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Quote from Lee Smolin in Scientific American:

There are some lazy ideas about unification that reflect uncritical thinking, such as the idea that the more fundamental a phenomena [sic] is the more symmetry it must have. When you think seriously about the problem you realize it must be exactly the opposite. Roger Penrose use to say this, and indeed the insight that the most fundamental theory can have no symmetries goes back to Leibniz.

Also does anyone know what exactly Leibniz had to say on the matter?

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  • $\begingroup$ I don't know what Leibniz thought about the matter and I am not sure it is particularly relevant in a modern context, since he certainly didn't have the strong restriction on mathematical models of reality in mind that are emerging from relativity and quantum mechanics. The fundamental question goes much further than even Smolin drives it in this excerpt. Before you can even place THIS left of THAT and imagine that it could be the other way round, you have to find a way to establish how THIS is even different from THAT. At the current level of physics that's an axiom that needs an explanation. $\endgroup$
    – CuriousOne
    May 16, 2015 at 4:27
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    $\begingroup$ what leibniz though is relevant to understanding that quote $\endgroup$
    – innisfree
    Jul 6, 2015 at 15:50

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Lee Smolin doesn't mean that the most fundamental physical theory can have no symmetry. What he means is that symmetry shouldn't be the guiding principle in discerning fundamental physical theories. While symmetry is mathematically useful, it doesn't provide a sufficient reason to accept a theory, this goes back to Leibniz's principle of sufficient reason. Smolin wants physicists to abandon trying to find timeless laws and symmetries, and like biology understand how laws evolve; he advocates a theory of cosmological evolution. Note: I don't agree or disagree with Smolin, I am just stating what he believes. This blog site should help you. Here, Leibniz's other principles of network relations, indiscernibles, etc. are used to explain Smolin's argument.

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In Smolins Time Reborn, he argues based on Liebniz theory of indiscernibles that symmetries can't be fundamental although in a footnote he states this doesn't hold for gauge symmetries.

Liebniz's principle of indiscernibles simply means that no two distinct things exactly resemble each other. I'm not sure quite what Smolin says by about symmetries follow from this. But here is one guess, Spin-Statistics relies on the fact that any two electrons are exactly the same and so can be swapped without changing the system. This is permutation symmetry. But according to Liebniz, no two distinct electrons can be the same and so this symmetry doesn't hold.

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  • $\begingroup$ He's called Leibniz, not Liebniz. $\endgroup$
    – Ruslan
    Apr 17, 2021 at 22:47

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