Quaternion Space-Time and Matter

Abstract

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.