The multiple universes proposed by Tegmark are causally disconnected; nothing that happens in one of them can in principle influence what happens in the others. So we cannot do experiments with other universes. (This is different from quantum physics, where the parallel branches start connected, and for a short time we can interact with them.)
We could try to provide an indirect evidence. If we can make the theory more specific—what exactly counts as a possible universe, and what measure do the universes have—perhaps we could make statements in the form of “X % of universes have a property P”, and then compare it with the properties of our universe. For example, if we could list 100 properties that universes have with probability 50%, and then find out that our universe has approximately half of them, that could be considered a statistical evidence. Assuming that our universe is a typical one; but statistically speaking, that is what we should assume. Problem is, some of these properties may interfere with a possibility of life, so maybe it should instead be “X % of universes containing life have a property P”… which is easy to say, but I have no idea how to do it (how do you, looking at mathematical equations describing a universe, determine the probability or measure of life in such universe).
Note that this is connected with problems such as “why does anything exist, instead of nothing” and “why these laws of physics, instead of different laws”. Tegmark hypothesis provides a kind of explanation for both: our laws of physics are just the local rules of this universe, other universes have other rules; and there is nothing special about a universe existing, things that are in the same universe exist relatively to each other (and don’t exist relatively to things in other universes).
In some sense, this has similar aesthetics as the Einstein’s relativity—which may sound like a stupid argument, except that some scientific discoveries were indeed made this way: by assuming that more symetric laws are somehow better than the less symetric ones, or that rules using only local information are somehow better than the ones assuming some global state. Or more simply, if we take the progress of science as “there is nothing special about Earth, there are many planets” and “there is nothing special about this random situation, there are many parallel quantum worlds”, it feels like “there is nothing special about this universe existing, there are many alternative universes” continues the pattern.
Which doesn’t mean that everything is (equally likely) possible, just like the theory of relativity doesn’t mean that. I think that Tegmark hypothesis still assumes that more simple universes are in some sense more likely than the less simple ones (which explains why our universe is understandable, sometimes by relatively short equations, as opposed to having zillions of insanely complex rules), and a more serious theory built on this could possibly give us some specific numbers and equations. -- But again, the anthropic principle complicates this: maybe there are universes with laws of physics more simple than ours, but much less friendly to evolution of an intelligent life. This would be difficult to put into an equation.
See Mathematical universe hypothesis on Wikipedia.
The multiple universes proposed by Tegmark are causally disconnected; nothing that happens in one of them can in principle influence what happens in the others. So we cannot do experiments with other universes. (This is different from quantum physics, where the parallel branches start connected, and for a short time we can interact with them.)
We could try to provide an indirect evidence. If we can make the theory more specific—what exactly counts as a possible universe, and what measure do the universes have—perhaps we could make statements in the form of “X % of universes have a property P”, and then compare it with the properties of our universe. For example, if we could list 100 properties that universes have with probability 50%, and then find out that our universe has approximately half of them, that could be considered a statistical evidence. Assuming that our universe is a typical one; but statistically speaking, that is what we should assume. Problem is, some of these properties may interfere with a possibility of life, so maybe it should instead be “X % of universes containing life have a property P”… which is easy to say, but I have no idea how to do it (how do you, looking at mathematical equations describing a universe, determine the probability or measure of life in such universe).
Note that this is connected with problems such as “why does anything exist, instead of nothing” and “why these laws of physics, instead of different laws”. Tegmark hypothesis provides a kind of explanation for both: our laws of physics are just the local rules of this universe, other universes have other rules; and there is nothing special about a universe existing, things that are in the same universe exist relatively to each other (and don’t exist relatively to things in other universes).
In some sense, this has similar aesthetics as the Einstein’s relativity—which may sound like a stupid argument, except that some scientific discoveries were indeed made this way: by assuming that more symetric laws are somehow better than the less symetric ones, or that rules using only local information are somehow better than the ones assuming some global state. Or more simply, if we take the progress of science as “there is nothing special about Earth, there are many planets” and “there is nothing special about this random situation, there are many parallel quantum worlds”, it feels like “there is nothing special about this universe existing, there are many alternative universes” continues the pattern.
Which doesn’t mean that everything is (equally likely) possible, just like the theory of relativity doesn’t mean that. I think that Tegmark hypothesis still assumes that more simple universes are in some sense more likely than the less simple ones (which explains why our universe is understandable, sometimes by relatively short equations, as opposed to having zillions of insanely complex rules), and a more serious theory built on this could possibly give us some specific numbers and equations. -- But again, the anthropic principle complicates this: maybe there are universes with laws of physics more simple than ours, but much less friendly to evolution of an intelligent life. This would be difficult to put into an equation.