At the heart o f the quantum revolution is Heisenberg's uncertainty principle. This tells us, roughly speaking, that all physical quantities that can be observed are subject to unpredictable fluctuations, so that their values are not precisely defined. Consider, for example, the position x and the momentum p o f a quantum particle such as an electron. The experimenter is free to measure either of these quantities to arbitrary precision, but they cannot possess precise values simultaneously. The spread, or uncertainty, in their values, denoted by Ax and Ap respectively, are such that the product of the two AxLp, cannot be less than a certain constant number. Thus more accuracy in position must be traded for less in momentum, and vice versa. The constant that enters here (called Planck's constant after Max Planck) is numerically very small, so that quantum effects are generally only important in the atomic domain. We do not notice them in daily life.
It is essential to appreciate that this uncertainty is inherent in nature and not merely the result of technological limitations in measurement. I t is not that the experimenter is merely too clumsy to measure position and momentum simultaneously. The particle simply does not possess
simultaneously precise values of these two attributes.