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Heisenberg Uncertainty

Heisenberg sometimes explained the uncertainty principle as a problem of making measurements. His most well-known thought experiment involved photographing an electron. To take the picture, a scientist might bounce a light particle off the electron's surface. That would reveal its position, but it would also impart energy to the electron, causing it to move. Learning about the electron's position would create uncertainty in its velocity; and the act of measurement would produce the uncertainty needed to satisfy the principle.

Physics students are still taught this measurement-disturbance version of the uncertainty principle in introductory classes, but it turns out that it's not always true. Aephraim Steinberg of the University of Toronto in Canada and his team have performed measurements on photons (particles of light) and showed that the act of measuring can introduce less uncertainty than is required by Heisenberg’s principle. The total uncertainty of what can be known about the photon's properties, however, remains above Heisenberg's limit.

Contrary to what is often believed the Heisenberg inequalities (62) and the Robertson-Schr€odinger inequalities (64) are not statements about the accuracy of our measurements; their derivation assumes perfect instruments (see the discussion in Peres,20 p. 93). Their meaning is that if the same preparation procedure is repeated a large number of times on an ensemble of systems and is followed by either a measurement of xj or a measurement of pj, then the results obtained will have standard deviations Dxj and Dpj. In addition, these measurements need not be uncorrelated; this is expressed by the statistical covariances Dðxj; pjÞ appearing in the inequalities (64).

An uncertainty relation such as (4.54) is not a statement about the accuracy of our measuring instruments. On the contrary, its derivation assumes the existence of perfect instruments (the experimental errors due to common laboratory hardware are usually much larger than these quantum uncertainties). The only correct interpretation of (4.54) is the following: If the same preparation procedure is repeated many times, and is followed either by a measurement of x, or by a measurement of p, the various results obtained for x and for p have standard deviations, ∆ x and ∆ p, whose product cannot be less than h/ 2. There never is any question here that a measurement of x “disturbs” the value of p and vice-versa, as sometimes claimed. These measurements are indeed incompatible, but they are performed on different particles (all of which were identically prepared) and therefore these measurements cannot disturb each other in any way. The uncertainty relation (4.54), or more generally (4.40), only reflects the intrinsic randomness of the outcomes of quantum tests.

page 93 in Quantum Theory: Concepts and Methods by Peres

heisenberg_uncertainity.txt · Last modified: 2017/06/28 10:12 by jakobadmin