On the relation between the Feynman paradox and the Aharonov–Bohm effects
The magnetic Aharonov–Bohm (A–B) effect occurs when a point charge interacts with a line of magnetic flux, while its reciprocal, the Aharonov–Casher (A–C) effect, occurs when a magnetic moment interacts with a line of charge. For the two interacting parts of these physical systems, the equations of...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
IOP Publishing
2012-01-01
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| Series: | New Journal of Physics |
| Online Access: | https://doi.org/10.1088/1367-2630/14/9/093020 |
| _version_ | 1797751582913200128 |
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| author | Scot McGregor Ryan Hotovy Adam Caprez Herman Batelaan |
| author_facet | Scot McGregor Ryan Hotovy Adam Caprez Herman Batelaan |
| author_sort | Scot McGregor |
| collection | DOAJ |
| description | The magnetic Aharonov–Bohm (A–B) effect occurs when a point charge interacts with a line of magnetic flux, while its reciprocal, the Aharonov–Casher (A–C) effect, occurs when a magnetic moment interacts with a line of charge. For the two interacting parts of these physical systems, the equations of motion are discussed in this paper. The generally accepted claim is that both parts of these systems do not accelerate, while Boyer has claimed that both parts of these systems do accelerate. Using the Euler–Lagrange equations we predict that in the case of unconstrained motion, only one part of each system accelerates, while momentum remains conserved. This prediction requires a time-dependent electromagnetic momentum. For our analysis of unconstrained motion, the A–B effects are then examples of the Feynman paradox. In the case of constrained motion, the Euler–Lagrange equations give no forces, in agreement with the generally accepted analysis. The quantum mechanical A–B and A–C phase shifts are independent of the treatment of constraint. Nevertheless, experimental testing of the above ideas and further understanding of the A–B effects that are central to both quantum mechanics and electromagnetism could be possible. |
| first_indexed | 2024-03-12T16:50:38Z |
| format | Article |
| id | doaj.art-6ffedc5ff98a45fcb8f3e11d4278828f |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:50:38Z |
| publishDate | 2012-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-6ffedc5ff98a45fcb8f3e11d4278828f2023-08-08T11:10:40ZengIOP PublishingNew Journal of Physics1367-26302012-01-0114909302010.1088/1367-2630/14/9/093020On the relation between the Feynman paradox and the Aharonov–Bohm effectsScot McGregor0Ryan Hotovy1Adam Caprez2Herman Batelaan3Department of Physics and Astronomy, University of Nebraska—Lincoln , 208 Jorgensen Hall, Lincoln, NE 68588-0299, USADepartment of Physics and Astronomy, University of Nebraska—Lincoln , 208 Jorgensen Hall, Lincoln, NE 68588-0299, USADepartment of Physics and Astronomy, University of Nebraska—Lincoln , 208 Jorgensen Hall, Lincoln, NE 68588-0299, USADepartment of Physics and Astronomy, University of Nebraska—Lincoln , 208 Jorgensen Hall, Lincoln, NE 68588-0299, USAThe magnetic Aharonov–Bohm (A–B) effect occurs when a point charge interacts with a line of magnetic flux, while its reciprocal, the Aharonov–Casher (A–C) effect, occurs when a magnetic moment interacts with a line of charge. For the two interacting parts of these physical systems, the equations of motion are discussed in this paper. The generally accepted claim is that both parts of these systems do not accelerate, while Boyer has claimed that both parts of these systems do accelerate. Using the Euler–Lagrange equations we predict that in the case of unconstrained motion, only one part of each system accelerates, while momentum remains conserved. This prediction requires a time-dependent electromagnetic momentum. For our analysis of unconstrained motion, the A–B effects are then examples of the Feynman paradox. In the case of constrained motion, the Euler–Lagrange equations give no forces, in agreement with the generally accepted analysis. The quantum mechanical A–B and A–C phase shifts are independent of the treatment of constraint. Nevertheless, experimental testing of the above ideas and further understanding of the A–B effects that are central to both quantum mechanics and electromagnetism could be possible.https://doi.org/10.1088/1367-2630/14/9/093020 |
| spellingShingle | Scot McGregor Ryan Hotovy Adam Caprez Herman Batelaan On the relation between the Feynman paradox and the Aharonov–Bohm effects New Journal of Physics |
| title | On the relation between the Feynman paradox and the Aharonov–Bohm effects |
| title_full | On the relation between the Feynman paradox and the Aharonov–Bohm effects |
| title_fullStr | On the relation between the Feynman paradox and the Aharonov–Bohm effects |
| title_full_unstemmed | On the relation between the Feynman paradox and the Aharonov–Bohm effects |
| title_short | On the relation between the Feynman paradox and the Aharonov–Bohm effects |
| title_sort | on the relation between the feynman paradox and the aharonov bohm effects |
| url | https://doi.org/10.1088/1367-2630/14/9/093020 |
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