![]() ![]() ∆p x∆x ≥ ℏ/2, ∆p y∆y ≥ ℏ/2, ∆p z∆ z ≥ h̷/2īecause ħ is so small in comparison with macroscopic quantities of the same dimensionality, namely, action, the uncertainty relations are significant primarily for phenomena on the atomic (or smaller) scale and are not apparent in interactions of macroscopic bodies. If by the uncertainties in the coordinate and the momentum we mean the root-mean-square deviations of these physical quantities from their average values, then the uncertainty relation assumes the form Similar inequalities must be satisfied for any pair of canonically conjugate variables, for example, (1) the y-coordinate and the component of the momentum p y along the y-axis or (2) the z-coordinate and the component of the momentum p Z. ![]() A quantitative statement of the uncertainty principle is the following: if ∆x is the uncertainty in the value of the x-coordinate and ∆p x is the uncertainty in the component of the momentum along the x-axis, then the product of these uncertainties should have a magnitude not less than that of Planck’s constant ћ. (also indeterminacy principle), a fundamental proposition of quantum theory that asserts that no physical system can exist in states in which the coordinates of its center of mass and its momentum simultaneously assume completely determined, exact values. Heisenberg, The Physical Principles of the Quantum Theory (tr. ![]() The uncertainty principle has been elevated by some thinkers to the status of a philosophical principle, called the principle of indeterminacy, which has been taken by some to limit causality in general. Even so, its restrictions are sufficient to prevent scientists from being able to make absolute predictions about future states of the system being studied. It does not limit the accuracy of single measurements, of nonsimultaneous measurements, or of simultaneous measurements of pairs of quantities other than those specifically restricted by the principle. Such a description would require exact measurements of such quantities as position, speed, energy, and time, and these quantities cannot be measured exactly because of the uncertainty principle. ![]() On the large scale it is still possible to speak of causality in a framework described in terms of space and time on the atomic scale this is not possible. Because of the uncertainties existing at this level, a picture of the submicroscopic world emerges as one of statistical probabilities rather than measurable certainties. The value of Planck's constant is extremely small, so that the effect of the limitations imposed by the uncertainty principle are not noticeable on the large scale of ordinary measurements however, on the scale of atoms and elementary particles the effect of the uncertainty principle is very important. The principle also limits the accuracies of simultaneous measurements of energy and of the time required to make the energy measurement. According to the uncertainty principle, the mathematical product of the combined uncertainties of simultaneous measurements of position and momentum in a given direction cannot be less than Planck's constant h divided by 4π. The accuracy of a measurement is given by the uncertainty in the result if the measurement is exact, the uncertainty is zero. Uncertainty principle, physical principle, enunciated by Werner Heisenberg in 1927, that places an absolute, theoretical limit on the combined accuracy of certain pairs of simultaneous, related measurements. ![]()
0 Comments
Leave a Reply. |