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arXiv 2207.02689gr-qc
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宇宙的诞生是度量签名变化的结果

The birth of the Universe as a result of the change of the metric signature

T. P. Shestakova

摘要:

在本文中,我讨论的想法,我们的宇宙的诞生可能是一个结果的量子跃迁从一个物理连续与欧几里德签名的洛伦兹时空。安德烈·D.萨哈罗夫在古典主义的层面上,乔治·F. R.埃利斯和他的合作者,他们探索了经典爱因斯坦方程的解是否存在,它允许度量签名的变化。本文旨在探讨这一思想在量子引力水平上、在Wheeler-DeWitt理论框架内以及在引力量子化的扩展相空间方法中的可能实现。我打算回答这样的问题:哈特尔-霍金波函数是否意味着这样的实现?在量子引力的扩展相空间方法中,通过对物理连续统不同区域中度规的分量$g_{00}$施加特殊条件来描述签名的变化,如何实现这一想法?结论是,这个想法可以从形式的数学观点来实现,但它几乎不能帮助理解时空结构和时间本身是如何从一个无时间连续体中出现的。

英文摘要:

In this paper, I discuss the idea that the birth of our Universe may be a result of a quantum transition from a physical continuum with the Euclidean signature to a Lorentzian spacetime. A similar idea was expressed by Andrei D. Sakharov. At the classical level, the idea was studied by George F. R. Ellis and his collaborators, who explored if solutions to the classical Einstein equation exist which admit a change of metric signature. The present paper aims at examining possible realizations of this idea at the level of quantum gravity, in the framework of the Wheeler - DeWitt theory and in the extended phase space approach to quantization of gravity. I intend to answer the questions: Does the Hartle - Hawking wave function imply such a realization? How can this idea be realized in the extended phase space approach to quantum gravity, where the change of signature is described by imposing special conditions on $g_{00}$-component of the metric in different regions of the physical continuum? The conclusion is that the idea can be realized from a formal mathematical point of view, but it can hardly help in understanding how spacetime structure and time itself appeared from a timeless continuum.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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