arXiv 1407.69282014-07-25quant-phhep-th

光的量子元胞自动机理论

Quantum Cellular Automaton Theory of Light

Alessandro Bisio, Giacomo Mauro D'Ariano, Paolo Perinotti

备注：: 9 pages, 2 figures
发表信息：: Annals of Physics 368 (2016) 177-190
DOI：: 10.1016/j.aop.2016.02.009

摘要：

提出了一种基于量子元胞自动机的光量子理论。这种方法使我们有一个完整的自由电动力学的量子理论，包含一个假设的离散普朗克尺度。该理论特别相关，因为它提供了可以通过实验验证的宏观尺度的预测。我们证明了在小波矢量k的极限下，自由麦克斯韦方程是如何从文献[1]中的信息原理导出的两个Weyl QCA中产生的。在这个框架内，光子被引入作为一个由一对相关的无质量费米子组成的复合粒子，通常的玻色子统计恢复在低光子密度极限。我们推导出该理论的主要唯象特征，包括在真空中的色散传播，发生一个小的纵向极化，和饱和效应起源于费米性质的光子。然后，我们讨论这些影响是否可以通过实验测试，并观察到，只有色散效应与目前的技术是可访问的，从观测的脉冲的到达时间起源于宇宙学距离。

英文摘要：

We present a quantum theory of light based on quantum cellular automata (QCA). This approach allows us to have a thorough quantum theory of free electrodynamics encompassing an hypothetical discrete Planck scale. The theory is particularly relevant because it provides predictions at the macroscopic scale that can be experimentally tested. We show how, in the limit of small wave-vector k, the free Maxwell's equations emerge from two Weyl QCAs derived from informational principles in Ref. [1]. Within this framework the photon is introduced as a composite particle made of a pair of correlated massless Fermions, and the usual Bosonic statistics is recovered in the low photon density limit. We derive the main phenomenological features of the theory, consisting in dispersive propagation in vacuum, the occurrence of a small longitudinal polarization, and a saturation effect originated by the Fermionic nature of the photon. We then discuss whether these effects can be experimentally tested, and observe that only the dispersive effects are accessible with current technology, from observations of arrival times of pulses originated at cosmological distances.

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