This new paper by Fay Dowker is a wonderful introduction to the whole field of causal sets, how they may said to approximate GR, how to make them covariant, a new approach to quantizing, the current state of play, and challenges remaining from a frequent contributer to the field.

All in carefully reasoned English, hardly an equation is sight. Refreshing!

I' ve gotten halfway through the paper. I am not ready to buy the idea that spacetime can be represented as a Poisson distribution in a volume. Seems to me volume and space are roughly equivalent, so spacetime distributed over space should just yield time.....which is not, I think, the intended consequence.

I did like the idea of sprinkling to obtain a Poisson distribution, and Dowker's assertion that the Poisson distribution is the best representation of spacetime based on there being no preferred direction in a random (Poisson) distribution, as opposed to some kind of lattice structure, gave me something to think about.

I am wondering if this has to do with background independence, an idea I am still trying to connect. Can I say that "background independence" and "no preferred direction" are equivalent?

Then I wonder if the thirty degree anomalie in CMB is thought of as evidence of a cosmic background structure? And if there is such a universal background structure, what does this mean for background independence of theories at the microscopic scale?

I'll read the rest of the paper and be back here, good willing, later.

No, "no preferred direction" is called isotropy, Greek for "equal turning"; it's just one possible property of spacetime. Background independence means spacetime engages in give and take with matter. The matter acts on spacetime, and spacetime, in reacting to that, acts back on the matter.

By diagramming the finite causal sets (using arrow diagrams,) and by starting with the simplest diagram (one arrow,) one soon comes to the diagrams that have 3 arrows. One of these is the "time triangle," which has two separable paths with common startpoint and common endpoint. One path has a step-count of 2, the other path a step-count of 1. Since the two paths transpire in the same time interval, a relative frequency ratio is inherent in the time triangle formation. This is an energy ratio, in accord with Planck's E=hf. Its reciprocal is a wavelength ratio, comparing the durations of causal links from the two respective paths of the triangle. We obtain frequency and wavelength numbers without waves. Each causal link is thus a quantum of energy. This account of the "origin of mass" inspires further diagram constructions, until both the electron and the proton have been constructed. The mass-ratio of these two is then calculated to be 1:1836, which is the experimentally determined value. In short, all of physics, including the 4-D manifold, is constructible from causal sets.
Google my name to find the diagrams online. - Carey R. Carlson