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Quantum uncertainty, or more formally, the Heisenberg uncertainty principle, is a finding in quantum physics that states that one cannot simultaneously know both the exact position and exact momentum of a single particle. The uncertainty principle also gives mathematically precise (quantitative) confidence limits for pairs of measurements. Essentially, the more precisely you want to know one value, the more accuracy you must sacrifice in your measurement of the other.
Because of its association with the quantum mechanics revolution, quantum uncertainty has a lasting place in popular culture, where it is often misinterpreted. Quantum uncertainty in movies and films is sometimes used incorrectly to refer to large objects, when it really only applies to particles. Also, the idea of quantum uncertainty is often presented in a mysterious way, without the mention that the concept goes hand in hand with precise quantitative confidence bounds, which are not so mysterious.
The notion of quantum uncertainty caused a ruckus in the early 20th century, when physicists were trying to work out the particulars of quantum theory through conflicting interpretations. Neils Bohr and many other physicists advocated the Copenhagen interpretation, which states that the universe is fundamentally fuzzy at the lowest level, described by probability distributions rather than deterministically linked, well-defined states. Werner Heisenberg, who derived the uncertainty principle from the mathematical structure of quantum theory, also advocated the Copenhagen interpretation. Albert Einstein, however, did not, famously saying "God does not play dice".
The theory of quantum uncertainty, despite being packaged with mathematically precise confidence bounds, truly is quite mysterious. There are still disagreements in the physics community about whether the Copenhagen interpretation follows inevitably from quantum certainty. The contemporary alternative to the Copenhagen interpretation is the Many Worlds interpretation of quantum mechanics, which holds that reality actually is deterministic.
In the context of the great success of Newtonian mechanics for more than a century prior, physicists were greatly reluctant to give up deterministic theories without incredibly compelling evidence. So they attempted to come up with "hidden variable" theories, which tried to explain away quantum uncertainty as a high-level property that emerges from more fundamental deterministic interactions. However, a finding called Bell's inequality found that local hidden variable theories could not be used to describe quantum uncertainty without postulating faster-than-light correlations between all particles in the universe. However, nonlocal hidden variable theories are still proposed to explain a deterministic foundation behind quantum uncertainty.