Relativistic generalization of the Schrödinger-Newton model for the wavefunction reduction

We consider the model of the self-gravity driven spontaneous wavefunction reduction proposed by L. Diosi, R. Penrose et al. and based on a self-consistent system of Schrödinger and Poisson equations. An analogous system of coupled Dirac and Maxwell-like equations is proposed as a relativization. Regular solutions to the latter form a discrete spectrum in which all the "active" gravitational masses are always positive, and approximately equal to inertial masses and to the mass m of the quanta of Dirac field up to the corrections of order α2. Here α = (m/Mpl)2 is the gravitational analogue of the fine structure constant negligibly small for nucleons. In the limit α = 0 the model reduces back to the nonrelativistic Schrödinger-Newton one. The equivalence principle is fulfilled with an extremely high precision. The above solutions correspond to various states of the same (free) particle rather than to different particles. These states possess a negligibly small difference in characteristics but essentially differ in the widths of the wavefunctions. For the ground state the latter is α times larger the Compton length, so that a nucleon cannot be sufficiently localized to model the reduction process. © 2020 World Scientific Publishing Company.

Авторы
Редакторы
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Издательство
World Scientific Publishing Co. Pte Ltd
Номер выпуска
-
Язык
Английский
Страницы
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Статус
Опубликовано
Подразделение
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Номер
2040017
Том
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Год
2020
Организации
  • 1 Institute of Gravitation and Cosmology, Peoples' Friendship University of Russia, 6, Miklukho-Maklaya Str., Moscow, 117198, Russian Federation
  • 2 Mathematical Institute, Peoples' Friendship University of Russia, 6, Miklukho-Maklaya Str., Moscow, 117198, Russian Federation
Ключевые слова
equivalence principle; gravitational self-interaction; Regular solutions
Дата создания
10.02.2020
Дата изменения
10.02.2020
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/56540/