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The GHSZ Argument: A Gedankenexperiment Requiring More Denken
1University of Canterbury, Department of Mathematics and Statistics, Christchurch 8140, New Zealand.
Entropy (Basel, Switzerland)
|December 8, 2020
Summary
This reassessment finds a logical error in the Greenberger-Horne-Shimony-Zeilinger (GHZ) thought experiment, challenging its conclusion about high-dimensional local realism. The original argument contained contradictory premises, not an inherent inconsistency in quantum mechanics.
Area of Science:
- Quantum mechanics
- Foundations of physics
- Quantum information
Background:
- The Greenberger-Horne-Shimony-Zeilinger (GHZ) thought experiment is influential in quantum foundations.
- It claims to reveal an inconsistency in high-dimensional local realism.
- Revisiting this experiment after 25 years is crucial for understanding quantum mechanics.
Purpose of the Study:
- To reassess the GHZ thought experiment and its conclusions.
- To identify and explain the logical error in the original argument.
- To re-evaluate the implications for local realism and hidden variables.
Main Methods:
- Logical analysis of the GHZ thought experiment's premises and derivation.
- Examination of the mathematical notation used to describe electron spin entanglement.
- Comparison with established principles of quantum mechanics and Bell's inequality.
Main Results:
- The GHZ thought experiment contains a fundamental logical error.
- Contradictory premises (angles equaling both π and 0) were presumed.
- The notation was insufficient to represent the quantum entanglement involved.
Conclusions:
- The GHZ experiment does not demonstrate an inconsistency in high-dimensional local realism.
- The experiment highlights the importance of understanding symmetries in quantum systems.
- A re-evaluation of local realism and hidden variables is warranted in light of this finding.
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