基于规范理论的数标度对几何的影响
Effects of gauge theory based number scaling on geometry
摘要：
描述了数学的局部可用性（LAM）和时空相关数标度对物理学，特别是几何学的影响。LAM假设在每个时空点上都有独立的数学系统作为结构。扩展规范理论，使其包括选择数结构和其他基于数的结构的标度的自由度，导致基于标量玻色子场的时空相关标度因子。尺度对实验结果相互比较或与理论计算的比较没有影响。在LAM中，所有的理论表达式都是在某个参考点上的数学元素。更改参考点会引入（外部）缩放。具有空间或时间上的积分或导数的理论表达式包括不能通过参考点改变来移除的缩放因子（内部缩放）。线元素和路径长度，作为空间和/或时间上的积分，显示了缩放对几何体的影响。在一个示例中，当时间变为0（大爆炸时间）时，缩放因子变为0。当$t$变为0时，所有路径长度和物理量的值均被压缩为0。其他例子具有关于某个点$x.$的球对称缩放因子。在一种类型中，即黑洞，当任何点$y$和$x$之间的距离$d$变为0时，缩放因子变为无穷大。对于缩放白洞，当$d$变为0时，缩放因子变为0。对于黑洞，当$y$接近$x.$时，从参考点$z$到$y$的路径长度变得无穷大。对于白洞，路径长度接近一个远小于从$z$到$x.$的未标度距离的值
英文摘要：
Effects of local availability of mathematics (LAM) and space time dependent number scaling on physics and, especially, geometry are described. LAM assumes separate mathematical systems as structures at each space time point. Extension of gauge theories to include freedom of choice of scaling for number structures, and other structures based on numbers, results in a space time dependent scaling factor based on a scalar boson field. Scaling has no effect on comparison of experimental results with one another or with theory computations. With LAM all theory expressions are elements of mathematics at some reference point. Changing the reference point introduces (external) scaling. Theory expressions with integrals or derivatives over space or time include scaling factors (internal scaling) that cannot be removed by reference point change. Line elements and path lengths, as integrals over space and/or time, show the effect of scaling on geometry. In one example, the scaling factor goes to 0 as the time goes to 0, the big bang time. All path lengths, and values of physical quantities, are crushed to 0 as $t$ goes to 0. Other examples have spherically symmetric scaling factors about some point, $x.$ In one type, a black scaling hole, the scaling factor goes to infinity as the distance, $d$, between any point $y$ and $x$ goes to 0. For scaling white holes, the scaling factor goes to 0 as $d$ goes to 0. For black scaling holes, path lengths from a reference point, $z$, to $y$ become infinite as $y$ approaches $x.$ For white holes, path lengths approach a value much less than the unscaled distance from $z$ to $x.$
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