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arXiv 1105.4085physics.gen-ph
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关于狭义相对论中的时间间隔变换

On time-interval transformations in special relativity

A. V. Gopala Rao, K. S. Mallesh, K. N. Srinivasa Rao

摘要:

我们重新讨论狭义相对论中时间间隔的洛伦兹变换问题。我们的讨论基于时间间隔变换公式$ cΔt' = γ(cΔt - \vecβ \cdot Δ\vec{r}) $,其中$ Δt'$和$ Δt $是在两个惯性坐标系$ S $和$ S'$中给定事件对之间的时间间隔,这两个惯性坐标系由一个普通的助推器连接。我们观察到,当时间间隔变换公式中的一个框架被选为潜在事件对的规范框架时,爱因斯坦时间膨胀公式、多普勒公式和时间的同时性的相对性都成立。我们还讨论了通过在其中设置$ \vecβ \cdot Δ\vec{r}=0 $而得到的时间间隔变换公式的有趣特例$ Δt' = γΔt $,并论证了它为什么真的是\textbf{not}爱因斯坦时间膨胀公式。最后,我们提出了一些例子,涉及物质粒子,而不是光线,并强调了时间间隔转换公式作为一个计算工具,在课堂上的实用性。

英文摘要:

We revisit the problem of the Lorentz transformation of time-intervals in special relativity. We base our discussion on the time-interval transformation formula $ cΔt' = γ(cΔt - \vecβ \cdot Δ\vec{r}) $ in which $ Δt'$ and $ Δt $ are the time-intervals between a given pair of events, in two inertial frames $ S $ and $ S'$ connected by an general boost. We observe that the Einstein time-dilation-formula, the Doppler formula and the relativity of simultaneity, all follow when one the frames in the time-interval transformation formula is chosen as the canonical frame of the underlying event-pair. We also discuss the interesting special case $ Δt' = γΔt $ of the time-interval transformation formula obtained by setting $ \vecβ \cdot Δ\vec{r}=0 $ in it and argue why it is really \textbf{not} the Einstein time-dilation formula. Finally, we present some examples which involve material particles instead of light rays, and highlight the utility of time-interval transformation formula as a calculational tool in the class room.

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