On Particle Phenomenology Without Particle Ontology: How Much Local Is Almost Local?
On Particle Phenomenology Without Particle Ontology: How Much Local Is Almost Local?
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论没有粒子本体论的粒子现象学：多少局部性几乎是局部性的？
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
Chrysovalantis Stergiou
中科院分区：
文献类型：
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作者：
Aristidis Arageorgis;Chrysovalantis Stergiou
最近，克利夫顿和哈尔沃森试图在代数相对论量子场论中的粒子本体论缺失的情况下挽救粒子现象学。他们的想法是，粒子的探测是对局部可观测粒子的测量，该测量模拟了几乎局部可观测粒子湮没真空的测量。在这篇笔记中，我们认为局域粒子探测的测量应该从根本上模拟相对论量子场的探测整体方面。证明了在希尔伯特空间中建立的关于Minkowski时空的公理(Haag-Araki)量子场论中，不存在范数小于等于1的正可观量C，且满足以下条件：(1)真空态Ω中C的期望值为零，(2)在数学{H}中至少存在一个向量态Ψ，其中C的期望值不为零，以及(3)至少存在一个时空区域$mathcal{O}$，使得对C的非选择性测量使该区域的局部代数中所有可观测的期望值保持不变，而不管系统处于什么状态。这一结果揭示了关于局部性的直觉和关于因果关系的直觉之间的紧张关系：为了在缺乏粒子本体论的情况下挽救“粒子现象”，一个人必须假装具有关于局部性的“好”属性而关于因果关系的“坏”行为的“粒子”探测器。
Recently, Clifton and Halvorson have tried to salvage a particle phenomenology in the absence of particle ontology within algebraic relativistic quantum field theory. Their idea is that the detection of a particle is the measurement of a local observable which simulates the measurement of an almost local observable that annihilates the vacuum. In this note, we argue that the measurements local particle detections are supposed to simulate probe radically holistic aspects of relativistic quantum fields. We prove that in an axiomatic (Haag-Araki) quantum field theory on Minkowski spacetime, formulated in a Hilbert space $mathcal{H}$, there is no positive observable C, with norm less than or equal to 1, satisfying the conditions: (1) the expectation value of C in the vacuum state Ω is zero, (2) there is at least one vector state Ψ in $mathcal{H}$ in which the expectation value of C is different from zero, and (3) there exists at least one spacetime region $mathcal{O}$ such that the non-selective measurement of C leaves the expectation values of all observables in the local algebra of that region unaltered regardless of the state the system is in. The result reveals a tension between intuitions regarding localization and intuitions regarding causality: to save “particle phenomena” in the absence of particle ontology, one has to feign “particle” detectors with “good” properties as to locality but “bad” behavior as to causality.