To make the antenna efficient at radiating energy into space (or receiving energy from space), the key trick is to make use of standing waves. The shortest standing wave you can get is at half the wavelength, and relatively easy to feed in the center of the dipole. Full wave is also possible, but more difficult to "feed" by a cable if memory serves (which is where you get into practical aspects, such as feedline impedance matching = optimum energy coupling). Actually quarter-wave stubs are also possible and "resonant", but need to be fed at one end by a unipolar/single-ended transmission line... and the impedance match is not very good, AFAICT. You can indeed make the antenna shorter - this is typically done by putting a coil at the base of what was originally a quarter-wave stub. This is typical for short-wave radioes (CB comes to mind) or vehicle-mounted FM radio antennas etc. Note that by making the antenna physically smaller, you decrease its effective reception area, meaning that it "collects less energy" = has lower gain. Which results in worse SNR in the radio input. For the sexy small size, you have to give up some gain.
I'd like to point out one difference in the resonant properties, between a "lumped component" LC resonator and a "standing wave" type resonant dipole or cavity: if observed across the whole spectrum, an LC resonator has a single peak at the resonant frequency, but a "standing wave" type resonator actually has multiple peaks and notches, spread across the whole spectrum. And, if memory serves, the standing-wave notches are generally sharper than the peaks (at least my simulations in QUCS used to suggest that.)