Articles: Causal structure (2020), The Universe from Scratch (ArXiv 2005)
ArXiv: Renormalization Group Flow in CDT (2014); CDT and Cosmology (2017)
Video: Emergence of quantum spacetime from causal dynamical triangulations
Wikipedia: Causal Dynamical Triangulations (CDT)
Most recent email: Friday, 17 April 2021
Dear Prof. Dr. Renate Loll:
Is there any possibility that Causal Dynamical Triangulations (CDT) could be related to cubic close packing of equal spheres? Within the Wikipedia entry, I see that John Baez is among those who are editing that page. That’s excellent. That entry identifies just three people, you, Jan Ambjørn and Jerzy Jurkiewicz as its lead architects and then Fotini Markopoulou and Lee Smolin as people who’ve popularized it. I have come back to CDT because by its very nature, it must see the nothingness beyond-the-unseen and intuit, then articulate the very essence of a beginning point for space-time.
Causal dynamic triangulation describes a most fundamental process.
Yet, given our rather naive work since December 2011 (high school is high school) and our entirely idiosyncratic approach — going within the tetrahedron-octahedron the 112 base-2 steps to around the Planck scale then out the 90-steps to the current time — I also ask, “Could spacetime be fully 3-dimensional near the Planck scale?” In my stretched logic I see an infinitesimal sphere manifesting, sphere stacking and packing (from Kepler to Hales to Zong). CDT comes quickly but later. Possible or just silliness?
As usual I let scholars know when I quote them or use their image to go to this page or footnotes to discuss your work. Though still in process, you are back on today’s homepage here: https://81018.com/questions-1/ The footnotes and references are just now being developed. To attempt to facilitate discussions, I have asked a few questions of my visitors: https://81018.com/questions-1/#Questions I would be glad to send you another note with just those questions to facilitate a discussion. Thank you.
Third email: Tuesday, 18 June 2019
Yes, you are back up on our homepage today: https://81018.com/believed/
Essentially, inspired by Murray Gell-Mann, I thought you would want to know.
In light of the Ellis Physics on Edge harangue, virtually touching everyone who has been a leading thinker in the past 20 years, right to the final paragraph with Dawid-Rovelli, I repeat the John Wheeler 1986 statement within his article, “How Come the Quantum?” where he says, “Behind it all is surely an idea so simple, so beautiful, that when we grasp it — in a decade, a century, or a millennium — we will all say to each other, how could it have been otherwise?”
These simple numbers may bear him out: https://81018.com/chart/
Simple processes, like Euler’s equations and base-2 notation give us an entire range of unexplored numbers from the second notation to at least the 64th notation. That’s a science unto itself. Pure math, perhaps the string theorists could finally claim a home.
It is easy to write off simplicity, yet someday these numbers will be explored by the likes of somebody as informed as you are. Thank you.
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.
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.
[If we assume the very first instant of the universe is that which is defined by Planck Time and Planck Length and Planck Mass and Planck Charge and that there is a natural base-2 expansion, the 202nd notation includes the current day and time].
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?
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.
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 Causal Dynamical Triangulations (CDT): CDT and Cosmology:
• Non-renormalizability of perturbative quantum gravity
• FLRW paradigm: Physics Beyond the Standard Models of Particles, Cosmology and Astrophysic.
• 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
• Scale invariance and conformal symmetries