Did Physicists Generate a “Mini-Big Bang”?

Physicists are once again trying to use the LHC to  accidentally destroy the world :

The Large Hadron Collider has successfully created a “mini-Big Bang” by smashing together lead ions instead of protons.

The scientists working at the enormous machine on Franco-Swiss border achieved the unique conditions on 7 November.

The experiment created temperatures a million times hotter than the centre of the Sun.

[ . . . ]

“This process took place in a safe, controlled environment, generating incredibly hot and dense sub-atomic fireballs with temperatures of over ten trillion degrees, a million times hotter than the centre of the Sun.

“At these temperatures even protons and neutrons, which make up the nuclei of atoms, melt resulting in a hot dense soup of quarks and gluons known as a quark-gluon plasma.”

Quarks and gluons are sub-atomic particles - some of the building blocks of matter. In the state known as quark-gluon plasma, they are freed of their attraction to one another. This plasma is believed to have existed just after the Big Bang.

I’ve read enough science journalism to know to be skeptical of such bold claims, so I’ll wait for Steve Barr to weigh in before I believe the LHC really generated a “mini-Big Bang.”

However, the claim that I find to be almost as interesting is that the fireballs were “ten trillion degrees.” How do the researchers know something like that? While I only really understand three kinds of hot (hot, Texas hot, and Africa hot ( “Tarzan couldn’t take this kind of hot.” )), I recognize that there are more precise measurements.

Still, how do you figure a temperature is “ten trillion degrees” rather than, say, the relatively cool “one trillion degrees”? Anyone know enough about the topic to be able to explain how scientists estimate such temperatures? (I figure that while I’m not going to understand all the mini-Big Bang stuff, the “how do you measure hotness” is something I should be able to wrap my head around.)

UPDATE: Steve Barr explains how the temperature is determined:

It is easy to make a theoretical estimate of the temperature of the glob of stuff they produced at the LHC. They make this glob by smashing two large nuclei into each other at high energy. (a) First of all, they know much energy the nuclei have that are smashed into each other. How? Because they are applying electric fields of known strength to accelerate these nuclei for a known period of time. (They know how many times the particles have gone around the racetrack.) So they know how much energy the glob has that they have produced. (b) One also knows the volume of the glob, which is related to the combined volume of the two nuclei one has smashed together. Thus, one knows the energy density (energy per volume) of the glob. (c) If the glob has enough time to reach “thermal equilibrium” before it flies apart, then it will have a definite temperature. There is a well-known theoretical formula relating the temperature of a system of particles to its energy density. Basically, for a system of “relativistic” particles (ones going nearly the speed of light), the energy density goes as T to the fourth power.

So here is a very, VERY rough (“back of the envelope”) calculation that I am doing as I sit at my computer: Assume the particles are accelerated to an energy of about 1 TeV per nucleon (nucleon = proton or neutron), which is probably several times lower than the LHC actually gives them —- but on the other hand, the glob probably loses a lot of energy before it has a chance to come to equilibrium. 1 TeV means 10 to the 12 “electron Volts”. The radius of a nucleon is 10 to the -13 centimeters, which is equivalent to 2 times 10 to the 8 inverse electron Volts. Thus the energy density is (10^12 eV) x (2x10^8/eV)^3= 8 x 10^37 eV^4. This should be roughly T^4. So T comes out to be the fourth root of 8x10^37 eV^4, which is about 1.7 x 10^9 eV. Since 1 eV equals about 12,000 degrees centigrade, this comes out to be 2x10^13 degrees = 20 trillion degrees.

I am off by a factor of two, but this was the roughest of estimates, so I am happy to be that close. The theorists involved in heavy ion collision work do the calculations in a much more sophisticated way.

Now estimating the temperature in such a way is not the same as measuring it. I assume that by measuring various characteristics of the glob —- what kind of particles are radiated from it, for example —- they can indirectly infer its temperature. In particular, they can tell if indeed the nuclei “melted” to form a “quark-gluon plasma”. Theoretical calculations give this melting temperature to be several trillion degrees (I don’t know the number better off the top of my head).