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New developments in quantum mechanics

Yakir Aharonov

Published May 2, 1994• 1 citation
OpenAlex

Abstract

After a general introduction, some new developments on the more subtle predictions of Quantum Mechanics and their interpretation will be discussed. These include non-local topological effects, physics of pre- and post-selected quantum systems, and the question of observability of the Schrödinger wave itself.

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A weak measurement performed on a pre- and post-selected quantum system can result in an average value that lies outside of the observable's spectrum. This effect, usually referred to as an ``anomalous weak value'', is generally believed to be possible only when a non-trivial post-selection is performed, i.e., when only a particular subset of the data is considered. Here we show, however, that this is not the case in general: in scenarios in which several weak measurements are sequentially performed, an anomalous weak value can be obtained without post-selection, i.e., without discarding any data. We discuss several questions that this raises about the subtle relation between weak values and pointer positions for sequential weak measurements. Finally, we consider some implications of our results for the problem of distinguishing different causal structures.
Quantum mechanics with massive particles becomes an important tool for fundamental research and applied science since many previously named "Gedanken" experiments become feasible. Neutrons are massive particles which couple to gravitational, nuclear and electro-magnetic interactions and they are sensitive to topological effects as well. Therefore they are proper tools for testing quantum mechanics where several previously named "hidden" parameters become measurable. Widely separated coherent beams can be produced by means of perfect crystal interferometers and they can be influenced individually. Spinor symmetry, spin superposition and quantum beat effect experiments have been performed and topological phases have been observed. Recent experiments related to the decoherence problem have shown that interference effects can be revived even when the overall interference pattern seems to be incoherent. All retrieval processes involve inherently unavoidable losses which stem partly from the theory itself and partly from an imperfect environment. Related post-selection experiments shed a new light on questions of quantum non-locality and support the request for more complete quantum measurements in the future. A more rational explanation of non-locality effects may be obtained when the plane wave components outside the wave packets are included in the discussion. This can also help to discuss entanglement and contextuality effects in a new light. In all quantum experiments more information can be extracted by more complete quantum experiments which will be important in the future to get a better understanding of quantum physics. An example may be the consideration of the Compton frequency and of proper time effects of matter waves.
We address the problem of interference using the Heisenberg picture and highlight some new aspects through the use of pre-selection, post-selection, weak measurements and modular variables. We present a physical explanation for the different behaviors of a single particle when the distant slit is open or closed; instead of having a quantum wave that passes through all slits, we have a localized particle with non-local interactions with the other slit(s). We introduce a Gedanken experiment to measure this non-local exchange. While the Heisenberg and Schrödinger pictures are equivalent formulations of quantum mechanics, nevertheless, the results discussed here support a new approach to quantum mechanics which has lead to new insights, new intuitions, new experiments and even the possibility of new devices that were missing from the old perspective.