a grand unified theory
The Standard Model describes three of the four forces, the strong, weak, and electromagnetic, but it describes them as three separate interactions with three separate strengths, bolted together. Physicists have long suspected this is like seeing three colours of a single rainbow and not yet realizing they are one light. A grand unified theory is the conjecture that at very high energy these three forces merge into a single unified force, described by one symmetry and one coupling strength.
The clue comes from the running of the coupling constants: the strengths of the three forces are not fixed but change with energy, and when extrapolated upward using the Standard Model they very nearly meet at a single value near 10^16 GeV, the GUT scale. A grand unified theory embeds the Standard Model's separate symmetry groups (the SU(3) x SU(2) x U(1) of the strong, weak, and electromagnetic interactions) into one larger group, such as SU(5) or SO(10). Doing so places quarks and leptons in the same families, which implies they can transform into one another, and this generically predicts that the proton is not perfectly stable but can decay, with a lifetime longer than about 10^34 years.
Grand unification is a beautiful and well-motivated idea, but it is not established. Its cleanest prediction, proton decay, has been hunted in vast underground detectors for decades and never seen, ruling out the simplest SU(5) model. Still, GUTs remain attractive because they can explain why electric charge is quantized, offer a natural home for the baryon asymmetry, and hint at the deeper unification, including gravity, that a final theory would complete. Note that a GUT unifies three forces but not gravity; adding gravity is the further, harder step of quantum gravity.
In the simplest SU(5) model, a proton could decay via p to a positron plus a neutral pion, with a predicted lifetime around 10^31 years. The Super-Kamiokande detector, watching 50,000 tonnes of water, has seen no such decay, pushing the proton lifetime above 10^34 years and ruling that minimal model out.
The GUT signature is proton decay; not yet seen, ruling out the simplest models.
A grand unified theory unifies the strong, weak, and electromagnetic forces, but not gravity; combining all four is the separate, harder problem of quantum gravity. GUTs are strongly motivated but remain unconfirmed, since their hallmark prediction of proton decay has never been observed.