If the Tevatron was a metal detector sweeping across a proverbial beach, the beeps of discovery would have been coming in very close succession at the end of its life. It was, we have learned, extremely close to finding the treasured Higgs boson ... and then, last September, it shut down. Only another, more powerful detector, owned by someone else, will finally be able to grab it.
Add one more thing to the list of mysteries, theories, and unsubstantiated ideas that will be confirmed/denied/debunked if CERN ever gets the Large Hadron Collider up and running: hyperdrive spacecraft propulsion.
In 1924, German mathematician David Hilbert published a paper noting a pretty amazing side effect to Einstein's relativity: a relativistic particle moving faster than about half the speed of light should be repelled by a stationary mass (or at least it would appear to be repelled, to an inertial observer watching from afar).