IN quantum mechanics, theory and experimentation are the Mutt and Jeff of progress. The theoretical work sometimes gets done on the back of an envelope with a 59-cent pen. The experiments use particle accelerators costing billions of dollars. Why such massive machinery? Because many particles don't exist naturally, but appear only when other particles collide and disintegrate. Such collisions require immense energies. It's a bit like slamming two billiard balls together. Do it with the relatively low energy of a billiard cue, and they bounce off each other. Blast them into each other from cannons, however, and they'll probably disintegrate.

Today's particle accelerators cause a lot of disintegration. But some particles are so tough that they don't crack up even at these energies. To them, the four-mile track at Fermilab - the world's largest accelerator - is just a big billiard cue. Needed, say particle physicists, is an even bigger accelerator.

Enter the SSC - the superconducting supercollider - which the Reagan administration is proposing to build for $4.4 billion. The SSC, to be housed in a 53-mile oval tunnel, takes its name from the superconducting coils used to energize 10,000 magnets designed to hold the particles on course. The largest scientific machine ever built, it would make possible collisions at 20 times the energies now available.

The Department of Energy (which would fund and operate the facility, as it does Fermilab) is looking for a site that provides, among other things:

The right kind of geological structure for tunneling.

Access to 250 megawatts of electrical power to run the collider and 2,200 gallons of water a minute to help cool it.

Some 16,000 acres of land for building, and 53 miles of subsurface tunnel easements.

The SSC would be a plum for any state that could eventually land it. As a public-works project, it would be a tax bonanza: a nonpolluting industry with an estimated annual budget of $270 million, employing thousands of construction workers until its projected opening in 1996. Not surprisingly, 25 states submitted bids by last September's deadline. Seven finalists are now in contention: Arizona, Colorado, Illinois, Michigan, North Carolina, Tennessee, and Texas. In November or December, Energy Secretary John S. Herrington plans to select the site, subject to final confirmation by Congress next January.

Many scientists in the physics community, predictably, support the SSC. ``The SSC is going to clear up a major puzzle,'' says University of Texas physicist Steven Weinberg, a member of the initial site selection committee. That puzzle, he says, involves some aspects of supersymmetry, which holds that every particle has its opposite number. Some of these ``superpartners'' will come to light only at the energy levels provided by the SSC.

But opposition to the SSC is widespread within the scientific community. Some see it, in the words of one opponent, as a ``power grab'' by the American high-energy physics community, and feel that the only practical way to build the next generation of particle accelerators is through international cooperation. Others simply worry that, in an era of tight budgets, the SSC will suck federal research dollars away from other projects not only in physics but in other sciences as well.

Freeman Dyson, a theoretical physicist at the Institute for Advanced Study in Princeton, N.J., describes the project as an example of making a scientific decision ``for reasons which are mainly political.'' He would like to see funding go for a more modest electron-positron collider. Such a machine, he says, could be built without such long lead time and could be later modified to keep pace with new developments.

Opposition to the SSC may also arise in Congress. As long as there were 25 states vying for the site, support was eager. Now that only seven are contending, proponents worry that support may dwindle.

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