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Journal of Natural Science of Heilongjiang University

Agreement and disagreement about uncertainty relation

Lei Yang

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

Several different statements and proof methods of uncertainty relation are presented. The agreement and disagreement among these statements are compared and analyzed. New developments of relevant quantum theory are described in association with some recent experiments such as the Tonomura’s Electron Diffraction experiment and Zeilinger’s Neutron Diffraction experiment. These experiments fully proved that a single particle has wave nature. Uncertainty relation turns out to be a natural consequence of the wave nature of particles, so it is suitable for a single particle.

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Several different statements and proof methods of uncertainty relation are presented. The agreement and disagreement among these statements are compared and analyzed. New developments of relevant quantum theory are described in association with some recent experiments such as the Tonomura’s Electron Diffraction experiment and Zeilinger’s Neutron Diffraction experiment. These experiments fully proved that a single particle has wave nature. Uncertainty relation turns out to be a natural consequence of the wave nature of particles, so it is suitable for a single particle.
Abstract In 1925, de Broglie hypothesized that any material particle has an associated wave with /h p . Electron diffraction seems to support that Hypothesis. But then, the electron at rest will have infinite wavelength, and infinite wave phase velocity. This says that for a material particle, the de Broglie relation does not hold. Failed attempts to save the postulate, kept the flawed relation, and modified the waves into train waves, pilot waves, probability waves, … to name a few. We keep the de Broglie waves unchanged, and modify the relation. First, we observe that the Planck energy E h used by de Broglie defines virtual electromagnetic waves. Consequently, for any particle, the virtual electromagnetic wavelength is / /c h mc , and / /h m c . Refinement of de Broglie argument, indicates that /h mmay be x , Heisenberg’s uncertainty in the particle location. de Broglie’s later analysis supports this interpretation, and we offer an explanation to particle diffraction as a consequence of Heisenberg’s uncertainty. We apply / /h m c to obtain the dispersion relations for the de Broglie virtual waves.
Experimental investigations of quantum mechanical phenomena with neutron inter-ferometer and polarimeters are presented. Interferometry exhibits clear evidence of quantum-contextuality and polarimetry demonstrates conflicts of a contextual model of quantum mechanics á la Leggett. In these experiments, entanglements are achieved between degrees of freedom in a single-particle: spin, path and energy degrees of freedom are manipulated coherently and entangled. Both experiments manifest the fact that quantum contextuality is valid for phenomena with matter waves with high precision. In addition, another experiment is described which deals with error-disturbance uncertainty relation: we have experimentally tested error-disturbance uncertainty relations, one is derived by Heisenberg and the other by Ozawa. Experimental results confirm the fact that the Heisenberg's uncertainty relation is often violated and that the new relation by Ozawa is always larger than the limit.
An experiment with electrons The preceding chapters described the quantum behaviour of Nature in a general way. In order to show quantum uncertainty at work, it is useful to look at an actual experiment in detail. This demonstrates the practical consequences of the particle–wave duality. To keep things uncluttered, the experiment is only an idealized example, but it will serve to show when quantum interference occurs (wave behaviour) and when it does not (particle behaviour). I will try to demonstrate the intimate connection between the properties of waves and linear superposition, and the consequent uncertainty in the motion of quanta. For once I will try to be precise, so this exposition will be rather more technical than elsewhere. Those who wish to do so, may skip to Chapter 6 without much damage to their education. Before we begin, let me repeat the warning about the generality of analyses such as the one to be given here: I speak about ‘experiments’ or ‘observations’ only in order to make a connection with what a real person could do in a real laboratory, and not because the particle–wave duality is only a laboratory phenomenon that requires a conscious observer. Even though an electron does not wear a lab coat, it is subject to the uncertainty relations when it ‘observes’ other quanta.
The notion of uncertainty in the description of a physical system has assumed prodigious importance in the development of quantum theory. Overcoming the early misunderstanding and confusion, the concept grew continuously and still remains an active and fertile research field. Curious new insights and correlations are gained and developed in the process with the introduction of new 'measures' of uncertainty or indeterminacy and the development of quantum measurement theory. In this article we intend to reach a fairly uptodate status report of this yet unfurling concept and its interrelation with some distinctive quantum features like nonlocality, steering and entanglement/ inseparability. Some recent controversies are discussed and the grey areas are mentioned.