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I understand the definitions "theorem" and "conjecture" in mathematics, but I wasn't sure for physics. I mean, if it's proved mathematically, it's a theorem, otherwise it's a conjecture. But for physics (i.e. when the idea is meant to correspond to a physical reality - and - can only said to 'true' if tested experimentally), how does one make a distinction?

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closed as off topic by Qmechanic, Ron Maimon, Warrick, Ebenezer Sklivvze, Manishearth Dec 27 '12 at 16:44

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I think this is off topic, but in physics, you say it's a valid theory if we know no exceptions, and you say it's an approximate theory if you know exceptions, but it works in a domain of validity. There are also theorems and conjectures, but usually proved at a slightly less exacting level of rigor. But the number of false physicist theorems has not been significantly higher than the number of false mathematician theorems per paper (although to be fair, the mathematician theorems usually require more involved longer proofs). –  Ron Maimon Sep 1 '12 at 4:10
    
In experimental physics I often heard 'conjecture' being used as a proposed theory/idea that has some merit and not been disproven. –  Alexander Sep 1 '12 at 13:31

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up vote 3 down vote accepted

In physics a theory is a mathematical model that provides a description of the real world in some limited circumstances. That is, it is a computational framework that allows us to feed in initial conditions and calculate what will happen.

All theories are approximate because they are based on assumptions that apply only within certain bounds. For example Newton's Theory of Gravitation gives a description of the Solar System that is pretty accurate (precession of Mercury apart). However we know that it fails at high speeds and energy densities and needs to be replaced by Einstein's Theory of general relativity. In turn we expect GR to fail at short distances and need to be replaced by some theory of quantum gravity.

As far as I know theorem means much the same in physics and maths, though the physics community is more pragmatic in the proof of theorems. I'm not sure that the word conjecture is used in any other than a casual way. In a sense all our theories are conjectures since they're not based on any rigorous mathematical proof.

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