希尔伯特第六问题的解：终极伽利略革命
The solution of the Sixth Hilbert Problem: the Ultimate Galilean Revolution
摘要：
我主张一个完整的物理理论，包括它的公理，其中必须包含没有物理原语。用煽动性的话来说：“来自非物理学的物理学”。虽然这看起来似乎是一种矛盾修饰法，但这是保持完全逻辑连贯性的捷径，因此理论是可证伪的。对于这样一个纯粹的数学理论，其物理内涵必须只与从公理到最终定理的数学解释有关。相反，当前两个主要物理理论的假设要么没有物理解释（如冯诺依曼的量子理论公理），要么包含物理原语，如“时钟”，“刚性杆“，“力”，“惯性质量“（如狭义相对论和力学）。这里提出的纯数学理论，尽管其适用范围有限（但不断扩大），但将具有数学真理的永恒有效性。这将是自然科学可以坚定依赖的理论。这种理论就是我认为的希尔伯特第六问题的解决方案。我认为，这样一个数学理论的原型例子是由物理学的新算法范式提供的，如在最近的量子理论和自由量子场论的信息理论推导。
英文摘要：
I argue for a full mathematisation of the physical theory, including its axioms, which must contain no physical primitives. In provocative words: "physics from no physics". Although this may seem an oxymoron, it is the royal road to keep complete logical coherence, hence falsifiability of the theory. For such a purely mathematical theory the physical connotation must pertain only the interpretation of the mathematics, ranging from the axioms to the final theorems. On the contrary, the postulates of the two current major physical theories either don't have physical interpretation (as for von Neumann's axioms for quantum theory), or contain physical primitives as "clock", "rigid rod ", "force", "inertial mass" (as for special relativity and mechanics). A purely mathematical theory as proposed here, though with limited (but relentlessly growing) domain of applicability, will have the eternal validity of mathematical truth. It will be a theory on which natural sciences can firmly rely. Such kind of theory is what I consider to be the solution of the Sixth Hilbert's Problem. I argue that a prototype example of such a mathematical theory is provided by the novel algorithmic paradigm for physics, as in the recent information-theoretical derivation of quantum theory and free quantum field theory.
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