N-Body Problem
The cluster focuses on the n-body and three-body problems in physics, discussing the lack of closed-form analytical solutions for their differential equations and the reliance on numerical simulations despite challenges like precision and chaos.
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Which just means there’s no closed form solution. You can simulate these bodies fine provided you have sufficient numerical accuracy and very accurate measurements of initial conditions (this is the part that’s practically impossible)
it's not really physics so much as numerical methods.
I'm not an expert on particle physics, but the verbiage sounds to me like one of the standard problems in physics: We can write the differential equations. But even simple differential equations can be unsolvable. For example, consider the simple Three Body Problem. The differential equations are simple enough that you can use them as an introduction to the concept of differential equations themselves, but the Three Body Problem is not in general solvable.The three body problem can gener
Yes, but it's a well-defined problem with known solution. As complexity goes, it's not exactly the n-body problem in an exact numerical simulation.
If that's counterintuitive, than the most basic physics already teaches you that many things are counterintuive. The 3-body problem does not have an analytical solution. We can't even properly simulate the solar system a couple of thousands of years ahead. Nearly everything in physics is numerical approximation, despite what theory would lead you to believe. After that, the halting problem is far from surprising.
Goes to show we just don't have the Math to understand large scale solutions to differential equations for the N-body problem.
Physics before computers and differential equations
what kinds of problems can we solve with an analytic solution to the 3 body problem instead of a numerical one?
Just to clarify, the GP is describing what is essentially the n body problem in physics [1]. There is in general no closed form solution for solving n-body problems, but and so numeric solutions are generally required.[1] https://en.wikipedia.org/wiki/N-body_problem
Math... lots and lots of math solutions. Like if it could figure out the numerical sign problem, it could quite possibly be able to simulate all of physics.