关于传统量子理论在量子引力中的地位的思考
Some Reflections on the Status of Conventional Quantum Theory when Applied to Quantum Gravity
摘要：
目前所有的量子引力方法基本上都采用标准的量子理论，特别是包括连续统量，如实数或复数。然而，我想指出，这可能是根本错误的，因为在标准量子理论中使用这些连续统量可以追溯到关于空间和时间性质的某些{ \em a priori}假设：这些假设可能与量子引力理论所采用的空间和时间观点不相容。我的猜想是，在某种尚未确定的意义上，每一种时空都有一种相应的量子理论，在这种量子理论中，连续统量不一定出现，而是被适合于特定时空的结构所取代。于是，Topos理论作为一种可能的工具出现了，它把与不同时空有关的这些不同理论“粘合”在一起。作为一个具体的例子，使用拓扑思想，我总结了最近的工作应用预层理论的科赫-Specher定理和分配值的物理量在量子理论。
英文摘要：
All current approaches to quantum gravity employ essentially standard quantum theory including, in particular, continuum quantities such as the real or complex numbers. However, I wish to argue that this may be fundamentally wrong in so far as the use of these continuum quantities in standard quantum theory can be traced back to certain {\em a priori} assumptions about the nature of space and time: assumptions that may be incompatible with the view of space and time adopted by a quantum gravity theory. My conjecture is that in, some yet to be determined sense, to each type of space-time there is associated a corresponding type of quantum theory in which continuum quantities do not necessarily appear, being replaced with structures that are appropriate to the specific space-time. Topos theory then arises as a possible tool for `gluing' together these different theories associated with the different space-times. As a concrete example of the use of topos ideas, I summarise recent work applying presheaf theory to the Kochen-Specher theorem and the assignment of values to physical quantities in a quantum theory.
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