It is true that CERN has 4 detectors/experiments but they are all centered around the LEP experiment. There are no experiments at CERN which deal with accelerating protons at this time. There is a planned experiment in 2005, when the Large Hadron collider takes over the tunnel at which the LEP is located. The experiment you refer to is not at CERN it is at RHIC in Brookhaven National Lab on Long Island, it is an attempt to create a quark gluon plasma, a form of matter which would have been present shortly after the big bang but before condensation of quarks into particles like protons and neutrons.
I am aware of the possibility of using wormholes to time travel, however you are still unable to travel back beyond the point of the creation of the wormhole. Even the Tipler cylinder does not allow a traveller to go back beyond the point at which the cylinder was made. It has been my view that in order to have controlled time travel you would need to have a description of the quantum structure of space-time, otherwise I do not see how you could undertake the calculations that would be needed. One reason it is not certain that a wormhole could be used to travel through time is because it is believed that quantum fluctations around the mouth of the wormhole would act to collapse it. Just as in a similar fashion quantum fluctations around the event horizon of a black hole act to make it radiate particles and eventually evaporate.
If you are a time traveller from 2036, how do you plan to retake your place there. Your presence in this time frame would, as you have pointed out, cause a “temporal divergence” from the natural sequence of events. If you believe in the multiverse theory, may I ask you if you have memories of an unknown uncle being around while you were young?