From the arrow of time in Badiali's quantum approach to the dynamic meaning of Riemann's hypothesis
The novelty of the Jean Pierre Badiali last scientific works stems to a quantum approach based on both (i) a return to the notion of trajectories (Feynman paths) and (ii) an irreversibility of the quantum transitions. These iconoclastic choices find again the Hilbertian and the von Neumann algebra...
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| Дата: | 2017 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут фізики конденсованих систем НАН України
2017
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| Назва видання: | Condensed Matter Physics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/157007 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | From the arrow of time in Badiali's quantum approach to the dynamic meaning of Riemann's hypothesis / P. Riot, A. Le Méhauté // Condensed Matter Physics. — 2017. — Т. 20, № 3. — С. 33001: 1–13. — Бібліогр.: 51 назв. — англ. |
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irk-123456789-1570072019-06-20T01:27:06Z From the arrow of time in Badiali's quantum approach to the dynamic meaning of Riemann's hypothesis Riot, P. A. Le Méhauté The novelty of the Jean Pierre Badiali last scientific works stems to a quantum approach based on both (i) a return to the notion of trajectories (Feynman paths) and (ii) an irreversibility of the quantum transitions. These iconoclastic choices find again the Hilbertian and the von Neumann algebraic point of view by dealing statistics over loops. This approach confers an external thermodynamic origin to the notion of a quantum unit of time (Rovelli Connes’ thermal time). This notion, basis for quantization, appears herein as a mere criterion of parting between the quantum regime and the thermodynamic regime. The purpose of this note is to unfold the content of the last five years of scientific exchanges aiming to link in a coherent scheme the Jean Pierre’s choices and works, and the works of the authors of this note based on hyperbolic geodesics and the associated role of Riemann zeta functions. While these options do not unveil any contradictions, nevertheless they give birth to an intrinsic arrow of time different from the thermal time. The question of the physical meaning of Riemann hypothesis as the basis of quantum mechanics, which was at the heart of our last exchanges, is the backbone of this note. Новизна останнiх наукових робiт Жана-П’єра Бадiалi бере початок з квантового пiдходу, який базується на (i) поверненнi до поняття траєкторiй (траєкторiї Фейнмана), а також на (ii) необоротностi квантових переходiв. Цi iконокластичнi варiанти знову встановлюють гiльбертiан i алгебраїчну точку зору фон Неймана, маючи справу зi статистикою за циклами. Цей пiдхiд надає зовнiшню термодинамiчну першопричину поняттю квантової одиницi часу (термальний час Ровеллi Коннеса). Це поняття, базис для квантування, виникає тут як простий критерiй розрiзнення мiж квантовим режимом i термодинамiчним режимом. Мета цiєї статтi є розкрити змiст останнiх п’яти рокiв наукових дискусiй, нацiлених з’єднати в когерентну схему як уподобання i роботи Жана-П’єра, так i роботи авторiв цiєї статтi на основi гiперболiчної геодезiї, i об’єднуючу роль дзета-функцiї Рiмана. Хоча цi варiанти не представляють жодних протирiч, тим не менше, вони породжують власну стрiлу часу, iнакшу нiж термальний час. Питання фiзичного змiсту гiпотези Рiмана як основи квантової механiки, що було в центрi наших останнiх дискусiй, є суттю цiєї статтi. 2017 Article From the arrow of time in Badiali's quantum approach to the dynamic meaning of Riemann's hypothesis / P. Riot, A. Le Méhauté // Condensed Matter Physics. — 2017. — Т. 20, № 3. — С. 33001: 1–13. — Бібліогр.: 51 назв. — англ. 1607-324X PACS: 05.30.-d, 05.45.-a, 11.30.-j, 03.65.Vf DOI:10.5488/CMP.20.33001 arXiv:1710.01558 http://dspace.nbuv.gov.ua/handle/123456789/157007 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
The novelty of the Jean Pierre Badiali last scientific works stems to a quantum approach based on both (i) a
return to the notion of trajectories (Feynman paths) and (ii) an irreversibility of the quantum transitions. These
iconoclastic choices find again the Hilbertian and the von Neumann algebraic point of view by dealing statistics
over loops. This approach confers an external thermodynamic origin to the notion of a quantum unit of time
(Rovelli Connes’ thermal time). This notion, basis for quantization, appears herein as a mere criterion of parting
between the quantum regime and the thermodynamic regime. The purpose of this note is to unfold the content
of the last five years of scientific exchanges aiming to link in a coherent scheme the Jean Pierre’s choices and
works, and the works of the authors of this note based on hyperbolic geodesics and the associated role of
Riemann zeta functions. While these options do not unveil any contradictions, nevertheless they give birth to
an intrinsic arrow of time different from the thermal time. The question of the physical meaning of Riemann
hypothesis as the basis of quantum mechanics, which was at the heart of our last exchanges, is the backbone
of this note. |
| format |
Article |
| author |
Riot, P. A. Le Méhauté |
| spellingShingle |
Riot, P. A. Le Méhauté From the arrow of time in Badiali's quantum approach to the dynamic meaning of Riemann's hypothesis Condensed Matter Physics |
| author_facet |
Riot, P. A. Le Méhauté |
| author_sort |
Riot, P. |
| title |
From the arrow of time in Badiali's quantum approach to the dynamic meaning of Riemann's hypothesis |
| title_short |
From the arrow of time in Badiali's quantum approach to the dynamic meaning of Riemann's hypothesis |
| title_full |
From the arrow of time in Badiali's quantum approach to the dynamic meaning of Riemann's hypothesis |
| title_fullStr |
From the arrow of time in Badiali's quantum approach to the dynamic meaning of Riemann's hypothesis |
| title_full_unstemmed |
From the arrow of time in Badiali's quantum approach to the dynamic meaning of Riemann's hypothesis |
| title_sort |
from the arrow of time in badiali's quantum approach to the dynamic meaning of riemann's hypothesis |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2017 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/157007 |
| citation_txt |
From the arrow of time in Badiali's quantum approach to the dynamic meaning of Riemann's hypothesis / P. Riot, A. Le Méhauté // Condensed Matter Physics. — 2017. — Т. 20, № 3. — С. 33001: 1–13. — Бібліогр.: 51 назв. — англ. |
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Condensed Matter Physics |
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