四元数时间、质量和粒子速度

摘要：

在这项工作中，我们建议使用真正的四元数的时间间隔的定义，从而在相对论性时空的另一种提法。我们继续进行的四元数定义的粒子质量，我们推导出使用质能等价。这导致了四元数质量色散关系，它等价于相对论性能量-动量色散，然而，所得到的四元数空间具有正的二次范数。然后，我们定义了四元数粒子速度，它可以应用于非抛物固态材料中的相对论粒子和电子。我们表明，相对论洛伦兹表达式只适用于时间，质量和速度的绝对值，而物理4-矢量量描述的实四元数。最后，我们引入了四元数电磁势，并证明了它对粒子质量和速度的影响。特别是，我们显示了静电势和粒子静止质量之间的直接联系。我们比较本模型的实验测量的电子速度在InSb中，我们证明了准相对论电子速度在高电场饱和。因此，看来物理量可以用实四元数表示，而它们的测量观测量和相对论性洛伦兹变换对应于四元数的绝对值。看来这里提出的四元数方法可以作为粒子物理学的另一种数学描述的基础。

英文摘要：

In this work, we propose using real quaternions for the definition of the time interval resulting in an alternative formulation of the relativistic space-time. We proceed with the quaternion definition of the particle mass that we derive using the mass-energy equivalence. This results in the quaternion mass dispersion relation, which is equivalent to the relativistic energy-momentum dispersion, however, with a positive quadratic norm of the resulting quaternion space. Then, we define the quaternion particle velocity, which can be applied to relativistic particles and electrons in non-parabolic solid-state materials. We show that the relativistic Lorentz expressions apply only to the absolute values of the time, mass and velocity while the physical 4-vector quantities are described by real quaternions. Finally, we introduce the quaternion electromagnetic potential and demonstrate that it has an effect on the particle mass and velocity. In particular, we show a direct connection between the electrostatic potential and the particle rest mass. We compare the present model to experimental measurements of the electron velocity in InSb where we demonstrate quasi-relativistic electron velocity saturation at high electric fields. Therefore, it appears that physical quantities can be expressed by real quaternions while their measured observables and relativistic Lorentz transformations correspond to the quaternion absolute values. It seems that the quaternion approach presented here can be used as a basis for an alternative mathematical description of particle physics.

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