Resolves to yes if/when any method of transmitting physical information faster-than-light is shown to be possible. Valid solutions of Einstein's field equations that may or may not be possible to actually construct (such as the Alcubierre drive) do not count. Resolves to no if/when this is shown to be impossible. I will probably require that we have a proper Theory of Everything before I feel comfortable resolving this market to no, but I could be convinced to resolve it sooner if given a compelling enough argument.
Specifically, the information must be able to travel from object A to object B and arrive before a beam of light that was sent at the same time and faced only empty space in between. Local FTL is not required; a traversable wormhole would qualify.
Update 2024-09-12 (PST): Breaking causality is not considered a disqualifying factor - solutions that violate causality may still qualify as valid FTL travel methods for market resolution purposes. (AI summary of creator comment)