在相对论中，模拟加速观测者需要什么样的数的性质？
What properties of numbers are needed to model accelerated observers in relativity?
摘要：
我们调查的可能结构的数字（作为物理量），加速观察者可以在狭义相对论建模。我们提出了一个一般公理化的加速观测器理论，它在每个实封闭的域上都有一个模型。我们还表明，如果我们想模拟某些加速观察者，那么并不是每个实封闭的场都是合适的，例如，匀加速观测器不能在实代数数的域上建模。因此，在序域的语言中，可以研究其上的均匀加速度的域类是不可公理化的。
英文摘要：
We investigate the possible structures of numbers (as physical quantities) over which accelerated observers can be modeled in special relativity. We present a general axiomatic theory of accelerated observers which has a model over every real closed field. We also show that, if we would like to model certain accelerated observers, then not every real closed field is suitable, e.g., uniformly accelerated observers cannot be modeled over the field of real algebraic numbers. Consequently, the class of fields over which uniform acceleration can be investigated is not axiomatizable in the language of ordered fields.
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