Can a theory of everything solve the oldest problem of turbulence?
Can we have unified theory of universe without solving the problem of turbulence?
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10$\begingroup$ Yes, a theory of everything does not mean every single emergent phenomenon in nature must been understood. $\endgroup$ – Charlie May 21 '20 at 12:11
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7$\begingroup$ Because it would describe the most fundamental rules of nature, from which everything else derives, including turbulence. Imagine you're playing chess, you don't have to know and understand every possible configuration that could exist on a chess board in order to understand how the pieces move and what the rules of the game are. This is like saying humans don't understand chess because we haven't played every single possible combination of moves. $\endgroup$ – Charlie May 21 '20 at 12:43
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3$\begingroup$ @VaibhavPankhala I've edited out your second title question ("why turbulence is still unsolved?"), because that's a very different question, that should be asked separately. Of course it's just a suggestion, but it might help preventing it from being closed. $\endgroup$ – stafusa May 21 '20 at 12:50
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3$\begingroup$ Humans don’t understand chess! E.g., is chess solved? en.wikipedia.org/wiki/Solving_chess $\endgroup$ – innisfree May 21 '20 at 13:02
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1$\begingroup$ At its heart, finding a theory of everything requires uniting Quantum Mechanics with General Relativity. One approach is to show that General Relativity is a macroscopic phenomena that emerges from the rules of Quantum Mechanics. So uniting these theories might require understanding how large scale phenomena emerge out of the rules that govern small scale, thus, shedding light on, or even solving the problem of turbulence. $\endgroup$ – cantorhead May 21 '20 at 22:41
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I’d like to answer by expanding the analogy made by @Charlie.
A theory of everything would be like knowing the rules of chess. We could understand all the rules, the pieces, and their moves and interactions. But there would remain many deep mathematical problems: e.g., what’s the perfect strategy in chess? It seems unlikely that this will be solved in our lifetimes. What’s even a good strategy? Knowing the rules does not mean that playing or understanding the game is easy.
So knowing a theory of everything would be like knowing the rules. Even with the rules, fully understanding the Universe would still be extremely challenging. There would still be very hard mathematical problems, like turbulence.
However, there’s no reason to think that the additional rules provided by string theory or another theory of everything would help at all explain turbulence. We already know the relevant rules for turbulence, we just can’t solve them.
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1$\begingroup$ It's funny that you say emergent problems are not likely to be solved in our lifetime as if the basic principles are likely to be found during our lifetime ;) Great answer tho, +1. $\endgroup$ – Dvij D.C. May 21 '20 at 13:22
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$\begingroup$ @innisfree can there be any hidden principles of universe in turbulence? $\endgroup$ – Vaibhav Pankhala May 22 '20 at 11:49
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Can we have unified theory of universe without solving the problem of turbulence?
Yes. Because the "unified" in the name refers to the basic interactions, from which in principle everything could be explained.
In practice, a hierarchy of models, with effective theories emerging from lower-level ones (think fluids laws from molecules' interactions, or quasiparticles in condensed matter) is likely to remain the most feasible and useful description.
