Energy density is steadily increasing. Hydrogen will be a short-term solution for medium/long haul flights, but will eventually be replaced by batteries.
Either go with an electric battery, or go with a hydrocarbon like kerosene or methane or so.
I made the original comment contemporary batteries ain't good for electric planes. And I would not bet on batteries becoming good enough anytime soon.
But I don't think physics prohibits anything here?
Things that involve metal-air reactions are basically fuel cells and don't count. If you go down that route, you'll quickly find yourself working with some kind of chemical fuel. They will suddenly look a lot like existing airplanes in terms of basic concept.
Ok, that definition works.
I would have gone with 'whatever people (in the future or now) use for powering their phones, laptops and electric cars' is by definition 'conventional' at that point in time.