四元数时空与物质

摘要：

在这项工作中，我们使用的四元数时间的概念，并证明它可以应用于四维时空间隔的描述。我们证明，四元数的时间间隔连同有限的光传播速度允许一个简单直观的理解的时间间隔测量在任意相对运动之间的信号源和观察者。我们导出了洛伦兹时间膨胀的四元数形式，证明了它的范数与传统的洛伦兹变换的表达式相对应，并表示时间间隔的测量值，从而使新理论与测量理论密不可分。我们确定观测者参考系中的时空间隔由共轭四元数表达式给出，这对于正确定义观测者参考系中的四元数导数是必不可少的.然后，对任意势函数进行四元数微分，得到广义洛伦兹力。势的第二个四元数导数导致类似于广义麦克斯韦方程组的表达式。最后，我们将所得的形式主义电磁和引力相互作用，并表明，新的表达式是类似于传统的表达式，除了额外的条款，有关的标量场，需要进一步的研究和实验验证。因此，基于Hamilton四元数的新的数学方法可以作为时空和物质统一理论的一个有用的基础。

英文摘要：

In this work, we use the concept of quaternion time and demonstrate that it can be applied for description of four-dimensional space-time intervals. We demonstrate that the quaternion time interval together with the finite speed of light propagation allow for a simple intuitive understanding of the time interval measurement during arbitrary relative motion between a signal source and observer. We derive a quaternion form of Lorentz time dilation and show that the norm corresponds to the traditional expression of the Lorentz transformation and represents the measured value of time intervals, making the new theory inseparable from the theory of measurement. We determine that the space-time interval in the observer reference frame is given by a conjugate quaternion expression, which is essential for proper definition of the quaternion derivatives in the observer reference frame. Then, we apply quaternion differentiation to an arbitrary potential, which leads to generalized Lorentz force. The second quaternion derivative of the potential leads to expressions similar to generalized Maxwell equations. Finally, we apply the resulting formalism to electromagnetic and gravitational interactions and show that the new expressions are similar to the traditional expressions, with the exception of additional terms, related to scalar fields, that need further study and experimental verification. Therefore, the new mathematical approach based on Hamilton's quaternions may serve as a useful foundation of the unified theory of space-time and matter.

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