对于狄拉克与朗道关于量子测量观念的冲突,考虑爱因斯坦与波尔关于物理实在论的争论和牛顿的关于测量的观点,借鉴经典物理实验的直接测量和间接测量的概念,本文尝试在量子力学框架内提出相应的概念,探讨将狄拉克的量子测量观念与朗道的部分观念,在量子力学中进行兼容。 For the conflict between the measurement ideas of Dirac and Landau, considering the argument about the physical reality between Einstein and Bohr, and Newton’s measurement idea, using the concepts of direct measurement and indirect measurement in classical physical experiments for reference, we try to put forward the corresponding concepts within the framework of quantum mechanics, and discuss the compatibility between Dirac’s measurement idea and a part of Lan-dau’s in quantum mechanics.
相互作用,被测系统与仪器状态变化,间接测量,直接测量,不同本征值的差值, Interaction Changes of States of Measured System and Instrument Indirect Measurement
Direct Measurement Difference of Different Eigenvalues狄拉克与朗道关于量子测量观念的冲突与部分兼容的探讨
狄拉克的量子力学论著中 [1] 有这样的叙述:“From physical continuity, if we make a second measurement of the same dynamical variable ξ immediately after the first, the result of the second measurement must be the same as that of the first. Hence after the first measurement has been made, the system is in an eigenstate of the dynamical variable, the eigenvalue it belongs to being equal to the result of the first measurement.” 这里译为:“由物理的连续性,如果第一次测量后,立即对相同的动力学变量ξ进行第二次测量,其结果必定与第一次的相同。因此,第一次测量完成之后,系统处于这个动力学变量的一个本征态,其本征值等于第一次测量结果。”这仍然是主流的量子测量的观念 [2] ,但也有论著没有涉及这种量子测量观念 [3] 。
(这是纠缠态,书中没有提到这一概念),能够以不同概率测到不同值fn。测量后的,除去一个概率幅的因子,就是电子的波函数。这一组函数并不正交,也不构成任一算符的本征函数组。这样量子力学中的测量结果是无法重现的。测量后,该电子就处于不同于初态的状态,量f一般不再取任何定值。对该电子紧接着作第二次测量时,会得到不同于第一次测得值。这最后两句的英文版书中的叙述为 [5] “After the measurement, however, the electron is in a state different from its initial one, and in this state the quantity f does not in general take any definite value. Hence, on carrying out a second measurement on the electron immediately after the first, we should obtain for f a value which did not agree with that obtained from the first measurement.”
牛顿对于测量有这样的观点 [9] :“Relative quantities are not the actual quantities whose names they bear but those sensible measures of them (whether true or erroneous) that are commonly used instead of the quantities being measured.” 参考中译本 [10] ,这里译为,相对的量并不是负有其名的那些量本身,而是这些量的可感知的度量(精确地或不精确地),它们通常用以代替被测的量。牛顿的观点,对于宏观系统的测量,相对(可感知)的量与量的本身常常不做区别;而用于微观系统的测量,在本文后面说明,直接测量的量显出了相对(可感知)的量与量的本身的区别。
关于量子测量的文献 [6] 中也给出了direct measurement (直接测量)和indirect measurement (间接测量)的定义。直接测量是:The measured object interacts directly with the classical measuring device are called “direct measurement”;间接测量是:An indirect measurement is a two-step process. In the first step the object interacts with a quantum system that has been prepared in advance in some special initial quantum state. This quantum system is called the “quantum probe.” The second step is a direct measurement of some chosen observable of the quantum probe。在量子力学的许多著作 [1] [2] [3] [4] [5] [14] - [22] 中都没有出现直接测量和间接测量的概念。
曾天海. 狄拉克与朗道关于量子测量观念的冲突与部分兼容的探讨Discussion of the Conflict and a Partial Compatibility between the Measurement Ideas of Dirac and Landau[J]. 现代物理, 2016, 06(06): 177-182. http://dx.doi.org/10.12677/MP.2016.66017
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