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The LHC was built to probe details of the electroweak symmetry breaking mechanism which is, as we believe today, responsible for generating masses of particles. We have proposed a method to probe the quartic boson interactions (γγ → γγ) in two-photon exchanges with forward proton tagging devices. Very small deviations from the Standard Model prediction, found for example in extra models with dimension, could become observable. These forward devices are already being constructed.