Consequences for Physics

Is the entire past and future history of our universe describable by a finite sequence of bits, just like a movie stored on a compact disc, or a never ending evolution of a virtual reality determined by a finite algorithm, such as in Example 2.2? Contrary to a widely spread misunderstanding, quantum physics, quantum computation (e.g., [3]) and Heisenberg's uncertainty principle do not rule this out [35]. In absence of contrarian evidence we might assume our universe is formally describable indeed, or at least sampled from a formally describable distribution -- if this assumption is false, then our world will forever remain beyond formal understanding.

As obvious from equation (13), the future of some observer evolving within such a universe depends on this prior distribution. More or less general notions of TM-based describability put forward above lead to more or less dominant priors such as $P^G$ on formally describable universes, $P^E$ and $mu^E$ on enumerable universes, $P^M$ and $mu^M$ and recursive priors on monotonically computable universes. Generally speaking, the theorems above show that any future corresponding to a history without any short description (given the appropriate TM type) is necessarily unlikely. To a certain extent, this justifies ``Occam's razor'' (e.g., [4]) which expresses the ancient preference of simple solutions over complex ones. A more detailed analysis can be found elsewhere [36].