Hey guys,
Please make sure to glance at https://community.wolfram.com/groups/-/m/t/2029731 project first. It looks for singularities in WMs and especially the ones that persist for at least 20 steps. Some very useful functions are used that look for the presence of singularities, filter WMs based on that criteria and also look at dimensionality of the system. Their conclusions reflect a disappointment of not finding a change in dimensions as they assume a Schwartz type of BH would have.
Before I dive into physics, let me add that I ran their 21 surviving BH models for a greater number of steps as I summarize in the attached picture (I tried to do 50 steps but some proved too computationally intensive while others I was able to run for 100s of iterations).
Four more models lost their singularities (bringing the total down to 17). Here are the questions we can still answer by looking further into this:
• Which remaining models BHs survive after 100, 200, 300 etc. steps?
• Can models reacquire singularities after losing them?
• If so, we need to map durations of BHs lifetimes and frequency of occurrence.
• Write new function that can identify # of singularities in a given system as well as whether any of them are nested (BH inside another BH).
Now for the physics…
Given a tiny # of steps that can be run on these models we are probably looking at vacuum fluctuations on a very small scale. That makes it unlikely to observe any BHs form via gravitational collapse (not enough steps).
What are these singularities then? To me, they look like topological BHs that have nothing to do with gravitational collapse and whose stability depends on the rewriting rules alone. Now imagine that our expanding universe forms these sub-plank BHs that leech some of the spacetime into pocket universes. WMs show that nothing special happens in those regions and that they expand same as everywhere else.
Our own vacuum can have a specific signature of these topological BHs. Average density and duration can not only affect our cosmological constant but also be a dark matter candidate. Moreover, one could try and match one of the WMs to our own universe based on these criteria.
Sooner or later, certain interesting WMs will need to be placed on the server cloud with large number of steps computed and stored to be explored by the community.
There is much more to discuss here but it’s probably a good start.
Legend: WM = Wolfram Model | BH = Black Hole | sub-plank = reference to Steven’s belief that these “atoms of space” are much smaller thank plank scale