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2) design an experiment to prove it

I think this is incorrect. A good experiment is designed to disprove the hypothesis. And so if the experiment fails to disprove, we've got one more vote of confidence in the hypothesis.

It's never possible to out-and-out prove any hypothesis. There's always going to be variables that we didn't think were relevant. All we can do is keep adding to the heap of evidence in its favor, by falsifying more and more objections to it.




>A good experiment is designed to disprove the hypothesis.

Statistical tests are often designed around a null hypothesis that is defined as the opposite of the hypothesis we are testing. Once we can reject that null hypothesis we have proven the hypothesis. So for the LHC you'd disprove something like "there is no particle of energy X" (the null hypothesis) by finding a definite signal at energy X, thus proving that the Higgs Boson exists (the initial hypothesis). Prove/Disprove are relative terms though as you can only have a degree of confidence X on the validity of the hypothesis.




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