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Do completely unpredictable events exist in nature? Classical theory, beingfully deterministic, completely excludes fundamental randomness. On thecontrary, quantum theory allows for randomness within its axiomatic structure.Yet, the fact that a theory makes prediction only in probabilistic terms doesnot imply the existence of any form of randomness in nature. The question thenremains whether one can certify randomness independent of the physicalframework used. While standard Bell tests approach this question from thisperspective, they require prior perfect randomness, which renders the approachcircular. Recently, it has been shown that it is possible to certify fullrandomness using almost perfect random bits. Here, we prove that fullrandomness can indeed be certified using quantum non-locality under the minimalpossible assumptions: the existence of a source of arbitrarily weak (butnon-zero) randomness and the impossibility of instantaneous signalling. Thus weare left with a strict dichotomic choice: either our world is fullydeterministic or there exist in nature events that are fully random. Apart fromthe foundational implications, our results represent a quantum protocol forfull randomness amplification, an information task known to be impossibleclassically. Finally, they open a new path for device-independent protocolsunder minimal assumptions.

Full randomness from arbitrarily deterministic events