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The Physics Teacher

Simple Uncertainty-Principle Experiment

Charles A. Sawicki

Published Jan 20, 2003• 2 citations
Publisher

Abstract

Recent discussions in TPT have considered the pros and cons of an early introduction of students to modern physics.1–4 In this regard, appropriate experiments with classical waves can help students understand some important but counterintuitive aspects of modern physics. I recently taught a summer course that introduced high school seniors who had graduated with some background in physics and algebra to aspects of quantum physics and relativity. In this paper I'll describe a simple experiment I used to introduce these students to uncertainty principles in quantum physics.

DOI
10.1119/1.1542043

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Recent discussions in TPT have considered the pros and cons of an early introduction of students to modern physics.1–4 In this regard, appropriate experiments with classical waves can help students understand some important but counterintuitive aspects of modern physics. I recently taught a summer course that introduced high school seniors who had graduated with some background in physics and algebra to aspects of quantum physics and relativity. In this paper I'll describe a simple experiment I used to introduce these students to uncertainty principles in quantum physics.
Abstract 1. In the general synthesis of classical dynamics with the quantum theory, the Uncertainty Principle plays a most useful part. It is of course only one aspect of the new mechanics, but it is a very helpful one since by its means it becomes easy to see where the old classical ideas broke down. The state of affairs in the quantum theory is not unlike that of the early days of relativity, when most of those who studied the subject felt the need of supporting the formal theory by seeing how the old ideas failed in specific cases. Here the formal theory is very abstract and is not easy to follow intuitively, and the Uncertainty Principle plays much the same rôle as did the examples of clocks and rods in relativity theory. For this reason it is more appropriate for illustrative examples, than for any extreme generality, and though a number of examples have been already given by Heisenberg and Bohr, it may not be amiss to have some more. There are probably some who will have shared my experience that it is often by no means easy to detect how the uncertainty enters into a given experiment, though once detected the arguments are usually very simple. In a recent conversation Professor Bohr criticised some rather careless remarks that I had made, and the present work was undertaken to clear matters up. It may be shortly described as a study of the Uncertainty Principle in connection with electrometers and magnetometers. It may be of interest to point out that the Uncertainty Principle can be regarded from a rather different aspect. The "resolving power" of optical instruments was discussed very fully by Rayleigh on wave principles, but as long as matter was regarded in the classical manner, a mechanical instrument could be considered as capable of measuring quantities with absolute accuracy. Now that we know that matter also has wave properties, there is need of a theory of the resolving power of mechanical instruments, and this is exactly what the Uncertainty Principle supplies.
The discovery of quantum mechanics at the beginning of our century led to a revolution of the physical world view. Modern experiments, made possible by new techniques on the border of the classical and the quantum regimes, offer new insights and better understanding of the quantum world and have an impact on new technological development. Therefore it seems important that students at university and in the final years of high school gain an appreciation of the principles of quantum mechanics. A suitable way seems to be through treatment of the EPR gedanken experiment (thought experiment).
This introductory text on the basics of quantum mechanics is intended to serve as a kind of travel guide through the quantum world. It starts by asking whether quantum physics is important, or weird, or incomprehensible. It explains why particles sometimes behave like waves, and how uncertainty and randomness enter physics, before explaining a number of historically important experiments. Modern topics, like magnetic resonance imaging (MRI) and quantum computing are also covered. Essential concepts, such as the uncertainty principle, are analyzed in depth, employing a slightly increased dose of mathematics. This is the English version of the first part of a manual intended as a companion to the "Treffpunkt Quantenmechanik" (meeting point quantum mechanics), a laboratory at TU Dortmund University, where high-school students can get acquainted with the wonderful world of quantum physics. The second part of the manual contains detailed instructions for the individual experiments available in the lab and is not available on the Internet.
We present a conceptually clear introduction to quantum theory, deriving the theory from scratch from the point of view of quantum information, with focus on developing intuition and dispelling misconceptions. Different subsets of these lectures were taught to a wide variety of audiences, including exceptional high-school students in the International Summer School for Young Physicists (ISSYP) at Perimeter Institute, 2nd-year physics undergraduates at the University of Toronto, and 4th-year physics and math undergraduate and graduate students at Brock University. The lectures are completely self-contained, including all the necessary mathematical background: complex numbers, linear algebra, and probability theory. They cover topics such as the axioms of quantum theory, qubits, superposition, entanglement, the uncertainty principle, unitary transformations and evolution, quantum gates, projective measurements, Bell's theorem, interpretations of quantum mechanics, the no-cloning theorem, quantum teleportation, quantum algorithms, density operators, mixed states, von Neumann entropy, the Bloch sphere, quantum decoherence, Hamiltonians, the Schrödinger equation, canonical quantization, quantum harmonic oscillators, wavefunctions, and much more. The lectures also contain 111 proof-based problems and 51 computational exercises.