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In the theory of multi-verses, we can imagine countless other universes where the constants of nature, including the amount of dark energy in a volume of space and possibly even shapes of hidden dimensions vary from one universe to another. Is there sound reasoning to believe that the mathematics of nature (or laws of nature) would be the same in other universes?

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  • $\begingroup$ Similar question here: physics.stackexchange.com/questions/68987/… Also, an interesting answer here: quora.com/… $\endgroup$ – userLTK Feb 29 '16 at 4:24
  • $\begingroup$ Jack : there's no sound reasoning to believe in the theory of multi-verses. Particularly since the constants of nature aren't constant. See NIST, the fine structure constant is a "running" constant. Which means it isn't constant. $\endgroup$ – John Duffield Feb 29 '16 at 13:51
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    $\begingroup$ the theory of multi-verses? $\endgroup$ – user1569 Feb 29 '16 at 14:48
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    $\begingroup$ I didn't check physics stack exchange. userLTK is right (almost the same question). The answer given has a link to a fun paper describing different "Levels" of multiverses arxiv.org/pdf/0905.1283.pdf . Level IV would have different mathematics. In fact the argument could be made that "all possible" Laws of Nature exist in other universes. I'm afraid my question is a little too philosophical. $\endgroup$ – Jack R. Woods Feb 29 '16 at 16:54
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First of all it has to be stated that it is difficult to have a scientific discussion about multiple universes. The problem with multiple universes is that it can be logically deducted from assumptions and hypotheses, but not tested nor empirically verified. This makes discussions around this topic, like string theory, highly "religious".

There are different multiverse theories coming from cosmology, physics and philosophy. One of the theories comes from the cosmological theory of cosmic inflation. Cosmic inflation states that there are always fluctuations on the microscopic level and this results in energy waves that can form into matter and anti-matter pairs. The cosmic inflation now states that at the beginning of our universe there was a cosmological constant or a big vacuum that is by nature unstable and caused the microscopic fluctuations to happen on a cosmic size and thus resulted in a rapid expansion of the early universe. This cosmic inflation is a variation of the (hot) big bang theory, that explains a number of observations in the universe that are not explained by the (hot) big bang theory. What it doesn't explain is that if I have an energy fluctuation at microscopic level, it can happen that this energy wave splits into two matter pairs or an anti-matter/matter pair. Later these pairs annihilate each other and what has happened at microscopic level evens out on macroscopic level. However, when particles appear at microscopic level, what needs to happen to let these particles exist for a longer time to have stars evolve from this matter.

Now back to the multiple universes. The going theory now is that if such a thing can happen to our universe, such a thing can happen in the endless vastness that contains our universe and multiple universes can start and exists next to each other. These multiple universes might also explain that when I have a cosmic fluctuation, I have two universes that come into existence. One with the matter and one with the nati-matter. Bear in mind!!!! These are all philosophical hypotheses and none of it can be verified, falsified or empirically tested.

If I now have made it logically possible to have multiple universes coming from different cosmic fluctuations, I can now have different universes. For instance, I can have for each matter universe a corresponding anti-matter universe to get the energy balance evened out. Now if I have several universes with each different compositions, I can also have universes where, at least, the laws of nature apply differently. In a universe without dark matter, laws of physics apply differently. Whether the "laws of nature" are totally different in other universes, is difficult to scientifically proof. Especially with theories that are build on our laws of nature.

When you think we're already on thin ice here, philosophers can make it even more unreal. If I have cosmic fluctuations that can happen under different circumstances, which result in universes with different compositions that then have a different application of the laws of nature, I can equally well argue that there will be universes where certain laws of nature don't exists, while there are some particles that don't exist in that universe.

So, to answer your question briefly, there are theories that say there are other universes that have different laws of nature. However, multiverse theories are highly speculative and are difficult to proof. So, whether these theories are right, we'll probably will never know.

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