复数与物理实在
Complex Numbers and Physical Reality
摘要：
物理学和数学发展的某些方面使人们开始思考复数与我们周围现实之间的关系。如果把数看成两个量的关系，那么从复数存在的事实和公认的数的定义来看，给所有的物理量赋值是必要的。量的基本性质是它的多或少，因此复量的领域，如果它存在，就有必要进行排序。提出了字典序可以应用于复杂物理量的假设。一组排列的复数很自然地排列在一条直线上，在这种情况下，这条直线代表一个非阿基米德复数轴。所有的物理量都位于相关的非阿基米德复数值轴上，形成了一个新的实在--“复值”世界。因此，我们得到的结论，所得到的非阿基米德复数值轴可以作为一个例子的理想的数学对象-超实数轴。因此，非阿基米德复数轴上的微分和积分可以用非标准分析的方法来实现。一个新的“复值”现实的某些属性，它与我们的“现实”世界和复杂的物理量的实验检测的可能性进行了讨论。
英文摘要：
Some aspects of the development of physics and the mathematics set one think about relation between complex numbers and reality around us. If number to spot as the relation of two quantities, from the fact of existence of complex numbers and accepted definition of number it is necessary necessity complex value to assign to all physical quantities. The basic property of quantity to be it is more or less, therefore field of complex quantities, if it exists, it is necessary is ranked. The hypothesis was proposed that lexicographic ordering may be applied to the complex physical quantities. A set of the ranked complex numbers is quite natural to arrange on a straight line that represents in this case a non-Archimedean complex numerical axis. All physical quantities are located on the relevant non-Archimedean complex numerical axes, forming a new reality - "complex-valued" world. Thus, we get the conclusion that the resulting non-Archimedean complex numerical axis may serve as an example of the ideal mathematical object - hyperreal numerical axis. So, differentiation and integration on the non-Archimedean complex numerical axis can be realized using methods of nonstandard analysis. Certain properties of a new "complex-valued" reality, its connection with our "real" world and possibility of experimental detection of complex physical quantities are discussed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
