We show that the phenomena explained by quantum mechanics can alternatively be explained as a breakdown of probability theory without the need for wave-particle duality or the idea that a particle does not have a unique path in space. The single-particle Lagrangian consistent with the reformulated quantum mechanics is derived and specialized to the Schrödinger and Klein-Gordon theories. The usual paradoxes of quantum mechanics are explained. A connection to gravity is proposed. Probability theory is restored in the classical limit.