Space versus Time: Unimodular versus Non-Unimodular Projective Ring Geometries?
Space versus Time: Unimodular versus Non-Unimodular Projective Ring Geometries?
复制标题
空间与时间：单模与非单模射影环几何？
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
P. Pracna
中科院分区：
文献类型：
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作者：
M. Saniga;P. Pracna
定义在环上而不是场上的有限射影（点阵）几何最近被认为对量子信息理论具有重要意义。我们相信，在这些几何图形中隐藏着更多的潜力，等待着物理学的释放。存在特定的环，其射影空间具有两种主要不同的基本成分（点和/或高秩线性子空间），它们彼此复杂地交织在一起——单模和非单模。我们推测这两个射影的“自由度”可以分别与物理的空间和时间维度相关联。我们的假设是在最小的三元环上的投影线上说明的。论证了时间与空间的根本区别和复杂联系，甚至勾勒出观测到的时空宏观维度（3+1）和时间箭头的环形几何胚芽。还提到了这种推测模型的其他一些概念含义（如物理系统的层次结构）。
Finite projective (lattice) geometries defined over rings instead of fields have recently been recognized to be of great importance for quantum information theory. We believe that there is much more potential hidden in these geometries to be unleashed for physics. There exist specific rings over which the projective spaces feature two principally distinct kinds of basic constituents (points and/or higher-rank linear subspaces), intricately interwoven with each other -- unimodular and non-unimodular. We conjecture that these two projective "degrees of freedom" can rudimentary be associated with spatial and temporal dimensions of physics, respectively. Our hypothesis is illustrated on the projective line over the smallest ring of ternions. Both the fundamental difference and intricate connection between time and space are demonstrated, and even the ring geometrical germs of the observed macroscopic dimensionality (3+1) of space-time and the arrow of time are outlined. Some other conceptual implications of this speculative model (like a hierarchical structure of physical systems) are also mentioned.