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The logical structure of quantum theory is unchanged if we replace the usual complex probability amplitudes with real amplitudes, but the physics is in general quite different. Here I consider a specific model within real-amplitude quantum theory in which a hypothetical binary quantum system, the ubit, substitutes for the complex phase factors of the standard theory. In a certain limit, this model yields an effective theory that looks very much like ordinary quantum theory, but it exhibits spontaneous decoherence of isolated systems. In our model the ubit has no location and can interact with everything; so the model itself is highly nonlocal. Nevertheless, the effective theory that emerges from the model does not allow instantaneous signaling. Host: Sebastian Deffner |