Looks like there are some people working on the “all quantized universes exist” angle:
Jürgen Schmidhuber’s Computable Universes page.
I just read “The Cosmic Landscape” by Leonard Susskind. Susskind believes that the small magnitude of the cosmological constant (119 zero digits after the decimal) compared to a randomly generated constant (which is likely to be close to to unity) leads to a multiple universe explanation. The actual choice of universe in which we live is constrained (and enabled) by the Anthropic Principle (AP). We exist in a habitable universe (where the constant is within a range consistent with life). Other universes exist in the Multiverse where things are not fine tuned, but nobody is there to notice.
Susskind further makes a distinction between the Landscape (set of possible universes) and Multiverse (set of actual universes). Universes can actually be born from other ones through quantum fluctuations and it seems that Susskind thinks that only those Universes born from others are “real”.
However, that seems arbitrary. What is the reason that only some of the universes in the Landscape exist, assuming they are all consistent? There is no “prime motive”, so no set of universes is preferred over any other set. Just because a Universe can arise from another, doesn’t seem to give its existence additional justification. For example, assume Universe A can give rise to B and C. Then on the other hand we have D that can give rise to E and F. If we say B exists (is in the multiverse) and E does not (in the Landscape but not in the Multiverse), what is the reason for that?
Additionally, Susskind speaks of the Landscape as being created by varying parameters of String Theory. The question here is what are the limits? All theories can be embelished or modified with additional rules and constructs. Different Landscapes can be created. Why choose one Landscape over another?
I would like to propose an extension to these ideas. Here is what I propose:
Note that a mathematical construct is not just what humans can conceive of – it’s the class of all possible ones.
I found a few other mentions of similar ideas. The canonical references seems to be Max Tegmark:
I believe a couple of additional features apply that I haven’t seen in other people’s theories: 1. randomness is a given at the bottom, because all perturbation exist, and universe must smooth it out 2. the measure problem means that the universe must be quantized and finite.