Position Measurements Obeying Momentum Conservation

Position measurements obeying momentum conservation.

We present a hitherto unknown fundamental limitation to a basic measurement: that of the position of a quantum object when the total momentum of the object and apparatus is conserved. This result extends the famous Wigner-Araki-Yanase theorem, and shows that accurate position measurements are only practically feasible if there is a large momentum uncertainty in the apparatus.

Optimal Joint Measurements of Position and Momentum

The distribution of measured values for maximally accurate, unbi-ased simultaneous measurements of position and momentum is investigated. It is shown, that if the measurement is retrodictively optimal, then the distribution of results is given by the initial state Husimi function (or Q-representation). If the measurement is predic-tively optimal, then the distribution of results is related to t...

Approximate Momentum Conservation for

Learning about Momentum Conservation

A system has been designed in which explanation-based learning is applied to classical mechanics. An overview of the fully-implemented system and an example run by it are presented. From the example the system acquires a general formula describing how the momentum of a collection of objects changes over time. The derivation of this formula is prompted by the analysis of a human's solution to a ...

Conservation of Energy Implies Conservation of Momentum: How We Can Explain Conservation of Momentum to Before-Calculus Students

In solving physics problems, it is often important to use the laws of conservation of energy and momentum. While most people have intuitive understanding of energy and of its conservation, there is usually no intuition behind momentum, and known textbook derivations of conservation of momentum use calculus – which is usually taught after momentum. In this paper, we show how the law of conservat...