On Saturday, December 22, 2018 at 8:33:54 PM UTC-6, Brent wrote:
> On 12/22/2018 12:04 PM, Philip Thrift wrote:
> https://www.eurekalert.org/pub_releases/2018-12/lsu-be122018.php
> Theoretical physicists developed a theory called loop quantum gravity in 
> the 1990s that marries the laws of microscopic physics, or quantum 
> mechanics, with gravity, which explains the dynamics of space and time. 
> Ashtekar, Olmedos and Singh's new equations describe black holes in loop 
> quantum gravity and showed that black hole singularity does not exist.
> "In Einstein's theory, space-time is a fabric that can be divided as small 
> as we want. This is essentially the cause of the singularity where the 
> gravitational field becomes infinite. In loop quantum gravity, the fabric 
> of space-time has a *tile-like structure*, which cannot be divided beyond 
> the smallest tile. My colleagues and I have shown that this is the case 
> inside black holes and therefore there is no singularity," Singh said.
> "These tile-like units of geometry--called 'quantum excitations'-- which 
> resolve the singularity problem are orders of magnitude smaller than we can 
> detect with today's technology, but we have precise mathematical equations 
> that predict their behavior," said Ashtekar, who is one of the founding 
> fathers of loop quantum gravity.
> But is this consistent with https://arxiv.org/abs/1109.5191v2 which 
> showed spacetime to be smooth down to 1/525 of the Planck length?
> Brent
> "At LSU, we have been developing state-of-the-art computational techniques 
> to extract physical consequences of these physical equations using 
> supercomputers, bringing us closer to reliably test quantum gravity," Singh 
> said.
> Einstein's theory fails not only at the center of the black holes but also 
> to explain how the universe was created from the Big Bang singularity. 
> Therefore, a decade ago, Ashtekar, Singh and collaborators began to extend 
> physics beyond the Big Bang and make new predictions using loop quantum 
> gravity. Using the mathematical equations and computational techniques of 
> loop quantum gravity, they showed that the Big Bang is replaced by the "Big 
> Bounce."
> [ a short lecture on LQG: https://www.youtube.com/watch?v=QMpkFde3euA ]
> - pt

This question of measurements supporting "smoothness" of space vs. the 
"tile"-based model of LQG occurs to me too. The LQG people must have 
addressed it, one would think.

My idea is that the tiles (as they are called above) of LQG would need to 
have a fractal* nature, so LQG would somehow combine with scale relativity 
/ fractal spacetime [ https://en.wikipedia.org/wiki/Scale_relativity ].

What else could it be?

*This paper introduces a fractal partition class defined over a unit 
wrapped space. The cells of a fractal partition have self-similarity 
property and can be used as a set of tiles that can tile R<sup>n</sup> 
space periodically or quasi-periodically with non-uniform tiling density. 
An algorithm for generating set of fractal cells using Voronoi diagram 
computation is proposed with several applications in computer graphics and 
computational chemistry. *

- pt

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