arXiv quant-ph/98030251998-03quant-phgr-qc

测量问题与量子力学的约化公设

The Measurement Problem and the Reduction Postulate of Quantum Mechanics

Rodolfo Gambini

备注：: 5 pages, Revtex, no figures, minor changes and comments added

摘要：

众所周知，量子态的因果薛定谔演化与约化公设是不相容的，即使考虑了退相干。由标准归约假设引入的对因果演化的违反区分了某些系统（作为测量设备），其状态非常接近统计混合（作为退相干过程的结果）。在这些系统中，这种违反没有任何可观察到的影响。在任意的量子系统中，从初始密度矩阵到标准约化假设所预言的对角矩阵的转变，将导致薛定谔演化的完全崩溃，从而破坏量子力学的所有预言能力。我们在这里展示的是，有一个修改后的公设版本，允许平等地对待所有的量子力学系统。标准约化假设可以被认为是一个很好的近似，实用的目的，这个修改后的版本是一致的薛定谔演化和通过退相干与实验结果。在这种方法中，归约公设所起的物理作用是作为计算相对概率的工具，从而确定一致历史的概率。

英文摘要：

It is well known, that the causal Schrödinger evolution of a quantum state is not compatible with the reduction postulate, even when decoherence is taken into account. The violation of the causal evolution, introduced by the standard reduction postulate distinguishes certain systems (as the measurement devices), whose states are very close to statistical mixtures (as the ones resulting from the process of decoherence). In these systems, this violation has not any observable effect. In arbitrary quantum systems, the transition from the initial density matrix to a diagonal matrix predicted by the standard reduction postulate, would lead to a complete breakdown of the Schrödinger evolution, and consequently would destroy all the predictive power of quantum mechanics. What we show here, is that there is a modified version of the postulate that allows to treat all the quantum mechanical systems on equal footing. The standard reduction postulate may be considered as a good approximation, useful for practical purposes, of this modified version which is consistent with the Schrödinger evolution and via decoherence with the experimental results. Within this approach, the physical role played by the reduction postulate is as a tool for the computation of relative probabilities and consequently for the determination of the probabilities of consistent histories.

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