Ask Ethan: Where Is The Line Between Mathematics And Physics? - 0 views
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What, then, are you supposed to do when the mathematics gets more abstract? What do you do when you get to General Relativity, or Quantum Field Theory, or even more far afield into the speculative realms of cosmic inflation, extra dimensions, grand unified theories, or string theory? The mathematical structures that you build to describe these possibilities simply are what they are; on their own, they won't offer you any physical insights. But if you can pull out either observable quantities, or connections to physically observable quantities, that's when you start crossing over into something that you can test and observe.
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Now, string theory (or, more accurately, string theories) have their own constraints governing them, as do the forces in our Universe, so it isn't provably clear that there's a one-to-one correspondence between our four-dimensional Universe with gravity, electromagnetism, and the nuclear forces and any version of string theory. It's an interesting conjecture, and it has found some applications to the real world: in the study of quark-gluon plasmas. In that sense, it's more than mathematics: it's physics. But where it strays from physics into pure mathematics is not yet fully determined.
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If you describe the Universe precisely, and you can make quantitative predictions about it, you're physics. If those predictions turn out to be accurate and reflective of reality, then you're physics that's correct and useful. If those predictions are demonstrably wrong, you're physics that doesn't describe our Universe: you're a failed attempt at a physical theory. But if your equations have no connection at all to the physical Universe, and cannot be related to anything you can ever hope to someday observe or measure, you're firmly in the realm of mathematics; the divorce from physics will then be final. Mathematics is the language we use to describe physics, but not everything mathematical is physically meaningful. The connection, and where it breaks down, can only be determined by looking at the Universe itself.