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关于量子力学的时间对称表述

On a Time Symmetric Formulation of Quantum Mechanics

B. Reznik, Y. Aharonov

备注：
LaTex, 44 pages, 4 figures included. Figure captions and related text in sections 3.1, 4.2 are revised. A paragraph in pages 9-10 about non-generic two-states is clarified. Footnotes added
发表信息：
Phys. Rev. A 52, 2538 (1995).
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摘要：

我们进一步探讨的建议，描述一个预先和后选择系统的两个状态，这是由两个条件。从两态希尔伯特空间的正式定义和基本运算开始，我们系统地重新塑造了量子力学的基础-动力学，可观测量和测量理论-在两个状态作为基本量。我们发现了一个简单而有启发性的公式，它“统一”了两个互补的观测量：概率观测量和非概率的“弱”观测量。概率与“强耦合制度”中的测量有关。它们由双振幅（双态的投影）的绝对平方给出。非概率观测值是在足够“弱”的测量中观测到的，由两个振幅的线性组合给出。作为一个子类，它们包括埃尔米特算子的“弱值”。我们表明，在中间制度，人们可以观察到的概率和弱值的混合。所建议的形式主义和测量理论的一个结果是，非定域性和洛伦兹非协方差的问题，通常的处方与“减少”，可以消除。我们证明这一点的EPR实验和连续观测下的系统。

英文摘要：

We explore further the suggestion to describe a pre- and post-selected system by a two-state, which is determined by two conditions. Starting with a formal definition of a two-state Hilbert space and basic operations, we systematically recast the basics of quantum mechanics - dynamics, observables, and measurement theory - in terms of two-states as the elementary quantities. We find a simple and suggestive formulation, that ``unifies'' two complementary observables: probabilistic observables and non-probabilistic `weak' observables. Probabilities are relevant for measurements in the `strong coupling regime'. They are given by the absolute square of a two-amplitude (a projection of a two-state). Non-probabilistic observables are observed in sufficiently `weak' measurements, and are given by linear combinations of the two-amplitude. As a sub-class they include the `weak values' of hermitian operators. We show that in the intermediate regime, one may observe a mixing of probabilities and weak values. A consequence of the suggested formalism and measurement theory, is that the problem of non-locality and Lorentz non-covariance, of the usual prescription with a `reduction', may be eliminated. We exemplify this point for the EPR experiment and for a system under successive observations.

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