论文标题
上下文的普朗克参数和量子宇宙学的经典限制
A contextual Planck parameter and the classical limit in quantum cosmology
论文作者
论文摘要
我们建议，任何数量控制着海森堡的不确定性关系（对于给定的互补可观察对），应使用有效的Planck参数识别。通过此定义，不难找到普朗克参数取决于所研究区域的示例，时间有所不同，甚至取决于一个专注于哪一对可观察结果。在量子宇宙学中，有效的planck参数取决于所研究的共同体区域的大小，因此取决于所选区域和时间。使用此标准，可以预期经典限制，而不是大于planck长度的区域，$ l_ {p} $，而是对于大于$ l_ {q} =（l_ {p}^{2} h^{ - 1}} h^{ - 1}）^{1/3} $的那些大于$ l_ {q} =（l_ {p}^{2}^{2} h $ h $ h $ as是hubble parameter。在宇宙常数是动力学的理论中，即使在其他所有事物都被认为是经典的情况下，后者也可以保持量子。这些结果源自标准量化方法，但我们还包括更多的投机案例，其中临时Planck参数随着观察的长度尺度的规模不同。更像是，我们研究了类似互补概念影响热力学变量的可能性，例如温度和黑洞的熵。
We propose that whatever quantity controls the Heisenberg uncertainty relations (for a given complementary pair of observables) it should be identified with an effective Planck parameter. With this definition it is not difficult to find examples where the Planck parameter depends on the region under study, varies in time, and even depends on which pair of observables one focuses on. In quantum cosmology the effective Planck parameter depends on the size of the comoving region under study, and so depends on that chosen region and on time. With this criterion, the classical limit is expected, not for regions larger than the Planck length, $l_{P}$, but for those larger than $l_{Q}=(l_{P}^{2}H^{-1})^{1/3}$, where $H$ is the Hubble parameter. In theories where the cosmological constant is dynamical, it is possible for the latter to remain quantum even in contexts where everything else is deemed classical. These results are derived from standard quantization methods, but we also include more speculative cases where ad hoc Planck parameters scale differently with the length scale under observation. Even more speculatively, we examine the possibility that similar complementary concepts affect thermodynamical variables, such as the temperature and the entropy of a black hole.
