Existing, non-existing and other universes

“According to modal realism, possible worlds really exist” writes Jennifer Fisher in his book On Philosophy of Logic (p. 91.). This approach is based on modal logic that interprets true and false statements in relation to possible worlds: E.g. necessity means that the statement “is true in all possible words” (Ibid, p. 75.) and our actual world is nothing more than a world which was chosen from the set of other, existing ones. I don’t accept modal realism’s logic (after all, possibility isn’t equal to existence), but it is interesting from our point of view that the logic of modal worlds is similar to the logic of classic multiverse hypothesis that assumes the existence infinitely many words and this similarity shall lead us to a strange type of imaginable universes.
Max Tegmark interprets the multiverse as the manifestation of every mathematically possible world. It is a form of mathematical Platonism, and the main thesis is that on the one hand, anything is possible mathematically exists in reality. On the other hand, everything is governed by the rules of mathematics. “Mathematical” means in this case that every combination of different sets of physical laws and constants, or even different equations exist. In other words: according to Tegmark, all words can be described by mathematics and every imaginable combination is manifested in a really existing world. The core of Tegmark’s concept is that mathematics is equal to physics in a certain sense, since it describes the world ruled by physical laws.
But it is not sure that even our universe can be described perfectly by mathematics and perhaps only our belief suggests that every natural phenomenon is controlled by either deterministic, or probability or evolutionary laws. Inter alia, it is possible that the Great Unified Theory (GUT) doesn’t exist, since there is no mathematics to describe every connection. It is perhaps only about our inability to give a coherent description about reality, since our tools (including our minds, mathematics and logic) aren’t appropriate for it.
Or, it is imaginable that there are universes that cannot be described by mathematics at all: after all, mathematics is based on the presumption of the conservation of some rules. Thus, it is not necessarily well-founded to state that every universe is mathematical in nature. So we can imagine whole universes (albeit they wouldn’t be biofil) without mathematically interpretable natural laws. In other words: although they exist, they cannot be described by one or other mathematical form of physical laws.
Traditionally, we distinguish existing and non-existing worlds and the main sin of modal realism is that it intermixes these two categories. Now we can introduce a third kind of universes which differ from both the “existing” and “non-existing” ones and since per definitionem it is impossible to give a scientific description about their features, they don’t belong to the realm of physics.

The nature of the natural laws

Although both the existence and the nature of physical laws usually are taken for granted, it is worth examining these ideas’ origin, since it can influence even the approach of today’s science.
Aristotle developed a rather complicated idea about the causes (ending with a kind of “Formal Cause” – which “causes” the form). His “Final Cause” became the modern laws of nature and his “Efficient Cause” is close to modern cause (Barrow: World within World, p. 53). So following Aristotle’s logic we make a distinction between the laws and those phenomena they affect. But it is not surely a necessary distinction between causes and their subjects. The fundamental question is whether the laws exist in a certain sense or they are only practical descriptions of reality. According to Lee Smolin, supposing a kind of cosmic evolution and the existence of baby universes that are born with slightly modified natural laws than of their parent universe's, this “evolving laws seems to be a breakdown of the distinction between the state of a system and the law that evolves it.”
This hypothesis makes possible to imagine some different scenarios between the laws and those subjects that are affected by them.
1. Obviously, we can accept the traditional laws vs systems differentiation.
2. But it is more exciting to suppose that the formation of a baby universe means the formation (slightly) different laws. It can be happened three different ways.

• The first one means that the law formation is restricted to the moment of creation (whatever it means). After the Big Bang we have a certain amount of matter, energy etc. and it won’t change. Similarly, the laws are “finished” as well and they won’t change. On the other hand, Smolin supposes that different universes can be determined by different laws.
• But why to restrict the changes of natural laws for a very short period of time? A second solution proposes a longer, even continuous evolutionary process where the forming laws and the physical environment are in continuous interaction in the course of the universe’s history. According to this model, not only the initial laws of a new universe are different from its parent’s laws, but the changes can be influenced by some events in the history of the universe and slightly different initial conditions would result very different laws later.
• To make the story even stranger, there is the problem of the saltation hypothesis. In evolutionary theory not accepted to suppose that biological evolution produces its effects via large and sudden changes, but cosmology isn’t about earthly ecosystems’ biology. The laws of our Universe seems to be fixed today, but it is imaginable that this idle period when our physical laws are static is only a transitional state, and then a sudden saltation would happen in the future and the nature of the laws will radically change.