arXiv 0912.28452009-12quant-ph

非线性量子力学、叠加原理和量子测量问题

Nonlinear quantum mechanics, the superposition principle, and the quantum measurement problem

Kinjalk Lochan, T. P. Singh

备注：: Minor revision in Introduction. 23 pages. To appear in Pramana J. Phys

摘要：

我们目前对量子力学的知识和理解之所以被认为是不完整的，有四个原因。首先，线性叠加原理还没有在实验上测试过具有超过一千个原子的物体的位置本征态。第二，对于量子测量的过程没有一个普遍接受的解释。第三，对于观察到的事实，即宏观物体不是在位置本征态的叠加中发现的，没有普遍同意的解释。第四，也许也是最重要的，时间的概念是经典的，因此是量子力学之外的：应该存在一个不涉及外部经典时间的理论的等价重新表述。在本文中，我们认为，这样的重新制定的非线性量子理论的极限情况下，与非线性变得重要的普朗克质量尺度。这种非线性可以提供对上述问题的见解。我们使用一个物理激励模型的非线性薛定谔方程，以表明非线性可以帮助理解量子测量。我们还表明，虽然线性叠加的原则，原子系统的精度非常高，量子叠加的寿命变得越来越小，从微观到宏观对象。这可以解释在宏观物体中观察到的位置叠加的缺失[寿命太小]。它还表明，在可预见的未来，正在进行的实验室实验可能能够检测到介观物体的有限叠加寿命。

英文摘要：

There are four reasons why our present knowledge and understanding of quantum mechanics could be regarded as incomplete. Firstly, the principle of linear superposition has not been experimentally tested for position eigenstates of objects having more than about a thousand atoms. Secondly, there is no universally agreed upon explanation for the process of quantum measurement. Thirdly, there is no universally agreed upon explanation for the observed fact that macroscopic objects are not found in superposition of position eigenstates. Fourthly, and perhaps most importantly, the concept of time is classical and hence external to quantum mechanics : there should exist an equivalent reformulation of the theory which does not refer to an external classical time. In this paper we argue that such a reformulation is the limiting case of a nonlinear quantum theory, with the nonlinearity becoming important at the Planck mass scale. Such a nonlinearity can provide insights into the problems mentioned above. We use a physically motivated model for a nonlinear Schrodinger equation to show that nonlinearity can help in understanding quantum measurement. We also show that while the principle of linear superposition holds to a very high accuracy for atomic systems, the lifetime of a quantum superposition becomes progressively smaller, as one goes from microscopic to macroscopic objects. This can explain the observed absence of position superpositions in macroscopic objects [lifetime is too small]. It also suggests that ongoing laboratory experiments maybe able to detect the finite superposition lifetime for mesoscopic objects, in the foreseeable future.

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