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In 2012, the ALICE experiment at CERN achieved a temperature of 5.5 trillion kelvin (5.5 × 1012 K). This was regarded as the highest man-made temperature.

However, even this temperature seems relatively low, as according to the Boltzmann constant, the kT for 5.5 × 1012 K is about 473.95 MeV. This is far lower than the energies achieved at the LHC, which are on the order of more than 1,000,000 MeV, i.e. four orders of magnitude higher than "the highest man-made temperature".

The temperature was achieved during heavy ion (208Pb) collisions, which does not affect the calculation much, since the energy imparted to every proton within the ion is on the same scale as in proton-proton LHC operations.

Where, then, did four orders of magnitude of temperature go?

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    $\begingroup$ My guess, which could be completely wrong, is that in the LHC the particles are mostly moving together: the velocities are not randomly distributed. The definition of temperature as average energy (which is not the definition but let's roll with it) only applies in the rest frame, in which the particles are basically standing still with respect to each other. $\endgroup$ – Javier Feb 20 '17 at 13:38
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These article is made for publicity, so it needs some search LHC wiki to get to some numbers.

1) The main operation mode is proton-proton collisions. From LINAC to PSB(1.4GeV) to PS(26GeV) to SPS(450GeV) to LHC and here they get TeV energies. However, it is not very correct to speak about temperature when one proton hits another one at high speed.

2) Heavy ion collisions mode - one month/year - they accelerate Lead (or something heavy) to like 2.3 TeV/nucleon. Part of the nuclei just break and the nucleons fly to all directions. Part, hopefully, "stop" during the collision for a fraction of a second, while creating very dense and hot quark-gluon soup. It is the environment we can speak about a temperature. The subsequent explosion of this environment is studied in experiments like ALICE.

And from the citation in the article you can see, that the temperature is not simple kT, but rather needs lot of analysis, in a sense a selective summation of the particles leaving this hot dense spot:

"ALICE spokesman Paolo Giubellino says that the team’s measurement is relatively uncertain and, moreover, they haven’t yet converted an energy measurement into degrees."

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