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Eliezer_Yudkowsky comments on Open Thread: November 2009 - Less Wrong
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I'll bet that the LHC will not establish existence. It's not clear to me what would count as establishing non-existence.
There are papers that establish upper bounds on the energy of the higgs boson,
http://arxiv.org/abs/hep-ph/9212305
If the LHC can make particles up to those energy bounds (I don't know and don't have the time to figure it out), and it can be run for sufficient time to make it very unlikely that one wouldn't be created. Then you could establish probable non-existence.