The authors of this paper claim to show that other terms can be added to the quantum mechanical action that are consistent with current theory and experiment. However, some of these possible terms include conditions in the future that need to be taken into account and summed over. That is to say, what happens in the future could (according to this paper) affect what happens in the present.

Why the LHC? The authors argue that these sorts of time-violating interactions could be associated with whatever new particles we create at the LHC. For example, the production of a large number of Higgs particles in the future could have a backwards-in-time causal effect on the machine that produced them, stopping the machine from ever running.