Abstract
Self-interference, i.e. the interference of a quantum object with itself, is a fascinating phenomenon of quantum mechanics, which we discuss below in terms of the interaction-free quantum measurement. The experiment is based on the principle of the Mach–Zehnder interferometer (MZI). It shows the existence of quantum superpositions as clearly as the famous double-slit experiment, but it is by comparison formally and experimentally much ‘handier’, so that it is increasingly finding its way into textbooks. At the same time, it also allows for the treatment of further-reaching questions. That is why we meet the MZI not only in many modern basic experiments, but also for example in the field of quantum information, where we can realize basic functions of the quantum computer by means of the MZI and its components (see the closing remarks to this chapter).
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- 1.
The two beams can in principle be separated quite far apart. In this way, the non-classical effects of certain quantum-mechanical setups can be demonstrated more impressively than in the double-slit experiment.
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Thus, there are apparently physical effects influenced by potential but unrealized events, that is, events that could have happened, but did not actually occur. Such events are called counterfactual (not corresponding to the facts).
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A.C. Elitzur and L. Vaidman, “Quantum Mechanical Interaction-Free Measurements”, Foundations of Physics 23, 987 (1993).
- 4.
In order to avoid the militaristic note, some textbooks use ‘cracker test’ instead of ‘bomb test’, but this sounds a bit whimsical.
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“A physical experiment which makes a bang is always worth more than a quiet one. Therefore a man cannot strongly enough ask of Heaven: If it wants to let him discover something, may it be something that makes a bang. It will resound into eternity.” Georg Christoph Lichtenberg, Scrap Books, Vol. F (1147).
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This remark seems a bit exaggerated, but in fact the rods of the human eye can apparently react to even a single photon. The cones, responsible for color vision, need about 100 times stronger excitation. See e.g. Davide Castelvecchi, People can sense single photons, Nature, https://doi.org/10.1038/nature.2016.20282 (Jul 2016).
- 7.
The Feynman Lectures on Physics, 5th Edition, 1970, Vol II, p. 37-1: “Newton thought that light was made up of particles, but then it was discovered that it behaves like a wave. Later, however (in the beginning of the twentieth century), it was found that light did indeed sometimes behaves like a particle. Historically, the electron, for example, was thought to behave like a particle, and then it was found that in many respects it behaved like a wave. So it really behaves like neither. Now we have given up. We say: ‘It is like neither.”’ Richard P. Feynman, S. Tomonaga and J. Schwinger were awarded the Nobel Prize in Physics 1965 for their fundamental work in quantum electrodynamics.
- 8.
We note at this point, more generally, that the practice of declaring all things perceived to simply ‘exist’ may be inadequate. Instead, one should first look at perception itself and examine its predictability. Therefore, in quantum mechanics we need advanced methods, because we cannot come to grips with the ‘perceptions’ (observations, measurements) by simply using intuitive, classical instruments. To obtain the information relevant to quantum mechanics, we have to think and act in a largely formal manner.
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Not to be confused with the polarization states \(\left| h\right\rangle \) and \(\left| v\right\rangle \).
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For asymmetrical beam splitters (reflectance \(\ne \) transmittance), see the exercises.
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This is well known from linear algebra, e.g. when transposing or inverting matrices.
- 12.
Experiments are not confined to small distances. See e.g. F. Vedovato et al., Extending Wheeler’s delayed-choice experiment to space, Science Advances Vol. 3, no.10, https://doi.org/10.1126/sciadv.1701180 (Oct 2017), where a delayed-choice experiment is reported with a propagation distance of up to 3500 km.
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Pade, J. (2018). Interaction-Free Measurement. In: Quantum Mechanics for Pedestrians 1. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-00464-4_6
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DOI: https://doi.org/10.1007/978-3-030-00464-4_6
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