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.

我们建议无论控制海森堡不确定性关系的数量（对于给定的互补可观察对），都应使用有效的普朗克参数进行识别。有了这个定义，不难发现普朗克参数取决于研究区域，时间变化，甚至取决于人们关注哪对可观察物的例子。在量子宇宙学中，有效的普朗克参数取决于所研究的共同移动区域的大小，因此取决于所选择的区域和时间。使用此标准，期望的是经典极限，而不是对于大于Planck长度\（l_ {P} \）的区域，而是对于大于\（l_ {Q} =（l_ {P} ^ {2} H ^ {-1}）^ {1/3} \），其中H是哈勃参数。在宇宙常数是动态的理论中，即使在其他一切都被视为经典的情况下，宇宙常数也可能保持量子。这些结果来自标准的量化方法，但我们还包括更多的推测性案例，其中特设的普朗克参数随所观察的长度尺度而变化。从推测的角度出发，我们进一步研究类似的互补概念影响热力学变量（例如温度和黑洞的熵）的可能性。