论文标题
基于计算机的活动,以使用Rindler观察者了解适当的加速度
Computer based activity to understand proper acceleration using the Rindler observer
论文作者
论文摘要
使用特殊相对论的基本知识,我们在Excel和Python中设计了一个计算课堂实验。在这里,我们表明,使用任意速度$ u_ \ Mathcal {B} $的任何惯性观察者$ \ MATHCAL {B} $与Rindler Observer $ \ MathCal {R} $的唯一事件$ {e} $相关联。惯性观察者$ \ MATHCAL {B} $记录$ \ Mathcal {r} $的速度在每个瞬间都不为零,除非在此唯一的$ {e} $与$ \ Mathcal {r} $共同移动的情况下。在此事件中,$ \ Mathcal {B} $记录了$ \ Mathcal {R} $的最小距离,并在其全球沿线最大化$ \ Mathcal {R} $的最大加速度。当学生意识到惯性观察者衡量可变的本地加速度时,他们掌握了适当加速的概念,但对于所有惯性观察者来说,这种最大值都是相同的。由于Rindler观察者与可变的局部速度相关联,因此时间扩张因子不同。在适当的时间之前,我们以图形方式介绍了时间扩张的概念。我们假设$ \ MATHCAL {B} $相对于惯性观察者$ \ Mathcal {a} $移动,该{A} $在静止且其时钟在相遇时同步为零。
Using elementary knowledge of Special Relativity, we design a computational classroom experiment in excel and python. Here, we show that any inertial observer $\mathcal{B}$ with an arbitrary speed $u_\mathcal{B}$ is associated with a unique event ${E}$ along the worldline of Rindler observer $\mathcal{R}$. The inertial observer $\mathcal{B}$ records the velocity of $\mathcal{R}$ to be non-zero at every instant except at this unique ${E}$ where it is co-moving with $\mathcal{R}$. At this event, $\mathcal{B}$ records a minimized distance to $\mathcal{R}$ and a maximized acceleration of $\mathcal{R}$ along its worldline. Students grasp the concept of proper acceleration when they realise that though an inertial observer measures variable local acceleration but this maxima is the same for all inertial observers. Since the Rindler observer is associated with variable local velocity the time dilation factors are different. Parameterising the Rindler velocity by proper time we graphically present the concept of time dilation. We assume $\mathcal{B}$ to be moving with respect to an inertial observer $\mathcal{A}$ which is at rest and their clocks synchronize to zero when they meet.