The proposed machine, physicists say, is needed to complement the Large Hadron Collider now under construction at the European Center for Nuclear Research, or CERN, outside Geneva. That machine will be the world’s most powerful when it goes into operation this fall, eventually colliding beams of protons with 7 trillion electron volts of energy each. Physicists hope that by using it, they will detect a long-sought particle known as the Higgs boson, which is thought to endow all the other constituents of nature with mass. They hope, too, to discover new laws and forms of matter and even perhaps new dimensions of spacetime.  But protons are bags of smaller particles called quarks and gluons, and their collisions tend to be messy and wasteful. Because electrons and positrons have no innards, their collisions are cleaner, so they can be used to create and study with precision whatever new particles are found at CERN.  The hitch is that until the Hadron Collider proves its worth by actually finding something new, the governments of the world are unlikely to sign on to contribute a share of the billions needed for the new machine.  Particle accelerators derive their punch from Einstein’s equation of mass and energy. The more energy they can pack into their little fireballs, the farther back in time they can go, closer and closer to the Big Bang and perhaps ultimate truth about nature, allowing particles and laws that once ruled the cosmos, but have since vanished more completely than the dinosaurs, to briefly strut their stuff again. But as physicists have pushed inward and backward, their machines have gotten bigger and more expensive. Competitions between universities and laboratories turned into races between countries and then continents.  The Large Hadron Collider cost about $3.77 billion, according to CERN. But that total did not include the cost of digging the collider’s 18-mile-circumference tunnel, which had been used for a previous machine, the detectors, which cost upward of $1 billion, or most of the above-ground CERN complex, which has been a particle physics center for decades.  A proton collider that would have been bigger, the Superconducting SuperCollider, was canceled by the United States Congress in 1993. At the time its estimated cost had ballooned to $10.3 billion in 2007 dollars, according to Robin Staffin, associate director for high energy physics at the Department of Energy.  The International Linear Collider collaboration, led by a steering group that is headed by Shin-ichi Kurokawa, of Japan’s High Energy Accelerator Research Organization, consists of 1,000 scientists and engineers from 100 countries.  Physicists acknowledge that it could be years before the world commits to building the International Linear Collider, although jockeying for the costly privilege of playing its host has begun.  The committee priced three sites: near CERN in Switzerland, at the Fermi National Accelerator Laboratory in Batavia, Ill., and in the mountains of Japan, and found that so-called site-specific costs, like digging tunnels and shafts and supplying water and electricity, were nearly the same in each case, about $1.8 billion.  A version of this article appears in print on , on Page A11 of the New York edition with the headline: The Big Bang And the Bucks Set to Collide In Inner Space. Order Reprints| Today's Paper|Subscribe
A machine 20 miles long will recreate, at a cost of about $6.7 billion, conditions when the universe was only a trillionth of a second old.