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arXiv 1111.0457gr-qchep-thquant-ph
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量子宇宙学中时间的突现性与复数

The emergent nature of time and the complex numbers in quantum cosmology

G. W. Gibbons

摘要:

在量子力学中,时间的本质与使用复希尔伯特空间(而不是实希尔伯特空间)密切相关。当我们在时间相关的背景下考虑量子场论时,例如在宇宙学中,当正频率的概念不再被很好地定义时,这一点变得特别清楚。在缺乏时间取向的时空中,即没有可能定义时间之箭的时空中,人们被迫放弃复杂的量子力学。在量子宇宙学中,人们也必须面对这个问题。我用这一点来论证,这表明,在基本层面上,量子力学可能是真正的,而不是一个,而是大量的复杂结构。我将这些想法与其他建议,在量子引力时间演化可能不是单一的,可能实现的超散射矩阵,和CPT的状态。

英文摘要:

The nature of time in quantum mechanics is closely related to the use of a complex, rather than say real, Hilbert space. This becomes particularly clear when considering quantum field theory in time dependent backgrounds, such as in cosmology, when the notion of positive frequency ceases to be well defined. In spacetimes lacking time orientation, i.e without the possibility of defining an arrow of time, one is forced to abandon complex quantum mechanics. One also has to face this problem in quantum cosmology. I use this to argue that this suggests that, at a fundamental level, quantum mechanics may be really real with not one, but a multitude of complex structures. I relate these ideas to other suggestions that in quantum gravity time evolution may not be unitary, possibly implemented by a super-scattering matrix, and the status of CPT.

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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