观察者议会——反对量子力学的可观测量公理
The parliament of observers - Against the observable axiom of quantum mechanics
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中文总结 AI 辅助
本文挑战量子力学中可观测量与自伴算子对应的基本公理，指出其作为所有可观测量的形式化不充分，并质疑有界算子非交换代数作为“可观测量代数”的合理性。
中文摘要 AI 辅助
“数学在自然科学中不可思议的有效性”有时会给人留下这样的印象：自然科学，尤其是现代理论物理学，不过是一套形式化的装置。然而，物理学的一个关键挑战仍然是将日常经验的概念——无论是直接的还是通过任意复杂度的仪器中介的——与其数学形式化相对齐。这一点尤其适用于量子理论，它可以说是物理学史上最成功的理论。其核心假设之一假定：$可观测量与自伴算子相对应。$在这里，我们认为，量子形式主义的这一最基本前提在仔细审视下已然瓦解，至少当它被理解为同时适用于所有可观测量时是如此。换言之，我们挑战有界算子的非交换代数作为“可观测量代数”的充分形式化的角色，该代数被理解为允许一致经验解释的测量程序（的等价类）。
英文摘要
The 'unreasonable effectiveness of mathematics in the natural sciences' may at times give the impression that natural science, especially modern theoretical physics, is all but a formal apparatus. However, a key challenge of physics remains to align everyday notions of experience -- be it directly or mediated through instruments of arbitrary sophistication -- with their mathematical formalisation. This applies in particular to quantum theory, arguably the most successful theory of physics ever invented. One of its core assumptions postulates: $Observables\ correspond\ with\ self-adjoint\ operators.$ Here, we argue that already this most basic premise about the quantum formalism falls apart under careful scrutiny, at least when understood for all observables at once. In other words, we challenge the role of the noncommutative algebra of bounded operators as an adequate formalisation of the 'algebra of observables', understood as (equivalence classes of) measurement procedures that admit a coherent empirical interpretation.
发表机构
- Leibniz Universität Hannover（汉诺威莱布尼茨大学）
机构由 AI 辅助整理，请以论文原文为准。
