Elements of a physics case for a High-Energy LHC

I outline the elements of a physics case for a high-energy upgrade to the LHC. The motivations are centered around the perspective of “blue chip” ideas that solve the hierarchy problem: technicolor-like theories, supersymmetry, and extra dimensions. In each case there is the prospect that going to higher energies is not only desirable but needed for discoveries. Nevertheless, the results from experiment over the next few years, most especially at the LHC, will sharpen the arguments and enable a more enlightened decision between the various experimental options for the future. (Based on an October 14, 2010 presentation at the Malta HE LHC meeting.)