宇宙是离散的还是连续的？Is the Universe Discrete or Continuous?
Naval： 你说过，我们从德谟克利特时代的原子开始，往下到原子核，再到质子和中子，然后是夸克。借用费曼的话说，一路往下都是粒子。我们可以一直分下去。但并不是真的永远，对吧？到某个时候，你会撞上普朗克长度（Planck length）。
Brett： 有普朗克时间，有普朗克长度，甚至还有普朗克质量——那其实是一个相当大的质量。这些东西并没有什么物理意义。普朗克时间并不是最短的可能时间，普朗克长度也不是最短的可能长度。原因在于，这些普朗克量属于量子理论的范畴。但长度并不是由量子理论描述的，而是由广义相对论（general theory of relativity）描述的。在那个理论中，空间是无限可分的，不存在最短的可能长度或时间。
这揭示出分立与连续之间一种古老的紧张关系。量子理论似乎表明事物是分立的。例如，存在最小的金粒子——金原子；存在最小的电粒子——电子；存在最小的光粒子——光子。在量子理论中，我们有"分立性"这种观念，即存在一种最小的东西，其他一切皆由它构成。
但在广义相对论中，观念恰恰相反。它认为事物可以连续变化，而且数学要求事物必须是连续可变的，这样才能被微分等等。它的理念是，你可以无限地分割空间，也可以无限地分割时间。
物理学家明白，在我们物理学最基础的解释的最深层，存在着这一矛盾。这也是人们不断尝试统一量子理论和广义相对论的原因之一。现实的根本性质到底是什么？是事物可以无限分割，还是我们必须在某个地方停下来？如果它是无限可分的，那么量子理论可能不得不屈从于广义相对论。我们只是不知道。
Naval: You said that we went from atoms in the time of Democrates, down to nuclei, and from there to protons and neutrons, and then to quarks. It’s particles all the way down, to paraphrase Feynman. We can keep going forever. But it’s not quite forever, right? At some point you run into the Planck length.
Brett: There’s the Planck time, there’s the Planck length, there’s even the Planck mass, which is actually quite a large mass. These things don’t have any physical significance. It’s not like the Planck time is the shortest possible time, and it’s not like the Planck length is the shortest possible length. The reason for that is because these Planck things are part of quantum theory. But length is not described by quantum theory. It’s described by the general theory of relativity. And in that theory, space is infinitely divisible. There is no smallest possible length or time.
This illuminates an ancient tension between the discrete and the continuous. Quantum theory seems to suggest that things are discrete. For example, there’s the smallest possible particle of gold, the gold atom. There’s the smallest possible particle of electricity, the electron. There’s the smallest possible particle of light, the photon. In quantum theory, we have this idea of discreteness, that there is the smallest possible thing from which everything else is built.
But in general relativity, the idea is the opposite. It says things can continuously vary, and the mathematics requires that things be continuously variable so they can be differentiated and so on. The idea is that you can keep on dividing up space and you can keep on dividing up time.
Physicists understand that there is this contradiction at the deepest level of our most foundational explanations in physics. It’s one of the reasons why there are these attempts to try and unify quantum theory and general relativity. What is the fundamental nature of reality? Is it that things can be infinitely divisible, or is that we must stop somewhere or other? If it’s infinitely divisible, then quantum theory might have to be subservient to general relativity. We just don’t know.