Uncertainty principle

The uncertainty principle is a foundational concept in quantum mechanics that describes an inherent limit to the precision with which certain pairs of complementary physical properties of a particle can be simultaneously known. Specifically, the principle posits that the more precisely one measures a particle's position, the less precisely one can know its associated momentum, and vice versa. This mathematical constraint dictates that there is a fundamental tradeoff in measurement; one cannot determine both the exact position and the exact momentum of a particle simultaneously. This inherent limit is not due to flaws in measuring instruments, but is rather a built-in property of quantum systems themselves.