Listening to Professor Leonard Susskind talk about string theory I was struck by an insight. As a thought experiment, imagine that you have the smallest possible black hole. What happens to it? Can it exist? It seems totally consistent with QM and string theory that one can "pop into existance" as a virtual particle, but just like one you manage to create in an impossibly big accelerator it would decay in Planck time. But what would it decay into? A photon with Planck mass? And that could split into any particle/anti-particle pair, each with 1/2 a Planck mass ...
I'm enough of a mathematician and a student of some of the fields of math related to this physics to understand the contours of current developments in theoretical physics, but not advanced enough to do any of the math myself. The understanding is that at these scales lots of surprising things happen. For example, most physicists agree that at high enough energies, presumably at or about (related to) the Planck scale, all of the forces (and particles?) are unified. There must be a particle, a smallest (length or time, largest mass or energy) possible particle. A fundamental string, if you will. Maybe it all emerges out of the fundamental vibrations of these strings?
Continuing with our thought experiment, what if the smallest possible black hole has exactly one Planck mass? Mathematically this might be a degenerate string that because it isn't "vibrating" and is therefore zero-dimensional. A point particle, or maybe even the point particle. Again, I know enough math to think up some good questions and have intuitions about these possibilities, but not enough to really explore them rigorously. Whatever the mass of the universe is in Planck units, how many Planck particles would it take to make up the dark matter fraction? If these particles do exist, how would they interact? How would they move? Seems to me that there would be a "string soup" around them that would likely make them slow. They'd have to be slow, they are massive, even a "high temperature" would imply low velocities compared to the same temperature of lightweight particles. I imagine that they would merge and split a lot so that you would have populations of small numbers of Planck particles. What are the interactions of a gas of these small Planck molecules? Seems like big black holes could radiate these things as they evaporate as described by Hawking. The rate is likely small, but just how small?
It is entirely possible that such a gas would interact only rarely with regular (barionic) matter. The interaction might be primarily gravitational as most other interactions are prevented by the basic theory. I'm guessing, but what if the gravitational effects only get big on near approaches or even collisions, but these would be rare. I could see one exploting a solar system without hitting anything much, but scattering the masses wildly.
So, if you are someone who can do this sort of math, please take a look at these questions and tell me what you think. Are the basic intuitions sound and worth exploring further? Are there any testable experiments that can be done? If you can compute what to look for, I'd bet we already have observation data from astro-physics to decide many theoretical questions and exclude some of the speculated implications of such a theory. You might even be able to find candidates for Planck particles drifting about the Milky Way. Maybe they interact with the many neutrinos streaming about, and not interacting much with anything else. That could lead to testable theory.