Allow me to address a rather large elephant in this room.
Rex. You have started two similar threads now and in both of these you attempt to use established science, mainly physics, to establish the theory that the universe that we perceive is almost certainly illusory. In short, you are trying to provide a scientific proof for solipsism. Would that be fair?
The problem is that the physics that you are hoping to use to establish your theory only apply in the universe is as we perceive it. In other words,
prove your theory and the proof is immediately invalid!
Solipsism belongs in the realm of speculation. By its very nature, it cannot be disproved scientifically. It is nothing but an interesting mental diversion - until we wake up one morning in a tank in the Matrix.
Allow me now to address the concept of the Bolzmann Brain a little more fully.
The idea (as I understand your usage of the concept) is that a completely random universe is capable of throwing up any combination of particles and that, given infinite time, some of these combinations will be conscious entities possessing what they believe to be memories and sensory input from an outside universe - however, the probability is almost infinitely more likely that this data will be false.
This is interesting as a mental exercise but I can see flaws on a lot of levels.
Firstly, it would require a universe capable of continuously producing arrangements of particles of the required complexity such that consciousness could occur within that arrangement.
Our universe (as understood by modern physics) is not capable of producing
all combinations of particles. For example, it is not capable of creating any arrangement in which there is less overall entropy than any previous arrangement. It is not certain, therefore, that it is capable of producing any such conscious entity
randomly - the principles of natural selection of self-replicating molecules leading to the required complexity are another matter entirely, as is the implanted memories coming from genuine sensory input.
Secondly, even if such entities could arise randomly in this universe, the energy in the universe is finite and its net entropy is constantly increasing. This means that there will come a point where no localised system of the required complexity can arise - hence, there is
not an infinite duration within which the universe can 'try out' many different random brains.
Thirdly, even should there be a huge amount of randomly created brains out there, with randomly created memories, the odds are (as you quite rightly claim) almost infinitely against any one of them having true knowledge of the nature of their universe. However, the odds are also almost infinitely against them having any coherent and consistent knowledge of their universe
at all, however true or false it might be! The only safe bet as to how such an internally consistent and coherent set of knowledge could find itself lodged in a brain is that that brain actually experienced those things by some method.
My first and second points make it almost infinitely unlikely that a universe such as ours could throw up a Boltzmann Brain. The theory would therefore require a different kind of universe altogether, hence returning to my earlier point - it is pointless using human physics to argue the case.
My third shows that, if we are living inside the Matrix, we should be seeing a lot more glitches!