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arXiv 1104.0772quant-phgr-qchep-th
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相对论量子场中的瞬时空间局域投影测量是一致的

Instantaneous spatially local projective measurements are consistent in a relativistic quantum field

Shih-Yuin Lin

摘要:

假设量子力学中的测量假设可以扩展到量子场论,那么在某个时刻,在与相对论量子场局部耦合的物体上的局部投影测量将导致定义在与测量时刻相关联的整个时间片上的组合系统的波泛函的投影或坍缩,如果相关的自由度具有非零相关。这意味着,在同一个哈密顿系统中,但在不同的参考系中定义的波泛函将在不同的时间片上崩溃,通过相同的本地事件进行测量。这些测量后的状态是否相互一致?我们证明了Raine-Sciama-Grove探测器场系统的量子态在相同的初始时间片上以相同的初始高斯态开始,然后在不同帧中的不同时间片上被点状探测器的测量坍缩,当在相同的最终时间片上进行比较时,将演化到组合系统的相同状态,直到坐标变换。这种一致性是由相互作用的空间局部性和相对论系统中的一般协方差,以及测量的空间局部性和量子理论中量子动力学的线性来保证的。

英文摘要:

Suppose the postulate of measurement in quantum mechanics can be extended to quantum field theory, then a local projective measurement at some moment on an object locally coupled with a relativistic quantum field will result in a projection or collapse of the wavefunctional of the combined system defined on the whole time-slice associated with the very moment of the measurement, if the relevant degrees of freedom have nonzero correlations. This implies that the wavefunctionals in the same Hamiltonian system but defined in different reference frames would collapse on different time-slices passing through the same local event where the measurement was done. Are these post-measurement states consistent with each other? We illustrate that the quantum states of the Raine-Sciama-Grove detector-field system started with the same initial Gaussian state defined on the same initial time-slice, then collapsed by the measurements on the pointlike detectors on different time-slices in different frames, will evolve to the same state of the combined system up to a coordinate transformation when compared on the same final time-slice. Such consistency is guaranteed by the spatial locality of interactions and the general covariance in a relativistic system, together with the spatial locality of measurements and the linearity of quantum dynamics in its quantum theory.

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