Duplicating the Big Bang in Upstate New York?
I'm a physicist here at Fermilab who won the lottery to try and answer your question. You are refering to the work just beginning at the Relativistic Heavy Ion Collider (RHIC) at the Brookhaven National Laboratory (BNL) described in Madhusree Mukerjee's article in the March 99 issue of Scientific American. BNL is on Long Island about 60 miles east on New York City (about as far downstate in New York as you can get.) I've done experiments there before.
Short Answer - We've been colliding relativistic ions (protons) with relativistic anti-ions (anti-protons) at about ten times higher energy (or equivalently temperature) than RHIC plans, for the last ten years. If anything bad were going to happen we would have found out first.
Re-creating the big bang is a bit of artistic license in describing these kinds of experiments. In the beginning everything was VERY hot, even relative to the temperatures we can achieve with machines like RHIC or at Fermilab. These experiments heat matter to temperatures higher than we have ever achieved before. This lets us understand what happens at times closer to the big bang, when the whole universe was a hot as the two ions in our collisions. At eariler times still, the whole universe was even hotter. We're not re-creating the big bang, just getting closer to it.
The big question the RHIC folks are trying to answer is, in their languague: "Is there a quark-gluon plasma?". Translation - do protons and neutrons "melt" into their constitutents (quarks and gluons) if you get them hot enough? This is very important if you want to understand how the universe we see today evolved from the big-bang. If there is a quark-gluon plasma then, when the universe was so hot, it was made up of free quarks and gluons. These had to first condense into protons and neutrons before the evolution of the universe could move on to hydrogen, helium and ultimately stars, nucleo-synthesis, super-novae and us. The question is like asking: "Is there a fourth state of water in addition to steam, liquid and ice?". The answer to this question would surely effect more than just the chemistry of a cocktail.
RHIC is a far better place to try to answer this question than Fermilab. We start with 3 quarks (the proton), 3 anti-quarks (the anti-proton) and a pile of gluons (holding the quarks in each of those ions together). Trying to decide if they "boil" or not in the 10^-24 seconds during which the collision happens isn't easy. If I gave you 6 water molecules you would be hard put to tell me whether they were in the gaseous (steam) or liquid state. At RHIC they start with about 1000 quarks which should make questions of which state they are in a little easier to answer.
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