Interaction-free quantum measurements: A paradox?
Abstract
In Heisenberg’s famous discussion of the measurement of a particle’s position using a microscope, the momentum transferred to the particle by the scattered photon makes the particle’s momentum uncertain. It is shown that momentum is also transferred when the lack of a scattered photon is used to discover that the particle is absent from the field of view of the microscope (i.e., located outside the light beam). This apparent paradox, a transfer of momentum and/or energy to a missing particle by a light beam (without the scattering of a photon), is discussed and ’’resolved’’ using quantum measurement theory.
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Dicke found that energy conservation is violated in certain quantum mechanical measurement setups for arbitrarily long times.
“Dicke found some time ago that energy conservation is violated in certain quantum mechanical measurement setups for arbitrarily long times[24].”
From On a possibility to find experimental evidence for the many-worlds interpretation of quantum mechanics (1997) · cites this paper as [24]
Dicke holds that this poses no serious problem because the expectation value for the amount of energy violation turns out to be zero.
“He holds that this poses no serious problem because the expectation value for the amount of energy violation turns out to be zero (i.e. repeating the measurement many times, energy is lost as often as it is gained).”
From On a possibility to find experimental evidence for the many-worlds interpretation of quantum mechanics (1997) · cites this paper as [24]
In the MWI, Dicke's situation corresponds to worlds which have a different energy expectation value of the system immediately after they were created due to branching (one is higher and the other lower than before branching).
“In the MWI Dicke's situation corresponds to worlds which have a different energy expectation value of the system immediately after they were created due to branching (one is higher and the other lower than the one before branching[24]).”
From On a possibility to find experimental evidence for the many-worlds interpretation of quantum mechanics (1997) · cites this paper as [24]
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Kimble, H. J. (2008) · Nature · doi:10.1038/nature07127 · Cited by 6,023 · see citing works
The quantum-jump approach to dissipative dynamics in quantum optics
Plenio, M. B., & Knight, P. L. (1998) · Reviews of Modern Physics · doi:10.1103/revmodphys.70.101 · Cited by 1,515 · see citing works
Quantum mechanical interaction-free measurements
Elitzur, A. C., & Vaidman, L. (1993) · Foundations of Physics · doi:10.1007/bf00736012 · Cited by 673 · see citing works
Plaga, R. (1997) · Foundations of Physics · doi:10.1007/bf02550677 · Cited by 18 · see citing works
- Authors
- Dicke, R. H.
- Affiliations
- Princeton University (US)
- Corresponding author
- Dicke, R. H.
- Venue
- American Journal of Physics
- Published
- 1981-10-01
- Volume
- 49
- Issue
- 10
- Pages
- 925-930
- ISSN
- 0002-9505 (ISSN-L)
- 1943-2909
- OpenAlex
- W2024420387
- Cited by
- 231
- References
- 0
- Citations by year
- 2026: 9 · 2025: 3 · 2024: 6 · 2023: 8 · 2022: 8 · 2021: 4 · 2020: 6 · 2019: 36 · 2018: 3 · 2017: 4 · 2016: 8 · 2015: 2 · 2014: 7 · 2013: 5 · 2012: 17
- FWCI
- 0.29
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- American Journal of Physics (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and Classical Electrodynamics
- Keywords
- interaction-free measurement, quantum measurement theory, momentum transfer, energy transfer, quantum paradoxes, position measurement
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