This article revisits the historiography of the problem of inertial frames. Specifically, the case of the twins in the clock paradox is considered to see that some resolutions implicitly assume inertiality for the non-accelerating twin. If inertial frames are explicitly identified by motion with respect to the large scale structure of the universe, it makes it possible to consider the relative inertiality of different frames.
A variation of the clock paradox and a distinguishing feature of an inertial frame
时钟悖论的情况下，分析了前进和返回行程覆盖相同的<<distance>>（如所观察到的旅行双胞胎），但在不相等的速度。在这种情况下，静止不动的双胞胎观察到她姐姐在前进和返回途中所走过的距离是不同的。分析是使用狭义相对论的公式，唯一的一致性要求是，所有的意见是从任何一个选定的惯性系。分析表明，惯性系的一个定义特征应该基于与之共同运动的时钟的独特同步性的持续保持。发表于Journal of Physical and Natural Sciences第1卷，第1期，2007 http://www.scientificjournals.org/journals2007/articles/1102.pdf
Interpretation of relativistic, transverse, and longitudinal mass using the Lorentz transformation of reference time: Explanation of time dilation via spherical light clock
A realization of Mach's Principle: Clocks and rods - or something more fundamental?
本文实质上是对马赫原理实现的一种推测，我们通过两个问题的表述来详细分析：（A）全局惯性时空能与非平凡的全局物质分布相联系吗？(B)如果是，这种全球分布的一般性质是什么？这些问题是在一个极其简单的模型宇宙的背景下解决的，模型宇宙由只具有可数性的粒子组成，这些粒子存在于一个无形的连续体中。由于在这个模型宇宙中没有预先指定的时钟和棒的概念，我们被迫对空间和时间测量的性质进行基本的考虑。为了回答最初的两个问题，分析告诉我们，一个全局惯性时空可以与一个非平凡的全局物质分布相关联，并且这个分布必然是分形的，D=2。后者的结果进行了比较与现代调查的星系分布的结果（通常，乔伊斯，Montuori，拉比尼astro-ph/9901290，ApJ Lett 1999和本文中的其他参考文献），发现这种分布是准分形与D约= 2的小到中尺度，与中到大尺度的情况是一个相当大的争论的话题。因此，考虑到所考虑的模型极其简单，观测证据与这样的解释是一致的，即分析的观点以良好的一阶近似捕捉宇宙现实。我们认为这些结果的影响。
We reformulate Classical Mechanics as a timeless relativistic theory. Readers are introduced to a new class of reference systems, the binate frames, where physical events are identified with four position-coordinates -- no clocks are used. The binate frames are inertial and adaptable to relative motions. Analyses that use binate frames are valid at all energy levels. When desirable to do so, the results are easily expressed as in special relativity, in terms of space and time coordinates of inertial observers. Given the importance of mass-and-spring systems to theoretical physics, we analyzed …
In the derivation of Lorentz transformation, linear transformation between inertial frames is one of the most important steps. In teaching special relativity, we usually use the homogeneity and isotropy of spacetime to argue that the transformation must be linear transformation without providing any rigorous detail. Here in the first time we provide a solid mathematical proof of the argument that the transformation between two inertial frames must be linear because of the homogeneity and isotropy of spacetime.
It is well known that simultaneity within an inertial frame is defined in relativity theory by a convention or definition. This definition leads to different simultaneities across inertial frames and the well known principle of relativity of simultaneity. The lack of a universal present implies the existence of past, present and future as a collection of events on a four dimensional manifold or continuum wherein three dimensions are space like and one dimension is time like. However, such a continuum precludes the possibility of evolution of future from the present as all events exist forever …
In this paper the analogues of the Lorentz transformations for non-inertial reference frames have been obtained. A common case when the movement speed of one coordinate frame in relation to another one can have time derivatives of higher orders. The obtained transformations conserve invariance of the space-time interval, and in the particular case of inertial frames become the well-known Lorentz transformations. It is shown that the transition from classical mechanics to the theory of relativity is analogous to the consideration of the vibrating system described by the equation of the sine-Gor…
In this article we have developed a formalism to obtain the solution of Schroedinger equation in a non-inertial frame. The frame is moving relative to an inertial frame with an acceleration. The formulation has been developed using Lagrangian formalism as discussed in Classical Mechanics book by Landau and Lifshitz [1]. Hence we have obtained the Hamiltonian of the nucleons. Then using the standard form of canonical quantization rule, we have setup the Schroedinger equation in non-inertial frame. In the present study we have considered only the accelerated rectilinear motion of the non-inertia…
Comment on ``Torque or no torque? Simple charged particle motion observed in different inertial frames,'' by J. D. Jackson [Am. J. Phys. 72 (12), 1484-1487 (2004)]
