In 1954 the renowned physicist Enrico Fermi did a simple but depressing calculation about future particle accelerators. To create particles with an energy of 3 teraelectron-volts, he estimated, you’d have to build a ring 8,000 kilometers in radius at a cost of $170 billion. It was a rare instance of Fermi being wrong. The Large Hadron Collider achieved that energy level in 2010 with a 4-km ring for $10 billion. In large part, its success was brought to you by the letter ‘C’: the LHC collides particles with one another rather than smash them against a stationary target, as Fermi had envisioned. It also helped that magnets these days are stronger than Fermi dared dream. For Fabiola Gianotti, the LHC physicist who co-announced the Higgs boson two years ago, it’s an instructive tale for those who worry her field is reaching its limits. “The correct attitude is not to give up and say it’s impossible,” she says. “The correct attitude is to innovate.”

Last week she and her colleagues gathered at Columbia University to review LHC discoveries and talk about the future. Physicist/blogger Matt Strassler summarized some of the Higgs findings on his blog. Being personally engrossed by all things apocalyptic, I was fascinated when theorist John Ellis confirmed that the masses of the Higgs and of the heaviest known elementary particle, the top quark, place the universe on the brink of a catastrophic instability. At any moment, the vacuum could decay to a lower energy state, changing the laws of physics that govern our universe–an existential calamity that would wipe out every form of matter. To which your reaction should be: great news! The fact that we live on the edge of chaos is probably telling us something deep about the way the world is put together, as physicist Joe Butterworth blogged yesterday. (Besides, physicists might as well put a good spin on the vacuum instability, because if self-destruction is wired into the very laws of nature, there’s not a thing we could do to save ourselves.)

For now, the Higgs remains the LHC’s main output. No exotic particles or new forces have turned up–a null result that has disquieted not a few physicists. The speakers I saw at the meeting acknowledged their colleagues’ worries, but argued that these are still early days. When the LHC starts up again next year, it’ll have twice the energy. And if that’s still not enough to shake new particles loose, well, physicists are laying plans for even greater machines.

It doesn’t seem like an auspicious time to be talking about expensive new experiments, what with the state of science funding, especially in the U.S. But a yes-we-can attitude is spreading. How to build those machines in a time of austerity is the topic of a recently completed report that sets priorities for American physics, known as the Particle Physics Project Prioritization Panel, or P5. A guiding theme is that neither the U.S. nor any other nation can go it alone anymore. The U.S. should help the Europeans with a major LHC upgrade planned for about 2020, which will boost the number of particles it pumps out 10-fold, letting it capture rarer processes. The U.S. should pitch in on the International Linear Collider that Japan is considering and that would fire up in 2028 or thereabouts. And in turn the U.S. should internationalize its own neutrino laboratories.

Physicists see both the LHC v3.0 and the ILC (or a like contraption) as essential follow-ups to their recent discoveries. Both machines would perform extra-high-precision measurements to check whether the Higgs is playing its intended theoretical roles. For instance, a particle mass’s should be proportional to the strength of its interaction with the Higgs. Any deviations could indicate the shadowy influence of particles as yet unknown. Indeed, it’s quite likely that new particles would first betray themselves in this indirect way, much as the top quark made its presence felt in the behavior of known particles long before anyone actually created one. Neutrinos, too, may provide a backdoor to new physics.

Beyond the ILC, physics planners enter a dreamier realm of accelerators that fling particles with an energy of 100 TeV. Actually, not that dreamy: the U.S. very nearly built such a machine 20 years ago, the Superconducting Supercollider, so it’s entirely doable. Planners have already been colliding acronyms. CERN seems to have dropped VLHC (“Very Large Hadron Collider”) in favor of FCC (“Future Circular Collider”). China is also mulling a similar machine with its own abbreviation proliferation (CepC, SppC). And the P5 report says the U.S. shouldn’t be counted out, either. There’s lots of time for the country to get its groove back. The report recommends investing in the requisite technologies, notably magnets. The LHC’s magnets have a strength of 8 teslas. Ordinary superconductors might be cranked up to 16, which would be just enough to get 100 TeV out of a 100 km ring. Smaller rings or higher energies, Gianotti says, would demand magnets made of high-temperature superconductors.

One of the most eloquent voices in favor of a 100 TeV collider has been Nima Arkani-Hamed, whose ideas I blogged last year. In a panel discussion at last week’s meeting, he described how scientists may be motivated by the grand questions of existence–what is spacetime? why is the world quantum?–but in practice have to focus on incremental questions if they are to make progress. “One thing about being a professional scientist is not to ask the big question,” he said. “It’s to ask the next question.” But having completed the Standard Model, he said, physicists have reached a special moment. They now live at a time when the next questions are the big questions.

Fabiola Gianotti at the ATLAS detector. ATLAS Experiment (C) 2011 CERN