Time Dilation in Relativistic Quantum Decay Laws of Moving Unstable Particles
The relativistic quantum decay laws of moving unstable particles are analyzed for a general class of mass distribution densities which behave as power laws near the (nonvanishing) lower bound μ0 of the mass spectrum. The survival probability Pp(t), the instantaneous mass Mp(t), and the instantaneous...
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Wiley
2018-01-01
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| Series: | Advances in High Energy Physics |
| Online Access: | http://dx.doi.org/10.1155/2018/7308935 |
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| author | Filippo Giraldi |
| author_facet | Filippo Giraldi |
| author_sort | Filippo Giraldi |
| collection | DOAJ |
| description | The relativistic quantum decay laws of moving unstable particles are analyzed for a general class of mass distribution densities which behave as power laws near the (nonvanishing) lower bound μ0 of the mass spectrum. The survival probability Pp(t), the instantaneous mass Mp(t), and the instantaneous decay rate Γp(t) of the moving unstable particle are evaluated over short and long times for an arbitrary value p of the (constant) linear momentum. The ultrarelativistic and nonrelativistic limits are studied. Over long times, the survival probability Pp(t) is approximately related to the survival probability at rest P0(t) by a scaling law. The scaling law can be interpreted as the effect of the relativistic time dilation if the asymptotic value Mp∞ of the instantaneous mass is considered as the effective mass of the unstable particle over long times. The effective mass has magnitude μ0 at rest and moves with linear momentum p or, equivalently, with constant velocity 1/1+μ02/p2. The instantaneous decay rate Γp(t) is approximately independent of the linear momentum p, over long times, and, consequently, is approximately invariant by changing reference frame. |
| format | Article |
| id | doaj-art-41bcc030af31441fbe308de8b96cc8fe |
| institution | Kabale University |
| issn | 1687-7357 1687-7365 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in High Energy Physics |
| spelling | doaj-art-41bcc030af31441fbe308de8b96cc8fe2025-08-20T03:55:40ZengWileyAdvances in High Energy Physics1687-73571687-73652018-01-01201810.1155/2018/73089357308935Time Dilation in Relativistic Quantum Decay Laws of Moving Unstable ParticlesFilippo Giraldi0School of Chemistry and Physics, University of KwaZulu-Natal and National Institute for Theoretical Physics (NITheP), Westville Campus, Durban 4001, South AfricaThe relativistic quantum decay laws of moving unstable particles are analyzed for a general class of mass distribution densities which behave as power laws near the (nonvanishing) lower bound μ0 of the mass spectrum. The survival probability Pp(t), the instantaneous mass Mp(t), and the instantaneous decay rate Γp(t) of the moving unstable particle are evaluated over short and long times for an arbitrary value p of the (constant) linear momentum. The ultrarelativistic and nonrelativistic limits are studied. Over long times, the survival probability Pp(t) is approximately related to the survival probability at rest P0(t) by a scaling law. The scaling law can be interpreted as the effect of the relativistic time dilation if the asymptotic value Mp∞ of the instantaneous mass is considered as the effective mass of the unstable particle over long times. The effective mass has magnitude μ0 at rest and moves with linear momentum p or, equivalently, with constant velocity 1/1+μ02/p2. The instantaneous decay rate Γp(t) is approximately independent of the linear momentum p, over long times, and, consequently, is approximately invariant by changing reference frame.http://dx.doi.org/10.1155/2018/7308935 |
| spellingShingle | Filippo Giraldi Time Dilation in Relativistic Quantum Decay Laws of Moving Unstable Particles Advances in High Energy Physics |
| title | Time Dilation in Relativistic Quantum Decay Laws of Moving Unstable Particles |
| title_full | Time Dilation in Relativistic Quantum Decay Laws of Moving Unstable Particles |
| title_fullStr | Time Dilation in Relativistic Quantum Decay Laws of Moving Unstable Particles |
| title_full_unstemmed | Time Dilation in Relativistic Quantum Decay Laws of Moving Unstable Particles |
| title_short | Time Dilation in Relativistic Quantum Decay Laws of Moving Unstable Particles |
| title_sort | time dilation in relativistic quantum decay laws of moving unstable particles |
| url | http://dx.doi.org/10.1155/2018/7308935 |
| work_keys_str_mv | AT filippogiraldi timedilationinrelativisticquantumdecaylawsofmovingunstableparticles |