经典物理学中的不兼容的可观测量:在哈密尔顿力学中更仔细地观察测量
1Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
Physical review. E
|September 19, 2024
概括
经典物理学可能有类似于量子力学的测量限制. 测量一个属性不可避免地会扰乱其他不通勤的属性,揭示了一个经典的不确定性关系,对测量科学有影响.
科学领域:
- 物理学的基础 物理学的基础
- 经典机械 经典机械 经典机械
- 量子测量理论 量子测量理论
背景情况:
- 量子理论假设不兼容的测量,其中某些可观察到的对不能同时以任意精度知道,这与非通勤运算符相关的现象.
- 古典物理学,尽管在波桑括号和通换器之间存在平行,但缺乏其代数结构和测量局限性之间的内在联系.
- 主流观点认为测量不兼容性是一种独特的量子力学特征.
研究的目的:
- 为了研究经典哈密尔顿物理学中的测量局限性.
- 为了建立经典测量干扰和Poisson代数之间的联系.
- 探索测量不兼容性是否仅限于量子力学.
主要方法:
- 检查了古典测量作为一个系统和有限温度测量装置的共同演变.
- 推导出一个精度-干扰关系,类似于海森伯格的不确定性原理,用于经典的可观测物.
- 分析了Ozawa量子测量模型的经典适应.
主要成果:
- 确定了一个经典的海森伯格式的精度-干扰关系:测量一个可观测的干扰非Poisson-通勤可观测的.
- 经典的不确定性关系涉及一个设备特定的数量 (q-bar) 取代普朗克常数 (h-bar),这是有限的非零绝对温度.
- 经典的Ozawa模型没有违反衍生的经典关系,这表明不兼容可能是一个经典的现象.
结论:
- 测量不兼容性可能不仅仅是量子现象,也可能是古典物理学的特征.
- 经典物理学可能拥有一个非微不足道的贝叶斯认识论,与量子力学有形式上的相似之处.
- 结果表明在精度测量,纳米工程和分子机器方面有潜在的应用,并为量子基础研究提供了见解.
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