What do you call the idea that each universes have wholly different natural laws? Instead of, let's say, all universes sharing some common laws, I am talking about the idea that all universes have wholly different laws that are in no way connected to the law of any universe. Is there a word for such a belief, are there other relevant terms used by philosophers?
Physicist Max Tegmark has discussed different multiverse ideas including the more philosophical mathematical universe hypothesis in which every mathematically describable universe is equally real, which would include ones with totally different mathematical laws governing them. He has also written articles where he suggests a taxonomy of different "levels" of multiverse ideas, with the mathematical universe hypothesis being a "level 4 multiverse', see links to his articles on the subject here.
It should be noted though that in the inflationary multiverse theory, which he labels as "level 2" (and which was proposed not by Tegmark but by the physicist Andrei Linde), although there is still the idea that the most fundamental laws of physics are the same, there is also the idea that things like the types of different particles and their fundamental properties (masses, charges etc.) along with the properties of the different fundamental forces of nature (which in our part of the universe consist of electromagnetism, the strong and weak nuclear forces, and gravity) may vary from one region of space to another. In the theory, this would be due to a process called spontaneous symmetry breaking which is theorized to have caused different regions to settle on different vacuum states after the big bang, with the vacuum state determining many of the properties of the particles and forces. Physicist Alan Guth, who first proposed the theory of a brief period of rapid cosmic inflation shortly after the Big Bang, says here that
As soon as we had quantum field theory we knew that the vacuum was not a simple state: It was a very complicated state with all kinds of quantum fluctuations going on. And there was no reason at all why the energy of the vacuum should turn out to be zero or small. ... There is also the possibility that the vacuum energy is not determined at all by the fundamental laws of physics, but instead it’s determined anthropically, using the idea of a multiverse. It’s quite possible in the context of string theory that there are many vacuum-like states, and all of them are stable enough that they could provide the underpinnings of a universe. And the one that we happen to find ourselves in is determined by random choice. One would imagine that the universe would inflate eternally through all the different possible vacua of string theory, with infinite amounts of space of every type of vacuum produced — eventually.
Likewise the physicist John Baez says here that
The notion that certain physical facts that appear as "laws" are actually part of the state of the univese has in fact been rather respectable since the application of spontaneous symmetry breaking to the Weinberg-Salam model of electroweak interactions, part of the standard model. (Again, being my usual cautious self, I must note that a crucial piece of evidence for this model, the Higgs boson, has not yet been seen.) The notion of spontaneous symmetry breaking has become quite popular in particle physics and is a key component of all current theories, such as GUTs or string theory, that attempt to model the messy heap of observed particles and interactions by some pristinely symmetrical Lagrangian. The spontaneous symmetry breaking would be expected to have occured shortly after the big bang, when it got cool enough, much as a hot piece of iron will randomly settle upon some direction of magnetization as its temperature fall below the Curie temperature.
Outside of physics, there is also the philosophical idea of modal realism proposed by David Lewis, which says that all logically possible worlds are equally real. This would naturally include worlds with different laws of nature, though I don't think philosophers have come up with any specific terminology to distinguish the idea that other possible worlds with the same laws of nature are equally real from the idea that other possible worlds with different laws are equally real.
Physicists call this the multiverse hypothesis. Implicit in it is the idea that each separate universe may exhibit different values for the fundamental constants of nature, at least in the sense that the hypothesis itself is silent on what values those constants must take.
The anthropic principle states that in order for human observers to exist in any given universe, its fundamental constants must exist within certain numerical ranges, and in certain ratios- otherwise life would not have had the opportunity to evolve.