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Suppose two universes with the same amount of mass-energy and evolving according to the same natural laws, but having different initial conditions. Is the set of states that are reachable by the evolution of the first universe always identical to the set of states that are reachable by the evolution of the second universe? Note that I am not assuming that the universes are deterministic, but that they evolve indeterministically according to the known natural laws.

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Is the set of states that are reachable by the evolution of the first universe always identical to the set of states that are reachable by the evolution of the second universe?

Not necessarily. For example, if one of the physical laws is "magnetic monopoles are never created or destroyed" then universe A with an initial state that includes one or more magnetic monopoles will evolve through a different set of states from universe B with an initial state that includes no magnetic monopoles. You can always tell (in principle) whether you are in universe A or universe B by counting the magnetic monopoles in the universe.

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  • $\begingroup$ Thank you for your response. It was helpful. Can you give me other examples that are actual and not merely hypothetical? $\endgroup$ May 1, 2022 at 9:15
  • $\begingroup$ @MohammadAbu-Zidan No. Since we only have access to one actual universe and one actual history for that universe, any example involving an alternative universe or history must be hypothetical. $\endgroup$
    – gandalf61
    May 1, 2022 at 11:46
  • $\begingroup$ I meant to say that magnetic monopoles are hypothetical, and therefore that the law "magnetic monopoles are never created or destroyed" might not be relevant to the universe as we know it. I am instead asking for an example of a well-established law that allows us to infer that two equally massive universes with different initial conditions must have different sets of reachable states. I am actually not sure if magnetic monopoles are physically/logically possible. Knowing this would require some type of empirical evidence or a scientific argument in the form of a sound analogy. $\endgroup$ May 1, 2022 at 13:09
  • $\begingroup$ @MohammadAbu-Zidan Okay, if you don't like magnetic monopoles, suppose universe A starts with more matter than anti-matter, and universe B starts with more anti-matter than matter. $\endgroup$
    – gandalf61
    May 1, 2022 at 15:22
  • $\begingroup$ This is a wonderful example. Thank you. $\endgroup$ May 1, 2022 at 16:56

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