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For example, I often hear that life could not develop in a universe where the fundamental constants were even slightly changed, or where certain physical laws were different. But if we're dealing with an entirely different universe with different "rules", then why does life have to continue to follow "our" rules? Once you start making new rules / laws of physics and changing things around, then it appears that all bets are off and there's nothing stopping you from changing something else, including how life itself works. Why is it still meaningful to discuss what is "impossible" in alternate universes like these?

This is different from asking questions like "what if 2 + 2 = 5?", which obviously doesn't make sense because it violates our inherent reasoning about mathematics and logic itself, and thus would be impossible in any universe, not just ours. But a statement such as "life exists and the speed of light is only 10 miles per hour" is, on the surface, something that could hypothetically exist in some alternate universe by the very fact that I can make this statement and imagine it as being so, even though it obviously is not true of our reality.

Are there examples of logical impossibilities that, on the surface, seem like they could be possible in another universe because we can "imagine" it as being so, but in fact would violate logic in a non-obvious way? (I suppose one example might be the Halting Problem, which is a logical impossibility that wasn't discovered until Alan Turing's proof, and, until one reads and understands the proof for it, sounds perfectly reasonable to imagine in some alternate reality.)

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    Regarding "the speed of light is only 10 miles per hour," this may be of interest: physics.stackexchange.com/q/78684/195139
    – Sandejo
    Dec 19 '20 at 2:42
  • If a weight balance rounds to the nearest integer, and you put two objects weighing 2.4kg each one, 2+2=5. You might think that the problem is the balance. In such case, think that pi is neither 3.14 nor 3.14159265358989, so you've always been wrong about pi and all numbers. Every number we know is always an approximation to what we can call reality. There are no 1kg bread loafs. Not one in all human history.
    – RodolfoAP
    Dec 19 '20 at 2:50
  • You're referring to anthropic reasoning. "If the constants were slightly different life could not exist". Anthropic reasoning is just bad reasoning.The assumption is that there is a "space of possibilities", with the same laws of physics but different numerical values of constants of nature. So out of that space of possibilities our universe is improbable. But why would anyone consider this the space of possibilities. All we have is one universe. For all we know this is the only possible universe with probability 1. We don't have access to a meta-universe from which to calculate probabilities. Dec 19 '20 at 2:54
  • I agree with you that if we talk about alternate universes with differing constants, we might as well talk about alternate universes with differing laws. Not sure why the laws themselves are taken as unchangeable, but the constants are. Dec 19 '20 at 2:58
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    Because one can impose restrictions on what kinds of possibility are considered, and it is typically meaningless to consider "all bets are off" because our concepts will no longer apply, and there will be nothing to consider them with. In physical possibilities all laws of physics are kept fixed, in the possibilities from fine tuning arguments only variation of fundamental constants is allowed. The "life itself" talked about there is more or less "life as we know it". Changing "how life itself works" is pointless because whatever that might be will be a different concept.
    – Conifold
    Dec 19 '20 at 6:25
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Your question covers quite a range of issues.

  1. When we are just imagining possibilities, we can choose what to hold constant and what to consider a variable. In the example you give of imagining light travelling at 10 mph, we could imagine all the other laws and constants of physics remaining as they are. This is because as far as we currently know, the constant c is independent of other constants, though of course this might change as our knowledge advances. George Gamow used to write stories about a fictional Mr Tompkins who lived in a world where the fundamental constants were different in order to provide popular explanations of physics. A world with a slow speed of light featured in one of those. Possibly a slow speed of light would make stars impossible, or possibly it would make matter so abundant that some other phenomenon would make life possible. It is hard to say.

  2. That said, some changes are more radical than others. If the fine structure constant were even slightly different from its actual value, there would be no nuclear fusion and no stars and the universe would consist only of hydrogen, or maybe not even that. It is difficult to see how life could exist in that universe. Of course, we could choose to imagine such a universe as having other differences as well, including differences in the laws of nature, and then maybe life would be possible. However, there is no way to set out a space of possibilities that would allow us to talk of how probable such a universe is, so anthropic speculation is futile.

  3. To ask whether there could be universes where logic and mathematics are different from ours is a harder question than it appears. One position is that logic and mathematics are universal; another is that they are tools that we develop and use for making sense of our experience of our universe, and in a very different universe sentient beings might develop different tools from ours.

  4. Your last question about non-obvious impossibilities is also difficult, particularly because there are possibilities that lie at the edge of what might be considered logical or physical. For example, can we coherently imagine a universe in which the second law of thermodynamics does not apply? That law is usually described as a statistical law, so maybe it is mathematical in character. But on the other hand, the existence of a time-reversed universe does not appear to violate fundamental physical laws. Can we imagine a universe in which the Church-Turing thesis fails to hold and hypercomputers exist? It is difficult to see how, and it would completely change our understanding of computation, but maybe that is just a physical limitation of our universe and nothing more.

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Usually the kind of argument you are referring to posit the change of one constant while keeping the same models of physics we have established in our universe, and apply the rules to the new constant. This amounts to applying the same logical rules over different premises.

For example, if the speed of light C was 10 miles an hour the energy released by nuclear fusion (yielded by the formula E=MC^2) would be roughly a millionth of a billionth of what it is in our world. According to our knowledge of astrophysics, stars would not form and therefore life would not exist. The premises are contrived but the reasoning is sound.

In so far as the reasoning is sound, concluding to the impossibility of life is not more of a stretch than the impossibility of 1+1=3. The problem is not the reasoning, but the premises. The biggest and most reckless of which is to postulate that our understanding of physics is correct even in circumstances we can't observe and can't have any empirical knowledge about.

We can make calculations based on arbitrary and speculative premises, but we don't know what would really happen, and we have no way to ever check wether it is true. As long as we don't find another universe to observe (and of we can observe it, does it make sense to call it another universe?) all our reasoning about applying our rules to different premises is pure speculation. That's why that kind of argument is in fact pretty weak once properly analysed.

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