Deconfinement In Quark-Gluon Plasma
QCD (quantum chromodynamics, which is the physics of the strong force) confines all quarks and gluons into strong force bound systems called hadrons up to a certain threshold of energy.
All hadrons are naturally unstable except protons and bound neutrons, which are stable indefinitely. Free neutrons have a mean lifetime of about 15 minutes. All other hadrons have mean lifetimes before they naturally decay into something else on the order of microseconds to something on the order of 10
-24 seconds.
If you apply enough energy, protons and other hadrons in a system can dissolve into what is called a "
quark-gluon plasma", which is made up of deconfined quarks and gluons, and as noted in the link: "the formation of a quark–gluon plasma occurs at the temperature of T ≈ 150–160 MeV, the
Hagedorn temperature, and an energy density of ≈ 0.4–1 GeV/fm
3." It takes beam strengths vastly greater than 1-2 GeV to get that energy density, realistically, something on the order of low to mid-TeV energy beam strength.
CERN claims to have created such as state for the first time in the year 2000. The only experimental facilities currently capable of creating quark-gluon plasma the Large Hadron Collider at CERN and
Brookhaven National Laboratory's
Relativistic Heavy Ion Collider.
Quark-gluon plasma, a.k.a. QGP, is unstable and hadronizes (i.e. breaks up into confined quarks and gluons in hadrons) as it cools below the Hagedorn temperature. Only a tiny amount of it has been created in human history and the QCP created has been extremely short-lived.
QGP requires conditions too extreme to be created naturally in the post-Big Bang universe (after the first hour or two, or perhaps even less) by any known natural means.
Disrupting Protons To Make New Particles
Far less proton-proton collision energy is needed to lead to a high energy physics event that produces end products that are something other than two protons (some combination of leptons like electrons, muons, taus, and neutrinos, photons, and other hadrons, including hadrons more massive than the protons that were in the initial state, since their kinetic energy can be converted into mass), which could also credibly be described as splitting a proton.
The first experiment to accelerate a proton to break up an atomic nucleus was by
Cockroft and Walton in 1932, but that only broke up a residual nuclear force bond between particles in a meta-stable uranium atom. Over time, colliders and their immediate predecessor technologies grew more powerful (from the link in this paragraph):
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Proton-proton colliders starting in the 1960s were finally reaching a point where the collision could produce something other than two protons afterwards on a consistent basis, although there may have been examples of this earlier (in the 1950s) at somewhat lower energies (10s to 100s of MeVs) that I have missed in a brief review.