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Special Relativity at the Quantum Scale
It has been suggested that the space-time structure as described by the theory of special relativity is a macroscopic manifestation of a more fundamental quantum structure (pre-geometry). Efforts to quantify this idea have come mainly from the area of abstract quantum logic theory. Here we present a...
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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Public Library of Science
2014
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4274123/ https://www.ncbi.nlm.nih.gov/pubmed/25531675 http://dx.doi.org/10.1371/journal.pone.0115810 |
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author | Lam, Pui K. |
author_facet | Lam, Pui K. |
author_sort | Lam, Pui K. |
collection | PubMed |
description | It has been suggested that the space-time structure as described by the theory of special relativity is a macroscopic manifestation of a more fundamental quantum structure (pre-geometry). Efforts to quantify this idea have come mainly from the area of abstract quantum logic theory. Here we present a preliminary attempt to develop a quantum formulation of special relativity based on a model that retains some geometric attributes. Our model is Feynman's “checker-board” trajectory for a 1-D relativistic free particle. We use this model to guide us in identifying (1) the quantum version of the postulates of special relativity and (2) the appropriate quantum “coordinates”. This model possesses a useful feature that it admits an interpretation both in terms of paths in space-time and in terms of quantum states. Based on the quantum version of the postulates, we derive a transformation rule for velocity. This rule reduces to the Einstein's velocity-addition formula in the macroscopic limit and reveals an interesting aspect of time. The 3-D case, time-dilation effect, and invariant interval are also discussed in term of this new formulation. This is a preliminary investigation; some results are derived, while others are interesting observations at this point. |
format | Online Article Text |
id | pubmed-4274123 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2014 |
publisher | Public Library of Science |
record_format | MEDLINE/PubMed |
spelling | pubmed-42741232014-12-31 Special Relativity at the Quantum Scale Lam, Pui K. PLoS One Research Article It has been suggested that the space-time structure as described by the theory of special relativity is a macroscopic manifestation of a more fundamental quantum structure (pre-geometry). Efforts to quantify this idea have come mainly from the area of abstract quantum logic theory. Here we present a preliminary attempt to develop a quantum formulation of special relativity based on a model that retains some geometric attributes. Our model is Feynman's “checker-board” trajectory for a 1-D relativistic free particle. We use this model to guide us in identifying (1) the quantum version of the postulates of special relativity and (2) the appropriate quantum “coordinates”. This model possesses a useful feature that it admits an interpretation both in terms of paths in space-time and in terms of quantum states. Based on the quantum version of the postulates, we derive a transformation rule for velocity. This rule reduces to the Einstein's velocity-addition formula in the macroscopic limit and reveals an interesting aspect of time. The 3-D case, time-dilation effect, and invariant interval are also discussed in term of this new formulation. This is a preliminary investigation; some results are derived, while others are interesting observations at this point. Public Library of Science 2014-12-22 /pmc/articles/PMC4274123/ /pubmed/25531675 http://dx.doi.org/10.1371/journal.pone.0115810 Text en © 2014 Pui Kwong Lam http://creativecommons.org/licenses/by/4.0/ This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited. |
spellingShingle | Research Article Lam, Pui K. Special Relativity at the Quantum Scale |
title | Special Relativity at the Quantum Scale |
title_full | Special Relativity at the Quantum Scale |
title_fullStr | Special Relativity at the Quantum Scale |
title_full_unstemmed | Special Relativity at the Quantum Scale |
title_short | Special Relativity at the Quantum Scale |
title_sort | special relativity at the quantum scale |
topic | Research Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4274123/ https://www.ncbi.nlm.nih.gov/pubmed/25531675 http://dx.doi.org/10.1371/journal.pone.0115810 |
work_keys_str_mv | AT lampuik specialrelativityatthequantumscale |