The laws of our universe are such that they enable creation of something out of nothing. QM with its fluctuations and GR with its singularity describe the world which appeared from nothing.
Not any set of possible laws allow it. These laws are math objects, but they allow creation of something from nothing (most laws don’t do it). So only a subset of all math universe is able to create things. It creates natural cutoff between all possible math objects—only rather simple laws allow such type creation.
I would illustrate it with following example: Newtonian laws are not describing appearing of matter from nothing. So while purely Newtonian universe is conceivable and mathematically possible, it doesn’t exist as it existence would contradict its own laws.
But there is another set of laws: QM+GR—it describes how something could appear from nothing, and so existence of something doesn’t contradict these laws.
I think that there are other possible combinations of laws which internally consistently explain how something could appear from nothing. But such set may be very small, as more complex laws results in more contradictions.
So we have very natural cutoff in math universe—lets name it Generational Universe hypothesis (GUH). It said that only those universes exist which laws describes how they appear from nothing and also don’t have contradictions. GUH has stronger restrictions than CUH.
Logical universe hypothesis (LUH), which said that if nothing exists than 1 doesn’t exist and if 1 doesn’t exist than 2 doesn’t exist is also similar GUH, as it describes the generation of math objects. But it doesn’t explain properties of our universe.
But I like the idea how you consider whether the laws themselves allow creation of a new universe. So, it seems like the Tegmark mathematical universe provides “templates” for universes, but only a subset of these “templates” will actually create a working instance.
I got the following ideas about the spark.
The laws of our universe are such that they enable creation of something out of nothing. QM with its fluctuations and GR with its singularity describe the world which appeared from nothing.
Not any set of possible laws allow it. These laws are math objects, but they allow creation of something from nothing (most laws don’t do it). So only a subset of all math universe is able to create things. It creates natural cutoff between all possible math objects—only rather simple laws allow such type creation.
I would illustrate it with following example: Newtonian laws are not describing appearing of matter from nothing. So while purely Newtonian universe is conceivable and mathematically possible, it doesn’t exist as it existence would contradict its own laws.
But there is another set of laws: QM+GR—it describes how something could appear from nothing, and so existence of something doesn’t contradict these laws.
I think that there are other possible combinations of laws which internally consistently explain how something could appear from nothing. But such set may be very small, as more complex laws results in more contradictions.
So we have very natural cutoff in math universe—lets name it Generational Universe hypothesis (GUH). It said that only those universes exist which laws describes how they appear from nothing and also don’t have contradictions. GUH has stronger restrictions than CUH.
Logical universe hypothesis (LUH), which said that if nothing exists than 1 doesn’t exist and if 1 doesn’t exist than 2 doesn’t exist is also similar GUH, as it describes the generation of math objects. But it doesn’t explain properties of our universe.
Still infinite probably.
But I like the idea how you consider whether the laws themselves allow creation of a new universe. So, it seems like the Tegmark mathematical universe provides “templates” for universes, but only a subset of these “templates” will actually create a working instance.