In many physical situations in the world of classical physics it is not possible to measure a variable without changing its value a little. For instance, placing a Volt meter in parallel with a resistor allows a little current to flow through the meter. The current in the resistor is reduced a little and the measured voltage is lower than the voltage was without the meter in place.
This idea has deeper significance in atomic physics.
If the measurement of the position of an isolated electron is made by reflecting a photon the electron will be given energy and its position will be altered. Put another way we might now know where the electron was, but we don't quite know where it is now.
Heisenberg formalized the
idea by saying that we are, in principle, unable to state
accurately both the position and momentum of a particle
at the same time. The product of the uncertainties in Dx
and Dp ... DxDp ... must always be greater than
or equal to Plank's constant h, over 2p.
As an example of the uncertainty principle, consider an electron bound to a proton in the hydrogen atom. The angular momentum of the electron is stated exactly - the angular position of the electron is unknown in principle, that is, "unknowable".
In a Physics revision booklet put out by IB examiners in 2002 there is a slightly misleading statement. The diagram is redrawn at right. Read the caption carefully. If one did not understand what is meant, one might suppose that we don't know where the electrons are because we do not have an accurate theory (or model) of the atom? That is not the case.
The angular momentum of the electron shells is known exactly, which, applying Heisenberg's principle means that we have NO information about the angular position of the electrons. The electron is equally likely to be found in a ANY direction. `
The picture we all have (had) of an electron as a point particle orbiting a positive nucleus is not right. We need a new picture. One way out of the impasse is to interpret Schrodinger's wave functions as probability functions. The wave function is the probability of finding the electron at a point in space. In this interpretation the electron is thought of as a point particle which can at any given instant be anywhere in a region of space.
The illustration at right is an attempt to construct a diagram to illustrate this interpretation.
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Click here for a poor-man's diagram of 2p orbitals. |
Note: Werner Heisenberg was German. As a young man he worked with, Neils Bhor, a Danish Jew. They became close friends. The emergence of the Third Reich and the rise to power of the Nazis under Hitler in the 1930's, strained this relationship. Heisenberg was (circa 1942-43) believed to be working on plans to construct a nuclear bomb for the Nazis. In a strange meeting with Bhor he let slip the fact of his involvement. Bhor then informed the US and its allies of the German plans. Some time later, when pressed, Heisenberg was to advise Hitler that a German bomb could not be made operational in a reasonable time frame (one year), and the project was downgraded in favor of more immediate investment. It is a sad comment on the politics of the 20th century, that Bhor and Heisenberg went to their graves, without healing the rift that had developed between them
Heisenberg's idea applies to oranges and cars as well as electrons and alpha particles, but the effect is to small to measure.
 The cars appear to be stationary, but in principle the product DxDp is uncertain. The uncertainty is so small that the suggestion is absurd - if not logically impossible. |