theoretical Physics

Waterloo, Ontario, Canada

**Articles ArXiv**:

*The Paradigm of Kinematics and Dynamics Must Yield to Causal Structure*

*citations*

**Google Scholar***Spekkens toy model*

First email: February 7, 2019 at 12:50 PM

Dear Prof. Dr. Robert Spekkens:

In 1977, I joined David Bohm and his doctoral candidates to become a point, a line, a triangle and a tetrahedron (a three-hour seminar). In 1979 Viki Weisskopf helped arranged for me to meet and have a private one-on-one with John Bell at CERN. In 1980 I sent five months studying one day per week with Olivier Costa de Beauregard and another day with J.P. Vigiers, both at the Institut Henri Poincaré. Then, with my head spinning, I returned home to Boston and decided it was time to make a living.

In 2011 I returned to all those questions in a rather peculiar way. My nephew asked me to introduce the Platonic solids to his high school geometry students (about 80 students). Several were fascinated by the most simple internal structure of the tetrahedron and octahedron. With deference to Zeno, we started going within the tetrahedron by dividing the edges by 2. In 45 steps within we were looking at particle physics (and billions of tetrahedrons and octahedrons). In 67 more steps, we were looking at the Planck Wall and began examining the Planck base units. What happens to all those tetra-octa structures as everything gets infinitesimally smaller? We concluded, “They must be increasingly shared by everything. It’s hypostatic.”

Deciding to start with the Planck units, we multiplied back up to the classroom object and continued the 90 additional steps to the approximate age and size of the universe. Of course, it is a natural inflation and at the 144th notation, we were just over one second. At the 197th notation we were at the large-structure formation of the universe. With the 202nd doubling (10.9 billion years), we are just 2.9 billion years into it.

Is it at all meaningful?

Thank you.

Most sincerely,

Bruce