Radboud University High Energy Physics

Institute for Mathematics, Astrophysics and Particle Physics

Nijmegen, Netherlands

**Articles**: What is space?

Arxiv: Renormalization CDT and Cosmology

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Video: Emergence of quantum spacetime from causal dynamical triangulations

Wikipedia: CDT

Most recent (second) email: Sunday, 27 January 2019

Perhaps the earlier email (below) was buried. Perhaps this base-2 model is just too absurd to acknowledge. I am just a simple guy following simple logic.

On one of our homepages I suggest that these are our primary assumptions:

1. The Planck base units of length, time, mass and charge describe a real reality.

2. The conceptual door to this infinitesimal universe is where all four Planck base units concresce (*grow together*, yet individuate) to create a stream of infinitesimal spheres. Though physical, length-time are well below thresholds of measurement, the progression of mass-charge units can be studied. These four units are, in some manner of speaking, the Janus-face of each other and of light.

3.Conceptually, sphere stacking becomes cubic-closest packing; tetrahedrons and octahedrons emerge. Doublings begin. **Our universe emerges**. Their numbers eventually begin to define things within our current scientific realities. This is a natural inflation. And, it’s not dark.

Since December 2011, I have been carrying on in this light, slowly, intentionally, but naively. I wish somebody of your stature and command of all the academic fields involved would take a moment and put a stop to this effort *if* it is sheer poppycock. Thank you ever so much.

Sincerely,

Bruce

First email 21 October 2018

Dear Prof. Dr. Renate Loll:

Thank you for all your work linked (just above), particularly your efforts to discern “…*a consistent theory of quantum gravity which describes the dynamical behaviour of spacetime geometry on all scales*.”

Our focus has been on the Planck scale. We believe there it has more to contribute than meets the eye.

Between the Planck scale and “CERN-scale of measurements,” there are 67 doublings (or notations or causal sets) of the Planck base units. Perhaps it might be better to start at the first doubling and to observe the logical possibilities. Essentially we’d be building a unified theory of mathematics, yet this one would be based more on John Wheeler’s sense of simplicity (I love his introduction of this article, *How Come the Quantum?*) than on Robert Langland’s programs. Langland’s needs the plancksphere that both Max Planck and Wheeler anticipated. Might other factors like Causal Dynamical Triangulations (CDT), Regge calculus, fractal structure, 2-D spacetime, and the flavors of the simplex be included in an appropriate build-out and within an appropriate doubling? I think that the emergence at the Planck base units, the simplest plancksphere may well account for what we know as dark matter and dark energy. I believe it’s a relatively simple calculation.

Among all the people to whom I write, I suspect you can debunk this concept most quickly; or, you may be surprised at its simplicity and possibility. Of course, the derivative, discrete nature of space-time is necessary and I think we would do well to redefine the infinite with mathematical terminology and anticipate a finite-infinite transformation possibly further defining the renormalization process..

To say the least, I would enjoy hearing from you.

Most sincerely,

Bruce

PS. I first became aware of your work through the Perimeter Institute’s 2016 conference, *Time in Cosmology**. * I write letters to focus my thoughts in conjunction with the thoughts and work of a person who appears to be vibrant, open, in love with life, and filled with questions.

**Follow-up** (from *CDT and Cosmology*):

• Non-renormalizability of perturbative quantum gravity

• FLRW paradigm: Physics Beyond the Standard Models of Particles, Cosmology and Astrophysics

• Imposing homogeneity and isotropy on spatial slices of constant time t.

• So-called “backreaction” effect of inhomogeneities on smaller scales on the dynamics of the universe on larger scales

• “…an explicit realization of a non-perturbative, Planckian quantum dynamics…”

**More Work to do** (further research):

• Path integrals and Gaussian fixed point. See Assaf Shomer’s on page 7: “The derivation of the path integral formula in quantum mechanics of a massive particle involves chopping up the quantum evolution into very short time intervals and inserting complete sets of states between them.”

• Doplicher S, Fredenhagen K, Roberts JE (1995) The quantum structure of spacetime at the planck scale and quantum fields. Communications in Mathematical Physics 172(1):187–220

• Doboszewski, Juliusz ( jdoboszewski(at)gmail.com ) and Niels Linnemann ( niels.linnemann(at)unige.ch ), 2017, * How not to establish the non-renormalizability of gravity*

• Scale invariance and conformal symmetries