"At the heart of the quantum revolution is Heisenberg's uncertainty principle... roughly... all physical quantities... are subject to unpredictable fluctuations, so that their values are not precisely defined. ...[e.g., we are] free to measure [position x and the momentum p of a quantum particle] to arbitrary precision, but they cannot possess precise values simultaneously. The spread, or uncertainty, in their values, denoted by Ax and Ap... are such that [their] product... cannot be less than... [after Max Planck], numerically very small... so that quantum effects are generally only important in the atomic domain... not... in daily life. ...[T]his uncertainty is inherent in nature and not merely the result of technological limitations in measurement."

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Added on April 10, 2026
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Original Language: English