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.
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